artificial bee colony in optimizing process parameters of surface
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ARTIFICIAL BEE COLONY IN OPTIMIZING PROCESS PARAMETERS OF
SURFACE ROUGHNESS IN END MILLING AND ABRASIVE WATERJET
MACHINING
NORFADZLAN BIN YUSUP
A dissertation submitted in partial fulfillment of the
requirements for the award of the degree of
Master of Science (Computer Science)
Faculty of Computer Science and Information Systems
Universiti Teknologi Malaysia
FEBRUARY 2012
To my beloved family and friends, thank you for the endless support and
encouragement.
ACKNOWLEDGEMENT
Firstly I would like to thank Allah SWT the Most Merciful, Most
Compassionate. It is by God willing; I was able to complete this project within the
time given. I want to express gratitude to my supervisors, Assoc. Prof. Dr. Siti
Zaiton Mohd Hashim and Dr. Azlan Mohd Zain. This project would not be
accomplished without their guidance and support throughout period of time on doing
this project. I learned a lot of knowledge under their guidance. Thank you very much
Dr. Azlan Mohd Zain for improving both of my research and writing skills. I would
also like to thank to Kementerian Pengajian Tinggi (KPT) Malaysia and Universiti
Malaysia Sarawak (UNIMAS) for the scholarship that they provided during the
period of my study.
Special thanks to my examiners Prof. Dr. Siti Maryam Shamsudin and Dr.
Roselina Sallehuddin. Thank you for their constructive comments in evaluating my
project. Thank you to my family and friends for their support. And lastly thank you
to all post graduate staff and lectures Faculty of Computer Science and Information
System (FSKSM), UTM for their help and support.
V
ABSTRACT
The machining operation can be generally classified into two types which are
traditional machine and non-traditional (modem) machine. There are two types of
machining employed in this research, end milling (traditional machining) and
abrasive waterjet machining (non-traditional machining). Optimizing the process
parameters is essential in order to provide a better quality and economics machining.
This research develops an optimization algorithm using artificial bee colony (ABC)
algorithm to optimize the process parameters that will lead to minimum surface
roughness (Ra) value for both end milling and abrasive waterjet machining. In end
milling, three process parameters that need to be optimized are the cutting speed,
feed rate and radial rake angle. For abrasive waterjet, five process parameters that
need to be optimized are the traverse speed, waterjet pressure, standoff distance,
abrasive grit size and abrasive flow rate. These machining process parameters
significantly impact on the cost, productivity and quality of machining parts. The
ABC simulations are developed to achieve the minimum Ra value in both end milling
and abrasive waterjet machining. The results obtained from the simulation are
compared with experimental, regression modelling, Genetic Algorithm (GA) and
Simulated Annealing (SA). In end milling, ABC reduced the Ra by 10% and 8%
compared to experimental and regression. In abrasive waterjet, the performance was
much better where the Ra value decreased by 28%, 42%, 2% and 0.9% compared to
experimental, regression, GA and SA respectively.
vi
ABSTRAK
Secara umumnya, operasi pemesinan boleh dikelaskan kepada dua jenis iaitu
mesin tradisional dan mesin bukan tradisional (mesin moden). Terdapat dua jenis
pemesinan yang digunakan dalam penyelidikan ini, mesin pengisaran hujung
(pemesinan tradisional) dan mesin pelelas je t air (pemesinan bukan tradisional).
Mengoptimumkan proses parameter adalah penting untuk menyediakan kualiti yang
lebih baik dan ekonomi pemesinan. Penyelidikan ini membangunkan algoritma
pengoptimuman menggunakan algoritma koloni lebah buatan (ABC) bagi kedua-dua
mesin pengisaran hujung dan mesin pelelas jet air. Terdapat tiga parameter mesin
pengisaran hujung yang perlu dioptimumkan iaitu kelajuan memotong, kadar suapan
dan sudut meraih jejarian. Bagi mesin pelelas je t air terdapat lima parameter yang
perlu dioptimumkan iaitu kelajuan traverse, tekanan jet air, jarak standoff, saiz kersik
melelas dan kadar aliran yang melelas. Parameter pemesinan memberi kesan yang
ketara ke atas kos, produktiviti dan kualiti bahagian-bahagian pemesinan. Simulasi
ABC dibangunkan untuk mencapai nilai minimum Ra dalam kedua-dua mesin
pengisaran hujung dan mesin pelelas jet air. Keputusan yang diperolehi daripada
penyelidikan dibandingkan dengan eksperimen, pemodelan regresi, Algoritma
Genetik (GA) dan simulasi penyepuhlindapan (SA). Dalam mesin pengisaran hujung,
ABC mengurangkan Ra sebanyak 10% dan 8% berbanding dengan eksperimen dan
regresi. Di mesin pelelas jet air, prestasi adalah lebih baik dimana nilai Ra menurun
sebanyak 28%, 42%, 2% dan 0.9% berbanding dengan eksperimen, regresi, GA dan
TABLE OF CONTENT
CHAPTER TITLE PAGE
DECLARATION ii
DEDICATION iii
ACKNOWLEDGEMENT iv
ABSTRACT v
ABSTRAK vi
TABLE OF CONTENT vii
LIST OF TABLES x
LIST OF FIGURES xiv
LIST OF ABBREVIATION xvi
LIST OF SYMBOLS xvii
1 INTRODUCTION 1
1.1 Introduction 1
1.2 Statement of problems 4
1.3 Objectives of the Study 5
1.4 Scope of the Study 5
1.5 Significance of the Study 6
1.6 Organization of the Report 6
2 LITERATURE REVIEW 7
2.1 Minimization of surface roughness 7
2.2 Optimization of end milling and AWJ machining process 8
2.3 ABC optimization technique 10
2.3.1 Flow of ABC algorithm 13
V lll
2.3.2 ABC Pseudocode 14
2.3.3 Abilities and limitation of ABC 16
2.4 Previous research on ABC algorithm in various domain 17
2.5 Previous research in optimizing machining process parameters using soft computing technique 21
2.6 Experimental data of case studies 36
2.6.1 End milling machining 3 6
2.6.1.1 Experimental design 37
2.6.1.2 Experimental results 39
2.6.2 AW J machining 41
2.6.2.1 Experimental design 41
2.6.2.2 Experimental results 42
2.7 Summary 43
METHODOLOGY 44
3.1 Introduction 44
3.2 Research flow 47
3.3 Assessment of real experimental data 47
3.4 Regression modeling development 47
3.4.1 Regression modeling in end milling 48
3.4.1.1 Regression Model for Each Cutting Tool 49
3.4.2 Regression modeling in abrasive waterjet 54
3.5 ABC algorithm for optimization of process parameters 56
3.5.1 Justification of ABC control parameters 59
3.5.2 Steps for determination of the optimal process parameters 59
3.6 Validation and evaluation of ABC results 61
3.7 ABC optimization performances 61
3.7 Summary 65
ABC OPTMIZATION
4.1 Introduction
4.2 ABC optimization execution
4.3 Initial Phase
4.4 Employed-bee Phase
66
66
67
73
74
IX
4.5 Onlooker-bee Phase 75
4.6 Scout-bee Phase 76
4.7 Experiment 1 - ABC optimization parameters for endmilling 76
4.7.1 Colony size of 10 and limit of 30 77
4.7.2 Colony size of 20 and limit of 60 90
4.7.3 Colony size of 50 and limit of 60 103
4.7.4 Colony size of 100 and limit of 300 116
4.8 Experiment 2 - ABC optimization parameters for AWJ 129
4.8.1 Colony size of 10 and limit of 50 129
4.8.2 Colony size of 20 and limit of 100 142
4.8.3 Colony size of 50 and limit of 250 155
4.8.4 Colony size of 100 and limit of 500 168
4.9 Summary of end milling experimental results 181
4.10 Summary of AWJ experimental results 183
5 ANALYSIS OF RESULTS 186
5.1 Introduction 186
5.2 Analysis of results 187
5.2.1 Validation and evaluation of end milling results 187
5.2.2 Validation and evaluation of AWJ results 190
5.3 Summary 195
6 CONCLUSION AND FUTURE WORK 196
6.1 Introduction 196
6.2 Summary of work 197
6.3 Research summary and conclusion 198
6.4 Suggestion for future work 201
6.5 Summary 202
REFERENCES 203
X
TABLE NO TITLE PAGE
2.1 Control parameters of ABC 20
2.2 Previous researches in optimizing processparameters of Ra for traditional machining 23
2.3 Previous researches in optimizing processparameters of Ra for modem machining 30
2.4 Mechanical properties of Ti-6A1-4V 36
2.5 Properties of the cutting tool used in theexperiments 37
2.6 Levels of independent variables and codingidentification 38
2.7 Specification of the CNC machine 38
2.8 Ra values for real machining experiments 40
2.9 Levels of process parameters and codingidentification 41
2.10 Ra values for real machining 42
3.1 Uncoated Tool coeffients value 49
3.2 TiAIN coated Tool coeffients value 49
3.3 SNTr coated Tool coeffients value 50
3.4 Ra predicted values of regression modelling 51
3.5 Statistics and correlations for paired samples 52
3.6 Paired samples test 53
3.7 Predicted Ra values of AWJ Regression model 55
3.8 Justification of ABC control parameters 59
3.9 Parameters used in the numerical benchmarkfunction experiments 62
4.1 Control variables combination with limit of 30 77
4.2 The best value returned from 10 max cycles perran with limit of 30 79
LIST OF TABLES
4.3
4.4
4.5
4.6
4.7
4.8
5.9
4.10
4.11
4.12
4.13
4.14
4.15
4.16
4.17
4.18
4.19
4.20
4.21
4.22
4.23
4.24
XI
The best value returned from 20 max cycles perrun with limit of 30 81
The best value returned from 50 max cycles perrun with limit of 30 83
The best value returned from 100 max cycles perrun with limit of 30 86
Control variables combination with limit of 60 90
The best value returned from 10 max cycles perrun with limit of 60 92
The best value returned from 20 max cycles perrun with limit of 60 94
The best value returned from 50 max cycles perrun with limit of 60 96
The best value returned from 100 max cycles perrun with limit of 60 99
Control variables combination with limit of 150 103
The best value returned from 10 max cycles perrun with limit of 150 105
The best value returned from 20 max cycles perrun with limit of 150 107
The best value returned from 50 max cycles perrun with limit of 150 109
The best value returned from 100 max cycles perrun with limit o f l5 0 112
Control variables combination with limit of 300 116
The best value returned from 10 max cycles perrun with limit of 300 118
The best value returned from 20 max cycles perrun with limit of 300 120
The best value returned from 50 max cycles perrun with limit of 300 122
The best value returned from 100 max cycles perrun with limit of 300 125
Control variables combination with limit of 50 129
The best value returned from 10 max cycles perrun with limit of 50 131
The best value returned from 20 max cycles perrun with limit of 50 133The best value returned from 50 max cycles perrun with limit of 50 135
4.25
4.26
4.27
4.28
4.29
4.30
4.31
4.32
4.33
4.34
4.35
4.36
4.37
4.38
4.39
4.40
4.41
4.42
5.1
5.2
5.3
X l l
The best value returned from 100 max cycles perrun with limit of 50 138
Control variables combination with limit of 100 142
The best value returned from 10 max cycles perrun with limit of 100 144
The best value returned from 20 max cycles perrun with limit of 100 146
The best value returned from 50 max cycles perrun with limit of 100 148
The best value returned from 100 max cycles perrun with limit of 100 151
Control variables combination with Limit of 250 155
The best value returned from 10 max cycles perrun with limit of 250 157
The best value returned from 20 max cycles perrun with limit of 250 159
The best value returned from 50 max cycles perrun with limit of 250 161
The best value returned from 100 max cycles perrun with limit of 250 164
Control variables combination with limit of 500 168
The best value returned from 10 max cycles perrun with limit of 500 170
The best value returned from 20 max cycles perrun with limit of 500 172
The best value returned from 50 max cycles perrun with limit of 500 174
The best value returned from 100 max cycles perrun with limit of 500 177
Summary of ABC optimization results usingdifferent colony size and limit in end milling 183
Summary of ABC optimization results usingdifferent colony size and limit in end milling 185
Conditions to define the scale for optimal process parameters of end milling 189
Comparison of the optimal process parameters inend milling 190
Conditions to define the scale for optimal process parameters of AWJ 192
5.4 Comparison of the optimal process parameters in AWJ 193
5.5 Comparison of optimal Ra in end milling and AWJ machining 194
6.1 Reduction percentage of minimum surface roughness in end milling 198
6.2 Reduction percentage of minimum surface roughness in AWJ 199
6.3 Summary of minimum bee colony size and max number of cycles 200
6.4 Summary of level of the optimal process parameters 201
xiv
FIGURE NO
1.1
2.1
2.2
2.3
3.1
3.2
4.1
4.2
4.3
4.4
4.5
4.6
4.7
4.8
4.9
4.10
4.11
4.12
4.13
4.14
4.15
4.16
4.17
4.18
LIST OF FIGURES
TITLE
Parameters that affect Ra
Categories of milling
AWJ major components
Flow of ABC optimization
Flow of searching for optimum process parameters
Evolution of mean best values for Rosenbrock function
ABC Matlab program interface
Results of 10 max cycles per run with limit of 30
Results of 20 max cycles per run with limit of 30
Results of 50 max cycles per run with limit of 30
Results of 100 max cycles per run with limit of 30
Results of 10 max cycles per run with limit of 60
Results of 20 max cycles per run with limit of 60
Results of 50 max cycles per run with limit of 60
Results of 100 max cycles per run with limit of 60
Results of 10 max cycles per run with limit of 150
Results of 20 max cycles per run with limit of 150
Results of 50 max cycles per run with limit of 150
Results of 100 max cycles per run with limit of 150
Results of 10 max cycles per run with limit of 300
Results of 20 max cycles per run with limit of 300
Results of 50 max cycles per run with limit of 300
Results of 100 max cycles per run with limit of 300
Results of 10 max cycles per run with limit of 50
PAGE
2
8
9
13
46
63
68
78
80
82
85
91
93
95
98
104
106
108
111
117
119
121
124
130
4.19 Results of 20 max cycles per run with limit of 50 132
4.20 Results of 50 max cycles per run with limit of 50 134
4.21 Results of 100 max cycles per run with limit of 50 137
4.22 Results of 10 max cycles per run with limit of 100 143
4.23 Results of 20 max cycles per run with limit of 100 145
4.24 Results of 50 max cycles per run with limit of 100 147
4.25 Results of 100 max cycles per run with limit of 100 150
4.26 Results of 10 max cycles per run with limit of 250 156
M l Results of 20 max cycles per run with limit of 250 158
4.28 Results of 50 max cycles per run with limit of 250 160
4.29 Results of 100 max cycles per run with limit of 250 163
4.30 Results of 10 max cycles per run with limit of 500 169
4.31 Results of 20 max cycles per run with limit of 500 171
4.32 Results of 50 max cycles per run with limit of 500 173
4.33 Results of 100 max cycles per run with limit of 500 176
4.34 Comparison of the effect of colony size in end milling experiment 181
4.35 Comparison of the effect of colony size in AWJ Experiment 184
LIST OF ABBREVIATIONS
ABC - Artificial Bee Colony
AI - Artificial Intelligence
ANN - Artificial Neural Network
AWJ - Abrasive Waterjet
BP - Backpropagation
DE - Differential Evolution
EA - Evolutionary Algorithm
GA - Genetic Algorithm
NFL - No Free Lunch
NN - Neural Network
PSO - Particle Swarm Optimization
RSM - Response Surface Methodology
SA - Simulated Annealing
SNtr - Supemitride
TiAIN - Titanium Aluminum Nitrate
LIST OF SYMBOLS
Radial rake angle
Abrasive grit size
Feed rate
Standoff distance
Abrasive flow rate
W ateijet pressure
Surface Roughness
Cutting speed
Traverse speed
CHAPTER 1
INTRODUCTION
1.1 Introduction
In highly competitive manufacturing industries nowadays, the manufacturer
ultimate goals are to produce a high quality product with less cost and time
constraints. Thus, the flexible manufacturing system (FMS) has been introduced
since 1960 to achieve this goals by introducing the fully automation of computer
numerically controlled (CNC) machine tools. The idea of FMS is to provide a fully
automated machine that required a minimum supervision in 24 hours per day. In the
traditional FMS, it consists of a huge number of CNC which handled by complex
software and it is undeniable very costly. Nowadays, a smaller version of FMS is
being used which is commonly refer as Flexible Manufacturing Cell (FMC) where it
consists two or more CNC machines only. According to Mike et al. (1998), CNC
machine tools require less operator input, provide greater improvements in
productivity, and increase the quality of the machined part. Generally, the machining
operations can be classified into two types which are traditional and non-traditional
(modem). The traditional machining operations include turning, milling, boring, and
grinding while non-traditional or modem machining operations include abrasive
w aterjet machining, electron beam machining and photochemical machining.
2
According to Rao and Pawar (2009), the selection of machining process
parameters is a very crucial part in order for the machine operations to be success. To
choose the process parameters, it is usually based on the human (or manufacturing
engineers) judgement and experience. However, the chosen of process parameters
usually did not give an optimal result. This is due to in the machining processing; a
number of factors also could interrupt thus preventing in achieving high process
performance and quality (Bemados and Vosniakos, 2002). Figure 1.1 below showed
the machining parameters that affect surface roughness, Ra. To improve this quality,
one of the indications is by referring to the machining performances measures, Ra
(Zain et al, 2010a). In manufacturing, the quality of the product focused on the
surface texture particularly the Ra because it affects the product end results such as
the appearance, function and reliability. There are many factors to produce a specific
roughness such as in end milling where it depends on the cutting speed, feed rate,
velocity of the traverse, cooling fluids and the mechanical properties of the piece
being machined. Any small changes in one of these factors could affect the results of
the surface produced.
C - H i n n T n n i e P m n Br t i « Machining Parameters
SURFACEROUGHNESS
Cutting force variation
Workpiece Properties Cutting Phenomena
Figure 1.1 Parameters that affect Ra (Benardos and Vosnaikos, 2003
Various techniques have been considered by a number of researchers to
model and optimize machining problems. This technique includes statistical
regression, conventional optimization technique such as Taguchi method, response
3
surface methodology (RSM) and iterative mathematical search technique. Other
techniques such as Artificial neural network (ANN) and Fuzzy set-theory based
modelling also have been applied. Apart from that, a number of researches also have
been done using the concept of non conventional optimization technique such as
genetic algorithm (GA), simulated annealing (SA), particle swarm optimization
(PSO), tabu search (TS) and ant colony optimization (ACO).
The study of insect and animal behaviour has attracted many researchers
attention to better understand their colony and behaviour so that it could be modelled
to solve complex problems in real world. Ant colony optimization (ACO) for
example is one of the swarm intelligence techniques that were introduced by Dorigo
et al. (1996) which were inspired by the foraging behaviour of ants. Similar to the
concept of ACO, recently a new algorithm known as artificial bee colony (ABC)
algorithm was introduced by Karboga in 2005. This algorithm mimics the intelligent
behaviour of the honey bees swarm in foraging foods. ABC algorithm has been
applied in many applications particularly in job scheduling, optimization and data
clustering. A comparative study by Karaboga and Akay (2009) shows that standard
ABC gives an excellent performance for optimizing a large set of numerical test
unimodal function such as Sphere and Rosenbrock. It was found that ABC gave a
better result in terms of local and global optimization due to the selection schemes
employed and neighbouring production mechanism used. The results are then
compared with other swarm optimization algorithms such PSO, differential evolution
algorithm and evolution strategies. From the literature review, there is no research
has been carried out so far to apply ABC optimization techniques for optimization of
process parameters in end milling and abrasive waterjet (AWJ) machining. Recently,
a research was carried out by Rao and Pawar (2009) to optimize the process
parameter such as number of passes, depth of cut for each pass, speed and feed in a
multi-pass milling machining operations using non-traditional optimization
algorithms such as PSO, SA and ABC. The results showed that ABC and PSO
produced a better solution compared to SA where the convergence rate is higher and
the number of iterations is lowered.
4
Based on the previous research by Zain et al. (2010a, 2010b, 2010c), it shows
that the use of GA and SA give a promising result in minimizing Ra both in end
milling and AWJ machining compared to the experimental and regression modelling.
In Zain et al. (2010a, 2010b), GA and SA techniques were used to optimize the
process parameters in end milling machining operation.
The results showed that GA and SA have given a much lower Ra value when
compared to the experimental, regression model and response surface methodology
(RSM) technique by 27%, 26% and 50%, respectively. In Zain et al. (2010c) the
same optimization technique was used to optimize the process parameters in AWJ
machining operations. The results show both techniques produced a minimum
surface roughness value compared to experimental data and regression modelling. In
this study ABC algorithm is considered in minimizing Ra for both end milling and
AWJ machining. Consequently, the Ra of ABC is compared to Ra produced by
experimental, regression modelling, GA optimization and SA optimization.
The research question can be stated as:
How efficient is the performance o f ABC optimization to optimize process
parameters fo r minimizing surface roughness in end milling and AW J machining
operations compared to experimental, regression modelling, GA optimization and SA
optimization.
1.2 Statement of problems
5
Based on the problem statements mentioned above, the objectives of the
study are:
i. To develop ABC based algorithm in optimizing surface roughness of
machining process.
ii. To estimate the optimal set of process parameters in end milling and AWJ for
giving a minimum value of Ra.
iii. To validate the proposed method with the existing techniques such as,
experimental, regression modelling, GA optimization and SA optimization.
1.3 Objectives of the study
1.4 Scope of the study
The scopes of this study are:
i. The experimental data sets are based on the experiment conducted by
Mohruni (2008) for end milling machining operations and Caydas and
Hascalik (2008) for AWJ machining operations.
ii. The optimization approach method used is ABC algorithm.
iii. The performance and results are compared with experimental, regression
modelling, GA optimization and SA optimization.
1.5 Significance of the study
6
This study is to investigate the performance of ABC algorithm in optimizing
process parameters for minimizing Ra in both end milling and AWJ machining
operations. To indicate the effectiveness of this computational approach, the end
results which are the Ra values will be compared with experimental, regression
modelling, GA optimization and SA optimization. From the literature review, there is
no effort taken so far by researchers to apply ABC algorithm for the machining
optimization problems both in end milling and AWJ machining operation. So, it can
be concluded that this study gives a new contribution in the area of machining.
1.6 Organization of the thesis
This thesis consists of six chapters. Chapter 1 describes the introduction to
the research, problem background, problem statement, objective and scope of the
study. Chapter 2 presents the literature review of the study. Chapter 3 discussed
about the research methodology that applied in this study. Chapter 4 discussed the
implementation of ABC optimization while Chapter 5 discussed the analysis of the
results of ABC optimization. Finally, Chapter 6 discussed the conclusion and
recommended the future work of the research.
CHAPTER 2
LITERATURE REVIEW
2.1 Minimization of surface roughness
The evaluation on the appearance of an end manufacturing product usually
depicted as Ra. In order to get a high end quality product with a minimal Ra value, it
must be supported by a precise machine process and depending on the machining
conditions as well. According to Fu (2006), there are three decision variables to
minimize the machining conditions which are the cutting speed, the amount of
moving forward and the cutting depth. These setting are the means to cost-effective
machining operation.
A high quality milled surface must be able to completely improved material
piece in terms of weariness force and oxidization resistance. In order to get a
desirable quality of the detailed Ra, a proper process is needed because the Ra
additionally influences a number of functional qualities of material pieces, which
includes contact causing Ra, wearing, light reflection, heat transmission, ability of
distributing and holding a lubricant, coating, or resisting fatigue (Lou et al 1998).
Roughness is regularly an excellent analyst of the performance of a
mechanical component since irregularities in the surface appearance of nucleation
sites for fractures or oxidization may noticeable. Although roughness is usually
8
unwanted, it is not easy and costly to manage at some stage in manufacturing.
Diminishing Ra will usually exponentially boost its manufacturing expenses. This
often turns out when swapping between the manufacturing cost of a component and
its performance in application (Kadirgama et al, 2008).
2.2 Optimization of end milling and AWJ machining process
In the machining process, to cut the workpiece rapidly, it is usually supplied
into a spinning multiple tooth cutter. There are many combinations of machined
surfaces such as flat, angular, or curved. Traditional machining such as milling
machine, holds the workpiece, rotate the cutter and feeding the workpiece to the
cutter (http://www.mfg.edu/marc/primers/milling/index.html). There are three
categories of milling which are slab, face and end milling. These categories of
machining are shown in Figure 2.1 below.
Figure 2.1 Categories of milling (Kalpakjian and Schmid, 2009)
In manufacturing industries, the most regular process of removing metal is
recognized as end milling. In the end milling, there are three common controlled
parameters which are cutting speed (v), feed rate if) and radial rake angle (y).
(n’t SlahffldiliMr (b) Fare milling (c) End milling'
9
Non-traditional machining such as AWJ used a high forceful flow of water in
order to slash the workpiece. The high pressure of water (usually more than 900
mph) incredibly enables it to cut the hard workpiece such as metal and has been used
in the industries since 1980. The advantage of AWJ is that it never gets dry and
overheat compared to other cutting machining. Today, the CNC AWJ is usually used
to slash softer materials while the recent developed AWJ machining technology is
used for slashing harder materials. An example of major AWJ components
machining is illustrated in Figure 2.2.
Figure 2.2 AWJ major components (Echert et al, 1989)
According to Caydas and Hascalik (2008), the various advantages of AWJ
are including no thermal distortion, high machining versatility and flexibility, also
small cutting forces which means the machining has less pressured on the workpiece.
AWJ downsides and restrictions include producing deafening sound and untidy
10
operational setting. At a high traverse rates, the cutting of the material may build
narrowed edges on the kerf. Azmir and Ahsan (2008).
Five controlled tuning process parameters of AWJ that are considered in the
study. According to Hashish (1991) the most significance and precisely controllable
process parameters are water pressure (P), abrasive flow rate (Mj), je t traverse rate
(V) and diameter of focusing nozzle (d).
2.3 ABC optimization technique
Currently, there has been intensifying demand in growth of computational
models or methods that motivated by how animals interact and communicate among
each other to find food sources. Many optimization algorithms have been designed
and developed by adopting a form of biological-based swarm intelligence including
ABC algorithm. ABC is a swarm-based algorithm that mimics the foraging
behaviour of swarm honey bee. Similar to the concept of ACO and PSO, this
exploration algorithm is capable of tracing good quality of solutions. Honey bee is a
good example of well known social insects with self organisation and division of
labour for food collection through information sharing between employed and
unemployed foragers.
Three types of bees in the colony include employed, onlookers and scouts
bees. Each type of bee bears a different task. Employed bees that are currently
exploiting and searching are linked with the food sources. The unemployed bees or
scouts bees are associated with establishing new food sources either by searching the
environment surrounding the hives or waiting for the employed bees to share the best
food source location in the hives. Unemployed bees can be regarded as scouts and
onlookers bees. Without any supervision, the scout bees explore the location for new
11
food sources. It is a very exceptional situation if the scouts’ bees find out loaded
indefinite food sources by chance. In contrast, the onlookers bees that watched the
waggle dance are positioned on the food sources by using a probability based
selection process. The probability value which the food source is favoured by
onlookers increases while the quantity of the nectar amount increases. The employed
bees will share the information by performing a special dance called the waggle
dance in the hive dance floor. This dance contains much valuable information about
the food sources such as the location and the quality of the nectar. Based on the
dance, the scout bees later will explore the reveal food sources. The main steps of the
ABC algorithm are initialize the population, then position the employed bees on their
food sources, consign onlooker bees on the food sources based on the quality of the
nectar, followed by sending off the scouts to explore neighbourhood for learning new
food sources and finally revise the best food source found so far. The process of
searching for food is repeated in anticipation of the satisfied termination criteria
(Karaboga, 2005).
The three control parameters that perform significant role in the ABC
algorithm are as follows:
i. the number of colony size (SN) - the number of food sources or the
population size of the colony (the number of employed bees or
onlooker bees).
ii. the predefined value of limit (L) - the food source is assumed to be
deserted if a location or position cannot be enhanced (for unimproved
loop).
iii. the maximum loop for searching food (M)
The colony of the bees is made up of two groups. The first group of the
colony composed of the employed bees and the next group consist of the onlooker’s
bees. For each food source, there is no more than one employed bee. Consequently,
if a solution indicating a food source is not enhanced by a predetermined number of
trials, in that case the food source is deserted by the employed bee soon transformed
12
to scout bees. For the second group, the onlooker’s bee in the hives waits for the
employed bees to perform a special dance routine called the waggle dance and
chooses the food position according to the information given by the employed bees
in the dance.
13
2.3.1 Flow of ABC algorithm
Figure 2.3 below illustrates the flow of ABC algorithm.
Figure 2.3 Flow of ABC optimization (Karaboga, N., 2009
14
In Figure 2.3, there are three steps for each cycle after the initialization food
source position phase. The first step is initializing the employed bees to the food
source and determined the nectar quantity. Then the onlooker bees are initialized to
the food source and determined the nectar quantity. At the last step for the cycle, the
scout bees determined and the bees are initialized to the food sources at random.
During the initialization step, a set of food source position that signify a potential
solution are produced randomly. Then, the control parameters values are assigned.
Employed bees search for the best quality of food around the neighbourhood. The
bees will assess the nectar quality in the food source area. If the bees calculated a
high quantity of the nectar, it will memorize the food source position until it founds
new food sources that have much higher quantity of the current one. Thus, the pollen
or nectar quantity of the food source match to the quality of the solution signifies by
that food source. Once the process of searching for food source is finished, the
employed bees will go back to their hives and share the information (the best food
source position) to the onlooker bees. By doing a unique type of dance called the
waggle dance, the employed bees will start dancing while the onlookers bees will
extract information from this dance. The food source that has the most quantity and
quality will be chose the majority by the onlooker bees. After that, every onlooker
bees that has been assigned to each of the food source within the neighbourhood will
calculate the nectar amount.
2.3.2 ABC Pseudocode
The detailed pseudocode to solve the optimization is as follows, (Karaboga
and Akay, 2009):
1: Initialize the population of solutions xi,j
2: Evaluate the population
3: Cycle=l
4: Repeat
5: Produce new solutions (food source positions) x»i,j in the neighbourhood of xi,j for
the employed bees using the formula ui,j = xi,j + Oij(xi,j - xk,j) (k is a solution in the
neighbourhood of i, O is a random number in the range [-1,1] ) and evaluate them
15
6: Apply the greedy selection process between xi and x»i
7: Calculate the probability values Pi for the solutions xi by means of their fitness
values using the equation (2.1):
n (2 .1)
In order to calculate the fitness values of solutions we employed the following
equation (2.2):i
i , i f f > 0 f i t t = \ i+ fi * (2 .2)
( l + abs f ( i ) , i f f t < 0
Normalize Pi values into [0,1].
8: Produce the new solutions (new positions) x»i for the onlookers from the solutions
xi, selected depending on Pi, and evaluate them.
9: Apply the greedy selection process for the onlookers between xi and x»i.
10: Determine the abandoned solution (source), if exists, and replace it with a new
randomly produced solution xi for the scout using the equation (2.3):
Xij=minj+rand( 0,1)* (maxj -minj) (2.3)
11: Memorize the best food source position (solution) achieved so far
12: Cycle=cycle+1
13: Until cycle= Maximum Cycle Number (MCN)
16
2.3.3 Abilities and limitation of ABC
The abilities of ABC algorithm may possibly include the following (Rao et al,
2008; Karaboga N., 2009; Benala et al, 2009; Akay and Karaboga, 2010; Karaboga
D. and Akay, 2009; Rao and Pawar, 2010; Akay and Karaboga, 2009):
i. ABC algorithm does not need external parameters such as cross over
rate and mutation rate as in GA and DE.
ii. ABC algorithm introduces neighbourhood source production
mechanism which is the same as mutation process.
iii. ABC algorithm has less computation time required and offered
optimal solution due to its excellent global and local search capability.
iv. the probability of falling into the local optimum is low in ABC
algorithm because of the combination of local and global search.
v. ABC algorithm only employs fewer control parameters.
vi. the convergance rate of ABC algorithm is very high and only requires
a little iteration for convergence to the optimal solution.
vii. ABC algorithm combines both stochastic selection scheme and greedy
selection scheme.
viii. ABC algorithm does not need big number of colony size to solve
optimization problems with high dimensions.
The limitations of ABC may perhaps include the following (Kurban and
Besdok, 2009; Pei et al, 2009; Saeedi et al, 2009):
i. slow convergance rate.
ii. the artificial bee, can only move straight to one of the nectar sources of those
are discovered by the employed bees.
iii. the number of tunable parameters it employs.
17
2.4 Previous research on ABC algorithm in various domain
ABC is a recent swarm based intelligent algorithm that has been applied in
various applications to solve numerous problems and the performance of ABC
proved that it is an excellent algorithm. This is confirmed by a number of researches
that has successfully implemented ABC in different domain and problems.
In the domain of electrical and network-based, ABC algorithm has been used
to solve network configuration problem in distribution system (Rao et al, 2008). The
experiments results obtained showed that ABC outperforms the GA, differential
evolution (DE) and SA in terms of quality of the solution and computation
effectiveness. The authors stated that the advantages of ABC are it does not need
external parameters such as cross over rate and mutation rate as in GA and DE.
Moreover, ABC algorithm introduces neighborhood source production mechanism
which is the same as mutation process. In a research by Karaboga et al. (2010), ABC
has been proposed as a hierarchical clustering approach for wireless sensor networks
to maintain energy reduction of the network in lowest amount. From the results, it
showed that ABC algorithm outperformed over direct transmission and LEACH
algorithm. Also, ABC algorithm seems to be a promising solution for successful
operations in cluster based. In the research of Abu-Mouti and El-Hawary (2009), the
authors positive that ABC algorithm has excellent solution quality and convergence
characteristics. In the experiments, ABC has been used to minimize total system real
power loss for determining the optimal size, location and power factor for a
distributed generation (DG). The efficiency of ABC algorithm is confirmed where
the standard deviation of the attained results for 30 independent runs at every test
case is practically equivalent to zero.
In the domain of signal processing, ABC algorithm was implemented for
designing digital HR filters and its performance is compared with conventional
optimization algorithm (LSQ-nonlin) and PSO (Karaboga, 2009). ABC algorithm
shows a less computation time required and offered optimal solution compared to
18
PSO and LSQ-nonlin due to its excellent global and local search capability. The
algorithm is recommended as alternative approach for designing digital low- and
high-order HR filters.
In the domain of image processing, Benala et al. (2009) used ABC algorithm
to enhance image edge for hybridized smoothening filters as ABC algorithm claims
to be the most powerful neutral optimization technique for sampling a large solution
space. The results are then compared to GA. It was found out that ABC
outperformed GA in terms of speed in optimization and accuracy of results. The
authors claimed that in ABC algorithm the probability of falling into the local
optimum is low. This is because of the combination of local and global search since
the aim of the algorithm is to improve the local search ability of the GA without
degrading the global search ability.
In the domain of bioinformatics, ABC algorithm has been used by Bahamish
et al. (2009) to search the protein conformational search space to find the lowest free
energy conformation. In the research, four types of experiments are conducted and
100 independent runs were performed for each experiment. The results indicated that
the algorithm was able to find the lowest free energy conformation for a test protein
(i.e. Met enkephaline) of -12.910121 kcal/mol usign ECEPP/2 force field. Another
research attempted by Benitez and Lopes (2010). ABC algorithm was used to predict
protein structure using the three-dimensional hydrophobicpolar model with side-
chains (3DHP-SC). From the results, the researchers stated that the colony size
(number of bees) per hive has a significant influence in the quality of solutions and
suggested that larger colony leads to better results than the smaller ones.
In the scheduling and assignment problem, ABC algorithm was used to
identify optimum parameters for scheduling the manufacture and assembly of
complex products to minimize the combination of earliness and tardiness penalties
cost (Pansuwan et al., 2010). According to the authors, ABC algorithm performance
can be enhanced significantly after implementing the optimum parameter setting
19
identified through statistical design and analysis. In solving small to medium size
generalized assignments problems by Baykasoglu et al. (2010), the researchers
assured that ABC algorithm discovered all optimal solutions effortlessly compared to
the other 12 algorithms that was tested in the experiments.
In the domain of numerical optimization, a comparative study by
Krishnanand et al. (2009) shows that ABC gives an optimal result compared to the
other four biological inspired optimization algorithms which are Artificial Immune
(AI), Invasive Weed Optimization (IWO), GA and PSO. In the experiments, all five
algorithms are applied using multivariable Rosenbrock function and global minima
are constantly attained in ABC for extremely undersized dimensional problem. A
modified ABC algorithm is applied by Akay and Karaboga (2010) to solve real-
parameter optimization problem. In the study, ABC algorithm has been tested with
two group of functions which are unimodal function such as Sphere and Rosenbrock
function and composite function. The results show that ABC is efficient in terms of
local and global optimization due to the selection schemes employed and the use of
neighbouring production method. In Karaboga D. and Akay (2009), ABC was used
for optimizing a large set of numerical test functions and the results produced by
ABC algorithm are compared with the results obtained by GA, PSO, DE and
evolution strategies. Results show that the performance of the ABC is better than or
similar to those of other population-based algorithms with the advantage of
employing fewer control parameters.
2 0
Table 2.1: Control parameters of ABC
No Author, Year Number of test/
experiments
Number of colony size (SN)
Limit (L) Maximum loop (M)
1 Rao et al. (2008)
3 30 Not stated 20
2 Bahamish et al. (2009)
4 20 Not stated 1000
3 Karaboga(2009)
4 20 40 100
4 Baykasoglu et al. (2010)
2 150 Not stated 100
5 Abu-Mouti and El- Hawary (2009)
4 30 227 20
6 Benitez and Lopes (2010)
4 250 Not stated 6000
Table 2.1 shows the value of three control parameters of ABC optimization
such as number of colony, limit and maximum loop that has been used by various
researchers.
2.5 Previous research in optimizing machining process parameters using soft
computing techniques
From the literature review, there is a deficiency of research using ABC in
optimizing process parameters of Ra in machining areas particularly for traditional
and non-traditional machining. A research by Rao and Pawar (2010) applied non-
traditional optimization algorithm such as ABC, PSO and SA to optimize process
parameter in multi-pass milling machining. The results show that the convergence
rate of ABC and PSO algorithms are very high and involves only a little iteration for
convergence to the optimal solution. The accurateness of solution achieved by ABC
algorithm is better than the result obtained by using SA algorithm.
In Zain et al (2010a, 2010b, 2010c) GA and SA have been applied in
optimizing cutting condition for both end milling and AWJ. The results of GA and
SA show a significant potential and accomplishment in both machining operations.
In end milling machining, GA and SA decreased the Ra by 27%, 26% and 50%
compared to experiment data, regression model and RSM technique correspondingly.
While in abrasive waterjet machining, GA minimize the Ra by 27% and 41%
compared to experimental data and regression model respectively. The outcomes of
SA show a modest increments where it minimize the Ra by 28% and 42% compared
to data and regression model respectively.
Based on No Free Lunch (NFL) theorem, whichever two algorithms are
equivalent when their performance is averaged across all possible problems (Wolpert
and Mcready, 1997). Although GA and SA show good results in minimizing the Ra
values in both end milling and AWJ machining, ABC optimization algorithm is
applied in order to achieve more optimal values of Ra for both machining operations.
The NFL outcomes point out that matching algorithm to problems gives superior
average performance than does applying a fixed algorithm to all (Wolpert and
Mcready, 2005). The NFL is impossibility theorem where universal optimization
22
approach is impractical and a single approach can surpass another if it is specialized
to the structure of the particular problem under consideration (Ho and Pepyne, 2002).
Table 2.2 and Table 2.3 briefly summarized the previous research works that
have been accomplished in traditional and modem machining respectively to
optimize process parameters of Ra using a variety of optimization techniques.
Table 2.2: Previous researches in optimizing process parameters of Ra for traditional machining
Author/Year Techniques Cutting condition Process Results
lao and Pawar 2010)
ABC, PSO, SA
Feed per tooth, cutting speed, depth of cut
Milling The convergence rate of ABC algorithms is v high and involves only a little iteration for convergence to the optimal solution. The accurateness of solution achieved by ABC algorithms is better than results obtained by u SA algorithm.
lossain et al. 2009)
ANN Feed per tooth, cutting speed, depth of cut
Milling Performance of the neural network is very go( terms of concurrence with the experimental d<
Cadirgama et 1. (2008)
RSM,RBFN
Cutting speed, feed rate, axial depth and radial depth
Milling The feed rate has been identified as the most significant factors effecting Ra in the first ord( model and RBFN. RBFN predict Ra more pre compared to RSM.
Wang et al. 2009)
NN Spindle rate, feed rate, axial depth
Milling The maximal prediction error is about 10%, w the machining variables are chosen out of the variables range which is used for the NN moc training. The model is capable to predict the h well.
Wang et al. 2009)
GA Spindle rate, feed rate, axial depth
Milling The optimization results shows that the maxir removal rate can be attained in the certain ran Ra by selecting the right cutting parameters.
ring et al. 2005)
PSO Feed rate, depth of cut, grit size
Grinding PSO establishes the optimization of silicon ca grinding and hence assists the effective use of quality ceramics in industrial applications.
3odi and 'ingjian (2009)
ANN, GA Cutting speed, feed rate, depth of cut, diameter, slenderness ratio
Milling ANN and GA are both successful and efficien slender bar turning operations.
'ain et al. 2010a, 2010b)
GA, SA Feed per tooth, cutting speed, depth of cut
Milling, In end milling GA and SA decreased the Ra b; 27%, 26% and 50%.
Escamilla et al. 2009)
ANN, PSO Feed per tooth, cutting speed, depth of cut
Milling The results indicate that a system where neura network is used to model and predict process outputs andPSO is used to obtain optimum process param can be successfully applied to multi-objective optimization of titanium’s machining process
’l-Mounayri et 1. (2003)
PSO Feed per tooth, cutting speed, depth of cut
Milling The final model is able to predict the output (l Ra) of the system for new inputs (i.e. Feed rat depth of cut and spindle speed) with over 79°/ confidence.)
'ain et al. 2009)
ANN Feed per tooth, cutting speed, depth of cut
Milling The ANN technique has decreased the minim value of the experimental sample data by aboi 0.0126(j,m, or 5.33%.
amanta et al. 2008)
ANN,adaptiveneuro-fuzzyinferencesystem(ANFIS),multivariateregressionanalysis(MRA)
Spindle speed, feed rate, and depth of cut
Milling Statistically all three models predicted roughn with satisfactory goodness of fit, the test performance of ANFIS was better than ANN MRA.
amanta, B. 2009)
ANFIS, GA Spindle speed, feed rate, and depth of cut
Milling The results show the effectiveness of the prop approach in modelling the Ra.
Uiarathi Raja nd Baskar 2010)
PSO Cutting speed, feed, depth of cut,
Turning It is observed that the machining time and Ra on PSO are nearly same as that of the values obtained based on confirmation experiments; it is found that PSO is capable of selecting appropriate machining parameters for turning operation.
rakasvudhisam t al. (2009)
SupportVectorMachine(SVM),PSO
Feed rate, spindle speed, and depth of cut
Milling The cooperation between both techniques can achieve the desired Ra and also maximize productivity simultaneously.
rinivas et al. 2007)
PSO Cutting speed, feed, depth of cut
Turning PSO give stable optimal feasible solutions wi1 reasonable computational time.
'osta et al. 2010)
HybridPSO-SA
Cutting speed, feed, depth of cut
Turning HPSO can be taken into account as a useful ai powerful technique for optimizing machining problems.
iao et al. 2008)
GeneticSimulatedAnnealing(GSA)
Feed rate, cutting speed and depth of cut
Milling The result shows that optimum machining parameters are superior to the handbook value can effectively shorten machining time.
ayuti et al. 2011)
Taguchi Spindle speed, feed rate, depth of cut, lubrication mode, tool type, tool diameter and tool wear.
Grinding The results showed an improvement of 8.91 °/ the measured Ra.
alanikumar, K. 2006)
Taguchi Cutting speed, feed rate, and depth of cut.
Turning The experimental results suggest that the mos significant process parameter is feed rate folic by cutting speed. The study shows that the Ta method and Pareto ANOVA are suitable for optimizing the cutting parameters with the minimum number of trials.
'"anda et al. 2010)
Taguchi Cutting speed, feed rate and depth of cut
Turning Low surface finish was obtained at high cutting speed and low feed rate. Therefore tin' cost saving are significant especially is real in application, and yet reliable prediction is obta by conducting machining simulation using FE software Deform 3D. The results obtained for using the proposed simulation model were in good agreement with the experiments.
/lotorcu, A.R. 2010)
Taguchi Cutting speed, feed rate, depth of cut
Turning The obtained results indicate that the feed rate found out to be a dominant factor among controllable factors on the Ra, followed by de cut and tool’s nose radius. The second order regression model shows that the predicted val were very close to the experimental one for R
Lilickap et al. 2010)
RSM, GA Cutting speed, feed rate, and cutting environment
Drilling The predicted and measured values were quite close, which indicates that the developed moc be effectively used to predict the Ra. The give model could be utilized to select the level of drilling parameters. A noticeable saving in machining time and product cost can be obtaii using this model.
/lurthy andLajendran2010)
ANN Cutting speed, depth of cut and feed rate
Milling The results show that the highest cutting spee medium feed rate and medium depth of cut produces lowest Ra. This study provides the optimum cutting conditions for end milling oi aluminium 6063 under minimum quantity lubrication machining.
uisalam andJarayanan2010)
IGA Speed, feed, and depth of cut
Turning The proposed algorithm was compared with t conventional genetic algorithm (CGA), and w found that the proposed IGA is more effective previous approaches and applies the realistic machining problem more efficiently than does conventional genetic algorithm (CGA).
s.lam et al. 2008)
RSM Spindle speed, feed rate, and depth
Milling A very good performance of the RSM model, terms of agreement with experimental data, w achieved. It is observed that cutting speed has most significant influence on Ra followed by and depth of cut.
)ktem, H. 2009)
ANN, GA Spindle speed, feed rate, and depth
Milling GA improves the Ra value from 0.67 to 0.59 p with approximately 12% gain. Then, machining time has also decreased from 1.28^ 1.0316 min by about 20% reduction based on cutting parameters before and after optimizati process using the analytical formulas. The fin measurement experiment has been performed verify Ra value resulted from GA with that of material surface by 3.278% error.
Lazfar and 'adeh (2009 )
NN, GA Spindle speed, feed rate, and depth
Milling Genetically optimized neural network system (GONNS) is proposed for the selection of the optimal cutting conditions from the experimei data when an analytical model is not available GONNS uses back-propagation (BP) type NN represent the input and output relations of the considered system. The GA obtains the optim operational conditions through using the NNs From this, it can be clearly seen that a good agreement is observed between the predicted and the experimental measurements.
lossain et al. 2008)
ANN Cutting speed, feed, and axial depth of cut.
Milling A very good predicting performance of the n< network, in terms of concurrence with experir data was attained. The model can be used for analysis and prediction for the complex relatk between cutting conditions and the Ra in meta cutting operations and for the optimization of for efficient and economic production.
/Tanna and alodkar (2008)
Taguchi Cutting speed, feed rate and depth of cut
Turning The developed optimality condition affects th economics of machining conditions. The grap representations also help to understand and an the effects of various input constraints at the optimum point and their significant influences production cost. The analysis can propose an effective methodology in advance for proper of machining parameters in practice, which m reduce the cost of unit production.
laq et al. 2008)
Taguchi Cutting speed, feed and point angle
Drilling Experimental results have shown that the resp in drilling process can be improved effectiveb through the new approach.
'hang et al. 2007)
Taguchi Feed rate, spindle speed and depth of cut
Milling An orthogonal array of Lg(34) was used; ANC analyses were carried out to identify the signi factors affecting Ra, and the optimal cutting combination was determined 1 seeking the best Ra (response) and signal-to-n ratio. Finally, confirmation tests verified that Taguchi design was successful in optimizing milling parameters for Ra.
Table 2.3: Previous researches in optimizing process parameters of Ra for modem machining
Author/Year Techniques Cutting condition Process Results
'ain et al. 2010c)
GA, SA Water pressure, abrasive flow rate, jet traverse rate, diameter of focusing nozzle
AWJ GA minimize the i?„by 27% and 41% and 28% and 42%.
Colahan and Qiajavi (2009)
SA Water pressure, abrasive flow rate, jet traverse rate, diameter of focusing nozzle
AWJ Computational results show that the propos solution procedure is reasonably effective.
aha et al. 2008)
Back-propagationneuralnetwork
Pulse on-time, pulse off- time, peak current, and capacitance
Wire electrodischarge machining (WEDM)
4-11-2 network architecture has been founc the optimal one, which can predict cutting and Ra with 3.29% overall mean prediction
Lao et al. 2010)
ABC, Harmony Search (HS), PSO
Amplitude of ultrasonic vibration, frequency of ultrasonic vibration, mean diameter of abrasive particles, volumetric concentration of abrasive particles, and static feed force.
Ultrasonicmachining(USM).
The results of the presented algorithms are compared with the previously published re obtained by using genetic algorithm (GA).
j u o et al. 2006)
ANN Beam angle, movement, speed and laser power
3D Laser cutting The ANN is very successful for optimizing parameters, predicting cutting results and deducing new cutting information.
4aji and ratihar (2010)
RegressionAnalysis,GA
Peak current, pulse-on- time and pulse-duty-factor
Electric discharge machining (EDM)
More or less 10% deviations in prediction responses had been reported for both of the the test cases.
asam et al. 2010)
Taguchi,GA
Ignition pulse current, Short pulse duration,Time between two pulses,Servo speed, Servo reference voltage, Injection pressure, Wire speed and Wire tension
WEDM Optimum values of control parameters for selected range and workpiece material are obtained.
omashekhar t al. (2009)
GA Gap voltage, capacitance and feed rate.
Micro Wire Electric Discharge Machining (|j,- WEDM)
Experiments were planned and conducted i DoE techniques. ANOVA was performed t out the significance of each factor. Regress models were developed for the experiment, results of Ra and overcut of the micro slots produced on aluminium. Then Genetic Algorithm (GA) was employed to detemiin values of optimal process parameters for th desired output value of micro wire electric discharge machining characteristics.
in et al. 2009)
Taguchi Machining polarity, peak current, auxiliary current with high voltage, pulse duration, no load voltage, and servo reference voltage
EDM Experimental results showed EDM is a fea process to shape conductive ceramics, and relationships between machining character] and parameters were examined. Moreover, machining parameter optimal combination in machining conductive ceramics via EDN were also determined.
'hen et al. 2010)
BPNN, SA Pulse on-time, pulse off- time, peak current, and capacitance
WEDM The results of proposed algorithm and confirmation experiments are show that the BPNN/SAA method is effective tool for th optimization of WEDM process parameters
Luo and Chang 2007)
Taguchi Rotational speed, feed, and depth of cut
Laser-assisted machining (LAM)
The findings indicate that feed, with a contribution percentage as high as 37.26%, the most dominant effect on LAM system performance, followed by rotational speed depth of cut. LAM’s most important advant its ability to produce much better workpiec surface quality than does conventional machining, together with larger material re rates (MRR).
LamakrishnanndLarunamoorthy2006)
Taguchi Pulse on time, wire tension, delay time, wire feed speed, and ignition current intensity.
WEDM Multi response S/N (MRSN) ratio was app measure the performance characteristics deviating from the actual value. Analysis o variance (ANOVA) is employed to i dent if) level of importance of the machining paran
on the multiple performance characteristics considered. Finally experimental confimiat was carried out to identify the effectiveness this proposed method. A good improvemer obtained.
'hen et al. 2010)
Taguchi Peak current, pulse-on- time and pulse-duty-factor
EDM The experimental results show that peak cu and pulse duration significantly affected M and SR, and the adhesive conductive mater was the significant parameter correlated wi EWR. In addition, the optimal combination levels of machining parameters were also determined from the response graph of sigr noise ratios for each level of machining parameters.
ahoo et al. 2009)
RSM Pulse current, pulse on time and pulse off time
EDM The roughness models, as well as the significance of the machining parameters, 1 been validated with analysis of variance. A attempt has also been made to obtain optim machining conditions using response optimisation technique.
Lanagarajan et 1. (2008)
Nondominatedsortinggeneticalgorithm(NSGA-II)
Pulse current, pulse on time, electrode rotation and flushing pressure
EDM The experimental results are used to develc statistical models based on second order polynomial equations for the different proc characteristics. Non-dominated solution se1 been obtained and reported.
/larkopoulos et 1. (2006)
ANN Pulse current and the pulse-on time
EDM A feed-forward artificial ANN trained wit Levenberg-Marquardt algorithm was finall selected. The proposed neural network take consideration the pulse current and the puls time as EDM process variables, for three different tool steels in order to determine tt center-line average (Ra) and the maximum of the profile (Rt) Ra parameters.
arkar et al. 2006)
ANN Pulse on time, pulse off time, peak current, wire tension, dielectric flow rate and servo reference voltage
WEDM The model is capable of predicting the resp parameters as a function of six different co parameters. Experimental results demonstr that the machining model is suitable and th optimisation strategy satisfies practical requirements.
enthilkumar t al. (2010)
NSGA - II Electrolyte concentration, electrolyte flowrate, applied voltage, and tool feed rate.
Electrochemicalmachining
The non -dominated sorting genetic algorit (NSGA-II) tool was used to optimize the E process parameters to maximize MRR and minimize Ra. A non -dominated solution se been obtained and reported.
Lao and Pawar 2010)
ABC Pulse-on time, pulse-off time, peak current, and servo feed setting
WEDM ABC is applied to find the optimal combin< of process parameters with an objective of achieving maximum machining speed for a desired value of surface finish.
/lohammadi et Taguchi Power, time-off, voltage, Turning wire The variation of Ra and roundness with1. (2008) servo wire tension, wire electrical machining parameters was mathematically
speed, and rotational discharge modelled by using the regression analysisspeed machining method. The presented model is verified b)
(TWEDM) of verification tests.
37
2.6 Experimental data of case studies
In this section, the experimental data of case studies of end milling and AWJ,
research attempted by Mohruni (2008) and Caydas and Hascalik (2008) are being
referred respectively. The experimental design and results are discussed.
2.6.1 End milling machining
The experiments conducted were using a material workpiece annealed alpha-
beta titanium alloy or named as Ti-6A1-4V. The chemical composition of Ti-6A1-4V
includes A l 6.37%, V 3.89%, Fe 0.16%, C 0.002%, Mo <0.01%, Mn <0.01%,
Si<0.01% and balance value of Ti. The mechanical properties of Ti-6A1-4V are
shown in Table 2.4. There are three category of end milling machining that employed
in the study namely uncoated carbide (WC-Co), two TiAIN coated carbide tools
which consist of PVD-TiAIN coated carbide tool and PVD with enriched Al-content
TiAIN coated carbide tools, also named Supemitride coating (SNTR). The properties
for each cutting tools are shown in Table 2.5.
Table 2.4: Mechanical properties of Ti-6A1-4V
Mechanical properties
Tensile strength (MPa) 960-1270Yield strength (MPa) 820Elongation 5D (%) >8Reduction in area (%) >25Density (g/cm3) 4.42Modulus of elasticity tension (GPa) 100-130Hardness (Hv) 330-370Thermal conductivity (W/mK) 7
38
Table 2.5: Properties of the cutting tool used in the experiments
Tool type WC- Co TiAIN coated Supemitridecoated
Substrate(wt%)
WC 94 94 94
Co 6 6 6
PropertiesGrade K30 K30 K30
Grain size (jam) 0.5 0.5 0.5
Coating
Process - PVD-HIS PVD-HIS
Coating thickness Monolayer (3-4
|am)
Monolayer (1
8 |am )
Film composition (mol-%AIN)
- Approx. 54 Approx. 65-67
2.6.1.1 End milling experimental design
In end milling machining Ti-6A1-4V, the 23-factorial design used level -1,0
and +1 coding variables which based on the design of experiments (DOE). Table 2.6
shows the level of independent variables and coding identification. Two of the
variables are kept constant which is axial and depth of cut with value of 5mm and
2mm correspondingly. The machining experiments are completed on a CNC MAHO
700S machining centre in wet state. The specification of the CNC machine is given
in Table 2.7. A device named Taylor Hobson Surftronic +3 was used to record and
compute the minimum Ra values for each cutting tool type. A total of five
measurements were accomplished at the setting of the length of cut on the
workpiece.
39
Table 2.6: Levels of independent variables and coding identification
Level in coded form
Independent
Variables
Units -1.4142 -1 0 +1 +1.4142
Cutting
speed, v
m/min 124.53 130.00 144.22 160.00 167.03
Feed ra te ,/ mm/tooth 0.025 0.03 0.046 0.07 0.083
Radial rake
angle, y
o 6.2 7.0 9.5 13.0 14.8
Table 2.7: Specification of the CNC machine
Brand CNC Flexible Machining Cell
Model MAHO 700S 5 Axis
Electrical data (Motor) 3 x 300 V 50Hz
No. of axes 5
Tool capacity 60
Spindle speed 20-6300 rpm
Controller Philip 432
40
2.6.1.2 End milling experimental results
There are eight data sources from each of two levels DOE 2k full factorial,
four centre and twelve axial points are performed on the 24 experimental
assessments for each cutting tool type. From the experimental results, the lowest Ra
values for /?uncoated is 0.23 jam which was given by the minimal process parameters
of v = 167.03m/min,/ = 0.046mm/tooth and y = 9.5°. For /?TiAlN the lowest Ra
values is 0.232(j,m which obtained by v = 160m /m in,/= 0.03mm/tooth and y = 13°.
And lastly for /?SNtr the lowest Ra values is 0.190|am which also achieved by v =
160m/min, / = 0.03mm/tooth and y = 13°. The minimum and average Ra are
calculated and results are shown in Table 2.8.
41
Table 2.8: Ra values for real machining experiments
Setting values of experimental cutting condition
Ra predicted values (jam)
No Datasource
v (m/min) /(mm/tooth)
Y (°) /?uncoated /tTiAIN /?SNtr
1 130 0.03 7 0.365 0.32 0.2842 160 0.03 7 0.256 0.266 0.1963 130 0.07 7 0.498 0.606 0 . 6 6 8
4 160 0.07 7 0.464 0.476 0.6245 130 0.03 13 0.428 0.260 0.2806 DOE
2 k160 0.03 13 0.252 0.232 0.190
7 130 0.07 13 0.561 0.412 0.6128 160 0.07 13 0.512 0.392 0.5769 144.22 0.046 9.5 0.464 0.324 0.329
1 0 144.22 0.046 9.5 0.444 0.380 0.4161 1 144.22 0.046 9.5 0.448 0.460 0.3521 2 144.22 0.046 9.5 0.424 0.304 0.40013 Centre 124.53 0.046 9.5 0.328 0.360 0.34414 124.53 0.046 9.5 0.324 0.308 0.32015 167.03 0.046 9.5 0.236 0.340 0.27216 167.03 0.046 9.5 0.240 0.356 0.28817 144.22 0.025 9.5 0.252 0.308 0.23018 144.22 0.025 9.5 0.262 0.328 0.23419 144.22 0.083 9.5 0.584 0.656 0.6402 0 144.22 0.083 9.5 0.656 0.584 0.6962 1 Axial 144.22 0.046 6 . 2 0.304 0.300 0.3612 2 144.22 0.046 6 . 2 0.288 0.316 0.36023 144.22 0.046 14.8 0.316 0.324 0.36824 144.22 0.046 14.8 0.348 0.396 0.360
Ra (minimum) 0.236 0.232 0.190
42
2.6.2 AWJ machining
In AWJ machining, the experiment condition material of machined
workpiece is Al 7075-T6 wrought alloy (AlZnMgCul.5). The chemical composition
of Al 7075-T6 wrought alloy includes Al 91.02%, Cu 1.65%, Mg 2.0%, Cr 0.23%,
Zn 5% and Mn 0.1%.
2.6.2.1 AWJ experimental design
The coded level form for the machining is based on DOE for the five process
parameters is defined in Table 2.9. During the experiments, a distance of 5mm from
the top of the cutting surface was taken for the measurements. A handy device named
SJ-201 was used to measure the average Ra. In order to examine the machined
surface another device named LEO 32 scanning electron microscope (SEM) was
used.
Table 2.9: Levels of process parameters and coding identification
Level in coded form
Independent Variables Units 1 2 3
Traverse speed, V mm/min 50 1 0 0 150
Waterjet pressure, P MPa 125 175 250
Standoff distance, h Mm 1 2.5 4
Abrasive grit size, d lm 60 90 1 2 0
Abrasive flow rate, m g/s 0.5 2 3.5
43
2.6.2.2 AWJ experimental results
A total of 27 experiments has been performed based on L27 Taguchi’s
orthogonal array to find the minimum and average value of Ra in AWJ machining
The lowest Ra values is 2.124 which was obtained by the following process
parameters V = 50, P = 125, h =1, d = 60, m = 0.5. The values for each
experimental AWJ process parameters and optimal Ra are shown in Table 2.10.
Table 2.10: Ra values for real machining
No Setting values of experimental process parameters Ra (nm)
V (m/min) P (MPa) h (mm) d (jam) m (g/s)
1 50 125 1 60 0.5 2.1242 50 125 1 60 2 2.7533 50 125 1 60 3.5 3.3524 50 175 2.5 90 0.5 4.3115 50 175 2.5 90 2 4.5416 50 175 2.5 90 3.5 5.1237 50 250 4 1 2 0 0.5 6.7898 50 250 4 1 2 0 2 7.5249 50 250 4 1 2 0 3.5 9.123
1 0 1 0 0 125 2.5 1 2 0 0.5 3.5751 1 1 0 0 125 2.5 1 2 0 2 4.4571 2 1 0 0 125 2.5 1 2 0 3.5 5.62813 1 0 0 175 4 60 0.5 7.01014 1 0 0 175 4 60 2 7.53515 1 0 0 175 4 60 3.5 7.89316 1 0 0 250 1 90 0.5 8 . 1 2 1
17 1 0 0 250 1 90 2 8.31218 1 0 0 250 1 90 3.5 9.16319 150 125 4 90 0.5 4.3282 0 150 125 4 90 2 5.1202 1 150 125 4 90 3.5 5.8522 2 150 175 1 1 2 0 0.5 6.14323 150 175 1 1 2 0 2 6.72124 150 175 1 1 2 0 3.5 7.78025 150 250 2.5 60 0.5 8.89026 150 250 2.5 60 2 9.12027 150 250 2.5 60 3.5 10.035
Ra (minimum) 2.124
44
2.7 Summary
This chapter has presented a literature review on optimization of both end
milling and AWJ machining operations. The efficiency of ABC algorithm was
shown in a various research of related domain and problems. Experiment designs for
Ra measurement based on Mohruni (2008) and Caydas and Hascalik, (2008) effort
have been discussed. In the next chapter, the methodology of ABC optimization for
finding the Ra values is presented.
CHAPTER 3
METHODOLOGY
3.1 Introduction
The primary focus of this section is to discuss and investigate the
methodology that is accomplished in this research. This includes discussing the
process flow that is required for the implementation of this research. This chapter
also explained each step involved in developing ABC algorithm to minimize Ra of
machining performance measurement.
Two types of machining operations are used in this research which is end
milling (traditional machining) and AWJ (modem machining). The experimental
data set was based on effort by Mohruni (2008) for end milling operation and Caydas
and Hascalik (2008) for AWJ operation. Subsequently, for each machining operation,
the regression model is developed and the Ra value is calculated. The most minimum
Ra value of predicted equation in each machining is used as the fitness function of
ABC. Consequently, ABC optimization is performed to find the optimal process
parameters for both machining operations. Finally, the results are evaluated with the
experimental, regression modeling, GA optimization and SA optimization.
46
Figure 3.1 Flow of searching for optimum process parameters
47
3.2 Research flow
In this part, the flow of the process for searching the optimal process
parameters that lead to Ra value is explained. There are four phases that is
implemented in this research, which are:
i. Assessment of real experimental data
ii. Regression modeling development
iii. ABC algorithm for optimization of process parameters
iv. Validation and evaluation of results
These phases and process steps for searching the optimal process parameters
are illustrated in the Figure 3.1.
3.3 Assessment of real experimental data
The evaluation and results of real experimental data for both machining
operations are discussed in Section 2.6. This experimental evaluation is based on
effort attempted by Mohruni (2008) and also Caydas and Hascalik (2008).
3.4 Regression modeling development
Regression modeling is concerned in predicting of one variable from one or
more variables and grants the scientist with a great tool and provides the information.
The information afterward allows the scientist to decide what action that needs to be
taken. The regression modeling is timeless and less costly to gather the information
to make the predictions (Stockburger, 1996).
3.4.1 Regression modeling in end milling
48
For end miling machining, three types of cutting tools which is uncoated
carbide (WC-Co) and two TiAIN coated carbide tools which comprise of PVD-
TiAlN coated carbide tool and PVD with enriched Al-content TiAIN coated carbide
tools or Supemitride coating (SNTr) will be assessed for the experiments.
The regular equation is defined precisely as (3.1) to discover the value of Ra
in end milling:
Ra = cv f l y m £' (3.1)
In equation (3.1), Ra is the calculated surface roughness in jam, v is the
cutting speed in m /m in,/is the feed in mm/tooth, y is radial rake angle in ° and c, k,
I, m are the model parameters approximated through experiments.
The equation (3.1) subsequently is linearized by executing a logic
transformation in (3.2) to develop regression model.
In Ra = In c + k In v + / ln /+ m In y + In £’ (3.2)
Equation (3.2) can be written as:
y = box o + b\X\ + biXi + 6 3 X3 + £ (3.3)
In equation (3.3), y is the logarithmic value of the experimental Ra, xq = 1 is an
artificial variable, x\, x2 and x3 are referring to the cutting condition values
(logarithmic transformations) of cutting speed (v), feed rate if) and radial rake angle
(y) correspondingly, £ is the logarithmic transformation of experimental error £’ and
bo, b\, hi and Z>3 are the model parameters to be estimated using the experimental
data.
Equation (3.3) can also be written as follows:
p — y - £ = Z>oXo + 6 1 X1 + biXi + 6 3 X3 (3.4)
49
In equation (3.4) y is the logarithmic value of the predictive (estimated) Ra. Then,
this equation will be proposed as the fitness function of the optimization solution.
3.4.1.1 Regression Model for Each Cutting Tool
The values of coefficients for each cutting tool are demonstrated in
Table 3.1, 3.2 and 3.3. Each of this value is reassigned in equation (3.4) and written
as follows:
y \ = /Tuncoated = 0.451 - 0.00267*1 + 5.671*2 + 0.0046*3 (3.5a)
y l = /tTiAIN = 0.292 - 0.000855*1 + 5.383*2 - 0.00553*3 (3.5b)
v3 = /?SNtr = 0.237 - 0.00175*1 + 8.693*2 + 0.00159*3 (3.5c)
Table 3.1: Uncoated Tool coeffients value
Unstandardizec coefficients Standardized coeffientsIndependent variable B Std.error Beta t Sig
1 (Constant) 0.451 0.175 2.582 0.018SPEED -2.67^-03 0.001 -0.277 -2.407 0.026FEED 5.671 0.811 0.805 6.994 0
RAKE ANGLE 4.60E-03 0.005 0.097 0.842 0.412 (Constant) 0.386 0.025 15.627 0
Table 3.2: TiAIN coated Tool coeffients value
Unstandardizec coefficients Standardized coeffientsIndependent variable B Std.error Beta t Sig
1 (Constant) 0.292 0.158 1.85 0.079SPEED -8.55E-04 0.001 -0.098 -0.854 0.403FEED 5.383 0.731 0.843 7.36 0
RAKE ANGLE -5.53E-03 0.005 -0.129 -1.122 0.2752 (Constant) 0.375 0.022 16.771 0
50
Table 3.3: SNTr coated Tool coeffients value
Unstandardizec coefficients Standardized coeffientsIndependent variable B Std.error Beta t Sig
1 (Constant) 0.237 0.116 2.042 0.055SPEED -1.75E-03 0.001 -0.14 -2.368 0.028FEED 8.693 0.539 0.954 16.143 0
RAKE ANGLE -1.59E-03 0.004 -0.026 -0.437 0.6672 (Constant) 0.392 0.032 12.261 0
Equations (3.5a) to (3.5c) are then used to compute the predicted Ra values,
and the results are potted in Table 3.4. To confirm the best regression model as the
fitness function in ABC algorithm, paired-sample t -test was performed, and the
results are summarized in Tables 3.5 and 3.6.
Table 3.4: Ra predicted values of regression modelling (Zain et al, 2010a)
Setting values of experimental cutting condition
Ra predicted values (jam)
No Datasource
v (m/min) /(mm/tooth)
Y (°) /?uncoated /?TiAlN /?SNtr
1 130 0.03 7 0.306 0.304 0.2592 160 0.03 7 0.226 0.278 0.2073 130 0.07 7 0.533 0.519 0.6074 DOE 160 0.07 7 0.453 0.493 0.5545 2k 130 0.03 13 0.334 0.270 0.2506 160 0.03 13 0.254 0.245 0.1977 130 0.07 13 0.561 0.486 0.5978 160 0.07 13 0.481 0.460 0.5459 144.22 0.046 9.5 0.370 0.364 0.36910 144.22 0.046 9.5 0.370 0.364 0.36911 144.22 0.046 9.5 0.370 0.364 0.36912 Centre 144.22 0.046 9.5 0.370 0.364 0.36913 124.53 0.046 9.5 0.423 0.381 0.40414 124.53 0.046 9.5 0.423 0.381 0.40415 167.03 0.046 9.5 0.310 0.344 0.32916 167.03 0.046 9.5 0.310 0.344 0.32917 144.22 0.025 9.5 0.251 0.251 0.18718 144.22 0.025 9.5 0.251 0.251 0.18719
Axial144.22 0.083 9.5 0.580 0.563 0.691
20 144.22 0.083 9.5 0.580 0.563 0.69121 144.22 0.046 6.2 0.355 0.382 0.37422 144.22 0.046 6.2 0.355 0.382 0.37423 144.22 0.046 14.8 0.395 0.334 0.36124 144.22 0.046 14.8 0.395 0.334 0.361
Ra (minimum) 0.226 0.245 0.187
52
Table 3.5: Statistics and correlations for paired samples
Pair Variable Mean N
Std.
deviation
Std.error
mean
Correlation
(Pearson)
Sig
Pair 1 EXP UNCO
REG UNCO
0.38558
0.38567
24
24
0.12088
0.10363
2.47E-02
2.12E-02
0.857 0.000
Pair 2 EXP_TiAlN
REG_TiAlN
0.37533
0.37587
24
24
0.10964
9.42E-02
2.24E-02
1.92E-02
0.859 0.000
Pair 3 EXP_SNTr
REG_ SNtr
0.39167
0.39100
24
24
0.1565
0.1509
3.19E-02
3.08E-02
0.965 0.000
Table 3.5 indicates that for each pair of regression modeling data are
positively correlated. With r (N= 24), pair 1 correlation is 0.857, pair 2 correlation is
0.859, and pair 3 correlation is 0.965. Whereas results in Table 3.6 signify that the
mean Ra value for pair 1 enhanced from the experimental result to the uncoated
regression model by 0.0000833, t{23)= -0.007, p = 0.995. The 95% confidence
interval ranges from -0.0264 to 0.0263 (including zero).
For that reason, the two means of experimental result and regression model
results are not drastically different from each other. The mean Ra value for pair 2 also
improved from the experimental result to the TiAIN regression model by 0.000542,
t{23)= -0.047, p = 0.963. The 95% confidence interval ranges from -0.0243 to
0.0232 (including zero), which also proves that the two means are not drastically
different from each other.
53
Table 3.6: Paired samples test
Paired differences
95% Confidence Interval of the difference
Pair Mean Std.
Deviation
Std.
error
Mean
Lower Upper T Df Sig.
(2
tailed)
Pair
1
-8.33E-05 6.24E-02 1.27E-02 -2.64E-02 2.63E-02 0.007 23 0.995
Pair
2
-5.42E-04 5.62E-02 1.15E-02 -2.43E-02 2.32E-02 -0.047 23 0.963
Pair
3
6.67E-04 4.13E-02 8.43E-03 -1.68E-02 1.81E-02 0.079 23 0.938
From Table 3.6, it can be seen that the mean Ra value for pair 3 however
reduced from the experimental result to the S N tr regression model by 0.000667,
?(23)=0.079, p = 0.938. The 95% confidence interval ranges from -0.0168 to 0.0181
(including zero). Thus, the two means too are not significantly different from each
other. As a conclusion, it could be summarized that the S N tr coated cutting tool has
given the highest positive correlation and is the only pair that indicated a reduction in
the mean Ra value from the experimental result.
As a result, it can be recommended that the predicted Ra equation of S N tr
coated tools as given in Equation (5c) is the best regression model and it is proposed
to be the fitness function of the ABC optimization.
3.4.2 Regression modeling in abrasive waterjet
54
To calculate the value of Ra in abrasive waterjet machining, it is defined
mathematically in (3.6):
Ra = cVqFf hs cf mu (3.6)
where Ra is the experimental (measured) in jam, V is the traverse cutting speed in
mm/min, P is the waterjet pressure in MPa, h is the standoff distance in mm, d is
abrasive grit size in jam, m is the abrasive flow rate in g/s, £' is experimental error,
and c, q, r, s, t, and u are the model parameters to be estimated using the
experimental data.
To develop the Regression model for estimating the Ra value, the
mathematical model given in (3.6) is linearized by performing a logarithmic
transformation as follows:
In Ra = In c + q In V+ r In P + s In h + t In d + u In m + In £' (3.7)
Subsequently, (3.9) can be written as:
y = boXo + b\X\ + bjXj + 6 3 X3 + 6 4X4 + 6 5 X5+ £ (3.8)
where y is the logarithmic value of the experimental Ra, x0 = 1 is a dummy variable,
xi, X2 , X3 , X4 and X5 are the process parameter values (logarithmic transformations) of
V, P, h, d and m, respectively, £ is the logarithmic transformation of experimental
error £' and bo, bi, b3 , b4 and bs are the model parameters to be estimated using the
experimental data.
Next, (3.8) can also be written as follows:
y = y - £ = Z>oXo + 6 1 X1 + bjXj + 6 3 X3 + 6 4 X4 + 6 5 X5 (3.9)
where y is the logarithmic value of the predictive (estimated) Ra.
Equation (3.9) can be extended to form a second-order polynomial regression
for surface roughness predicted equation and given as follows:
55
y = Ra = bo + bi V + bjP + b^h + b t\,d + b 5m + bn V~ + bjj P~ + b33 hr + b^ct + b 5 5 777“+ bnF^ + b i3^ + b i4F<i+ b\sVm + bi^Ph + bi_aPd + b25-Pw + b ^ h d + b 3 5 /? 777 +b45<iw (3.10)
As of the results of Caydas and Hascalik (2008), the final regression model
for surface roughness obtained is written as follows:
Ra = -5.07976+0.08169F +0.07912P - 0.34221 h - 0.08661 d - 0.34866m -0.00031V2 - 0.00012P2 + 0.10575h2 +0.00041 d2 +0.07590w2 -0.00008Fw -0.00009Pw +0.03089//w+0.00513Jw (3.11)
The predicted Ra results of AWJ Regression model are given in Table 3.7
Table 3.7: Predicted Ra values of AWJ Regression model (Zain et al, 2010c)
No Setting values of experimental process parameters Z?fl(nm)
V (m/min) P (MPa) h (mm) d (jam) m (g/s)
2 50 125 1 60 2 2.62915
4 50 175 2.5 90 0.5 4.00520
6 50 175 2.5 90 3.5 5.42532
8 50 250 4 120 2 7.69815
10 100 125 2.5 120 0.5 3.66819
12 100 125 2.5 120 3.5 5.55233
14 100 175 4 60 2 7.36548
16 100 250 1 90 0.5 7.96455
18 100 250 1 90 3.5 9.21330
20 150 125 4 90 2 4.98615
22 150 175 1 120 0.5 6.07837
24 150 175 1 120 3.5 7.79815
26 150 250 2.5 60 2 9.23448
Ra (minimum) 2.62915
Subsequently, (3.11) will be assigned as the objective function for optimization
solution of ABC.
3.5 ABC algorithm for optimization of process parameters
56
There are three important control parameters in ABC optimization algorithm,
which have been stated in section 2.3. The process flow of ABC algorithm is
illustrated in Figure 2.3. There are seven steps to optimize process parameters of end
milling and AWJ that will lead to minimum Ra values. The steps are discussed
below.
i. Selection of control parameter
ii. Evaluation of the nectar quantity in every food source
iii. Probabilities determination using the nectar quantity
iv. Compute the number of onlookers bees to be sent to the food sources
V . Compute the fitness of each onlooker bee
vi. Assess the most excellent solution
vii. Update the scout bee
Step 1: Selection of control parameter
The possible solution to the problem to be optimized is generally represented
by food source position. A set of food source position is produced randomly and the
values of control parameters (SN, L, M) of ABC algorithm are determined. The
number of food sources must be equal to the number of employed bees. The value of
each food source depends on the fitness value of the objective function given by
equation (3.5c) for end milling and equation (3.11) for AWJ. In Rao and Pawar
(2010), the results are not better than the results obtained using number of employed
bees of 5 and colony size is 16 (number of employed bees and onlooker bees). ABC
performs better with a smaller population size and the ideal population size depends
on the optimization goal (Aderhold, et al, 2010). The value of control parameters
selected is defined in Table 3.8.
57
Step 2: Evaluation of the nectar quantity in every food source
A new food source is determined by each of employed bees by moving them
to the food source within the neighbourhood and after that the amount of nectar is
evaluated. If the new food sources contain a higher amount of nectar, the employed
bees will forget the historical food sources and memorizes the new food sources.
Once the process of searching is completed, the employed bees will come back to
their hive and share the information (the food source position) with onlooker bees by
performing a waggle dance on the dance area. The value of each food source depends
on the fitness value of the objective function given by equation (3.5c) for end milling
and equation (3.11) for AWJ.
Step 3: Probabilities determination using the nectar quantity
The prospect of the food source is preferred by onlooker bee increases as the
nectar amount food source increased. The chance with of the food source located at
0i is selected by an onlooker bee can be calculated by using equation (2.1) and
equation (2.2).
Step 4: Compute the number of onlookers bees to be sent to the food sources
As mentioned in the previous step, the majority of onlookers bees determine a
food source area with a probability based on higher amounts of nectar. The number
of onlookers bees that send to the food sources is by multiplying the probability
values, Pi in step 3 with the total number of onlookers bees. This repetitive process is
stop once all the onlooker bees are distributed onto high nectar amounts of food
sources that have been decided by employed bees.
58
Step 5: Compute the fitness of each onlooker bee
The information of the particular prospect food source will be shared in the
hives by doing an attention-grabbing waggle dance. This waggle dance will be
observed by unemployed bees which later will hunt to make use of the food source.
Based on the waggle dance, the onlooker bee take off to the food sources located at
0i. The position of selected neighbourhood food sources is calculated in equation
(3.12):
0i(c+l) = 0i(c) + 0 (0i (c) - 0k (c)) (3.12)
where c is number of generation. In order to find out food source with more nectar
around 0i, <f>(c) is a randomly produced. A randomly produced index k is dissimilar
from i. The difference of the equivalent parts of 0i(c) and 0k(c) gives the value of
(j>{c). If the nectar amount Fi (c + 1) at 0i (c + 1) is higher than at 0i (c), then the bees
go to the hive and share information with others and the position 0i (c) of the food
source is changed to 0i (c + 1) otherwise 0i (c) is kept as it is. If the position 0i of the
food source i cannot be improved through the predetermined number of trials, then
that food source 0i is abandoned by its employed bee and then the bee becomes a
scout. The scout starts searching new food source, and after finding the new source,
the new position is accepted as 0i.
Step 6: Assess the most excellent solution
In each food source the most excellent position of onlooker bee is identified.
In each generation, the global best of the honeybee swarm in possibly will replace
the global best at preceding generation if it has improved fitness value.
59
Step 7: Update the scout be
The employed solution of employed bees will be compared to the scout
solution of the scout bees. Employed solution will replace the scout solution if it has
improved solution. If not, employed solution is shifted to the next generation with
no modification.
3.5.1 Justification of ABC control parameter
Based on the control parameters used by previous researchers that have been
summarized in Table 2.1, the three control parameters to develop the ABC
optimization algorithm for optimizing process parameters in end milling and AWJ
machining is justified in Table 3.8:
Table 3.8: Justification of ABC control parameters
Control parameters Justification
the number of colony size (SN) 16
the predefined value of limit (L) 100
maximum loop for searching food (M) 150
3.5.2 Steps for determination of the optimal process parameters
The main intention of the optimization process in this research is to find out
the optimal values of the process parameters that lead to the lowest value of Ra.
Therefore, the Regression models in (3.5c) and (3.11) will be proposed to be the
fitness function of the optimization solution for end milling and AWJ respectively.
The minimization of the fitness function values of equations (3.5c) and (3.11)
are subjected to the restrictions of the process parameters. The process parameters of
60
each machining are set by a range of values and initial points to present the
boundaries of the optimization solution.
In end milling, there are three process parameters which are the cutting speed
(v), feed rate if) and radial rake angle (y). The best possible value of feed rate if)
must be in the range of,
/m m < /< /m a x (3.13)
where /m,n is the minimum feed rate and /max is the maximum feed rate.
The cutting speed (v) must meet the range of equation (3.14),
Vmin — V ^ Vmax (3-14)
where vm]n is the minimum cutting speed and vmax is the maximum cutting speed.
The upper bound and the lower bound of radial rake angle must be in the range of,
Y m m < Y < Y m a x (3.15)
where is the minimum y min radial rake angle and is y max the maximum radial rake
angle.
For AWJ, there are five process parameters which are traverse cutting speed
(V), waterjet pressure (P), standoff distance (h), abrasive grit size (d), abrasive flow
rate (m). The minimum cutting speed ( V) value must be in the range determined by
minimum and maximum values of the cutting speed of AWJ.
Vmm < V < Vmax (3.16)
Where is the minimum cutting speed and Vmax is the maximum cutting speed.
The waterjet pressure (P), must meet the range of equation of 3.17.
P mill — P — P max (3.17)
where P mm is the minimum waterjet pressure and P max is the maximum waterjet
pressure.
The machining standoff distance range is given by equation (3.18),
h m ill — h < h max (3.18)
61
where h m]n is the minimum standoff distance and h max is the maximum standoff
distance.
The upper bound and lower bound of abrasive grit size (d) must be in the range of,
^n iin ^ d ̂ d max ( 3 - 1 9 )
where d mm is the minimum abrasive grit size and d max is the maximum grit size.
The upper bound and lower bound of abrasive flow rate are given in equation (3.20),
M mm — fx JTI max (3.20)
where m min is the minimum abrasive flow rate and m max is the maximum abrasive flow rate.
3.6 Validation and evaluation of ABC results
After the minimum Ra value is estimated based on the ABC optimization
algorithms, the results later will be validated and evaluated. The minimum Ra value
that estimated by ABC is optimistically a lesser amount of experimental, Regression
modelling, SA optimization and GA optimization. The equations in (3.13) to (3.15)
for end milling and equations (3.16) to (3.20) for AWJ that achieved at the last
iteration of ABC are preferred to be the range of values of the process parameters.
The values of the process parameters will lead to the minimal Ra value.
3.7 ABC optimization performances
ABC has been used recently by researchers to find optimal solution in
numeric optimizations problems. Some of the advantages of ABC algorithm include
strong robustness, fast convergence and high flexibility and employed less control
parameters. The performance of ABC is competitive with other algorithm such as
GA, PSO, DE and EA on many benchmark functions. The performance of ABC have
62
been assessed by Karaboga and Basturk (2008) to evaluate the performance of ABC
in optimizing the numerical benchmark function such as Schaffer, Sphere, Griewank,
Rastrigin and Rosenbrock. The results of ABC later is compared with differential
evaluation (DE), PSO, and evolutionary algorithms (EA). Table 3.9 below shows the
parameter values used in the experiments for each soft computing technique.
Table 3.9: Parameters used in the numerical benchmark function
experiments (Karaboga and Basturk, 2008)
Technique Parameters
1. DE i. Population size = 50ii. Crossover factor (CF) = 0.8iii. Scaling factor if) = 0.5
2. PSO i. Population size = 20ii. Inertia weight, (nr) = 1.0 —> 0.7iii. Lower bound of the random velocity rule weight, (cpmin) = 0iv. Upper bound of the random velocity rule weight, (cpmax) = 2.0
3. EA i. Population size =100ii. Crossover ratQ,p& =1.0iii. Mutation rate pm = 0.3iv. Mutation variance am = 0.01v. Elite size, n =10
4. ABC i. Colony size =100ii. Onlooker number, no = 50%iii. Employed bee number, no = 50%iv. Scout number, ns = 1v. Limit = «ex Dimension of the problem (D)
The experiments was repeated 30 times with different random seeds, and the
average function values of the best solutions found have been recorded as in Table
63
For Schaffer and Sphere numerical function, DE, EA and ABC could find the
optimum value but not PSO. For Griewank and Rastrigin function, DE and ABC
showed equal performance and found the optimum value but PSO and EA showed
the poorest results. For the Rosenbrock function, ABC gives the best optimum results
compared to the other four soft computing techniques.
The ABC algorithm is tested further to analyze its behavior under different
colony size which ranges from 10 to 100 and also the limit values for about 1000
iterations. From the results, as the population increases the algorithm produce better
results. As shown in Figure 3.2 below for Rosenbrock function, the optimum value
with 10 colony achieved is 9.2173464. The optimum value decrease to 0.159732
after the colony size increased to 50. The colony size is then increased to 100 and the
optimum value achieved for the function is 0.0852967. According to Karaboga and
Basturk, after a sufficient value for colony size, any increment in the value does not
improve the performance of the ABC algorithm.
Cyde
Figure 3.2 Evolution of mean best values for Rosenbrock function (Karaboga
and Basturk, 2008)
64
From the experiments, it shows that the performance of ABC is very good in
terms of the local and global optimization due to the stochastic selection schemes
employed and the neighbor production mechanism used (Karaboga and Basturk,
2008). They conclude that ABC is simple to use and robust optimization algorithm
and can be used efficiently in the optimization of multimodal and multi-variable
problems.
In this research, ABC was chosen as the optimization technique because of
some advantages it has compared to other optimization technique. For example, ABC
has less control parameters compared to other optimization techniques. ABC also
does not need a crossover operator like GA or DE. A simple operation based on
taking the difference of randomly determined parts of the parent and a randomly
chosen solution from the population is applied in ABC to produce a new solution
from its parent. This process increases the convergence speed of search into a local
minimum. In GA, DE and PSO the best solution found so far is always kept in the
population and it can be used for producing new solutions in the case of DE and GA,
new velocities in the case of PSO. However, in ABC, the best solution discovered so
far is not always held in the population since it might be replaced with a randomly
produced solution by a scout. For that reason, ABC produces superior results
compared to other optimization technique.
65
This chapter has discussed the methodology of the research. The process flow
and steps of searching the combination optimum process parameters that will lead to
minimum Ra are shown and further explained. The process flows consists of four
main phases. The first phases are the assessment of real experiments data based on
work by Mohruni (2008) for end milling and Caydas and Hascalik (2008) for AWJ.
In the second phase, the regression model is built and the best equation that gave
minimum Ra values will be selected and chosen as ABC fitness function. For the
third phase, ABC optimization algorithm will be used to find the best combination of
process parameters that give a minimum Ra value. Finally, the results will be
evaluated and compared with experimental, regression modelling, SA optimization
and GA optimization.
3.8 Summary
CHAPTER 4
ABC OPTIMIZATION
4.1 Introduction
The objective of this chapter is to describe the ABC optimization execution
and presents the experimental results of the study. In the previous chapter, the
methodology of the research has been discussed.
In this chapter, experiments for end milling and AWJ machining have been
conducted to find the minimum Ra value and the set of optimal process parameters
using ABC algorithm. There are four main phases in ABC optimization. These four
phases are discussed in details in the next section.
67
The execution process of ABC algorithm in optimizing process parameters of
Ra value in end milling and AWJ machining are divided into four main phases:
i. Initial phase
ii. Employed-bee phase
iii. Onlooker-bee phase
iv. Scout-bee phase.
The program is developed and run using MATLAB 2010 software. Figure 4.1 shows
the interface of the program. There are two objective functions that were used in
order to optimize the process parameters and find minimum Ra value in both end
milling and AWJ machining. For end milling, the objective function is:
Ra= 0.237 - 0.00175 jq+ 8.693 x2 + 0.00159 x3 (4.1)
where x\ is the cutting speed (v) in m/min, xn is the feed (f) in mm/tooth and X3 is the radial rake angle (y) in
For AWJ machining, the objective function is:
Ra = -5.07976 + 0.08169 xi + 0.07912 x2 - 0.34221 x3- 0.08661 x4- 0.34866 x5-
0.00031 x i2 - 0.00012 x2 2 + 0.10575 x3 2 + 0.00041 x4 2 + 0.07590 x5 2 - 0.00008 xi x5
- 0.00009 x2 X5 + 0.03089 X3 X5 + 0.00513 X4 X5 (4.2)
Where x\ is the traverse cutting speed (V) in mm/min, xi is the waterjet pressure (P)
in MPa, X3 is the standoff distance (h) in mm, X4 is the abrasive grit size (d) in jam
and lastly, X5 the abrasive flow rate (m) in g/s.
4.2 ABC optimization execution
68
Q Artificial Bee Algorithm Program
P r o c e s s P a r a m e t e r s O p t i m i z a t i o n o f S u r f a c e R o u g h n e s s i n E n d M i l l i n g a n d A b r a s i v e W a t e r j e t M a c h i n i n g
U s i n g A r t i f i c i a l B e e C o l o n y A l g o r i t h m
R r * = 0 . 2 3 7 — ( 0 . 0 0 1 7 5 x x l > + ( S . 6 9 3 x x 2 > + ( 0 . 0 0 1 5 9 x x 3 >
Min Value, Fitnes & Mean of Fitness/Cycle
1 r
0.9 -
0.8 -
0.7 -
0.6 -
0.5 -
0.4 -
0.3 -
0.2 -
0.1 -
0---------- 1---------- 1---------- 1---------- 1---------- 10 0.2 0.4 0.6 0.8 1
Function for: End Milling
Colony S ize :
Number of Run:
Max Cycles per Run :
Limit (abandoned food):
i— Parameters Range—
X1 X2 X3 X4 X5
Uppest Threshold:
Jl jE T 110
Lowest Threshold:
130 0.000375
All best valuesA'un
Num.Cycles MinValue X I
Ready
l° i Ii -I
Figure 4.1 ABC Matlab program interface
To find the optimal process parameters and minimum Ra values, both end
milling and AWJ have similar steps to be performed. The only difference is the
number of parameters to be optimized and the range of the process parameters. The
process parameters are referred to the threshold value for lower and upper
parameters. The upper threshold (UT) and lower threshold (LT) value for parameters
usually depends on the technical specification of the machining. The threshold range
value was taken from available reference and also based on previous experiments.
According to Zain et al. (2010a), there is no guideline yet given by the researchers
which could be followed in recommending the best combination for setting the value
of process parameters for the best optimal result.
69
In the experiments of both end milling and AWJ, ABC employed control parameters
are as follows:
i. Colony size refers to the number of bees in the colony (employed bees plus
onlooker bees).
ii. Limit where it controls of the number of trials to improve certain food source.
If a food source could not be improved within defined number of trial, it is
abandoned by its employed bee. In the ABC, the parameter limit is calculated
using the formula SN*D, where SN is the number of solutions and D is the
number of variables of the problem.
iii. Maximum Cycle per run defines the number of cycles for foraging. This is a
stopping criterion.
The problem specific parameters are:
i. Number of run defines the number of times to run the algorithm.
ii. Lower bound where it is the lower threshold (LT) value of problem
parameters.
iii. Upper bound where it is the upper threshold value (UT) of problem
parameters.
Each of the experiments has been repeated by 10 runs. It is important to note that
each run complete maximum cycle number. In the experiment, the values of
maximum cycle number and colony size tested were 10, 20, 50 and 100.
The UT and LT threshold value used for end milling in the experiments is as follows:
124.53m/min < x\ <167.03m/min (4.3)
0.025mm/tooth < x2< 0.083mm/tooth (4.4)
6.2 ° < x 3< 14.8° (4.5)
The UT and LT threshold value used for AWJ in the experiments is as follows:
50mm/min <x\ < 150 mm/m in (4.6)
125Mpa < x2 < 250Mpa (4.7)
1mm < X3 < 4mm (4.8)
60(j,m < X4 < 120(j,m (4.9)
0.5g/s < X5 < 3.5g/s (4.10)
The threshold value (upper and lower) for parameters which is set at initial (before
the program run) is affecting the result of ABC algorithm and the number of iteration
to be processed
71
The general pseudocode of ABC in optimizing process parameters of Ra in end
milling and AWJ machining:
Do Initial Step
{Define limit
Do initiate trial array = 0.
Do generate food matrix randomly which each value is within range UT and
LT.
Do calculate and get minimum objective value for food matrix.
Do calculate and get the best fitness value.
Do store first minimum value, best parameters pair value and fitness value.
}Iteration = 0.
While Iteration < maxCycle
Do Employed-bee Phase
{For i = 1 to number of food source
Determine randomly index of parameters ip) to be changed.
Determine randomly index of the value (z) to be changed.
Perform mutation for parameter P(i,z) and assign to new Solution
S (i,z).
Calculate S(/,z) = = S(/,z) + { (S(/,z)- S(/;,z))*random }.
Perform shift value in S(/',z) into between UT and LT.
Evaluate new Parameter S(/',z):
If it’s fitness value is better than P (i,z) then replace P (i,z) with
S (i,z) with greedy selection.
Reset trial (/) = 0.
Else increment trial (/).
End For
72
Do calculate probability.
}Do Onlooker-bee Phase
{Initiate control variable t = 0, iteration i = 0.
While t < number of food source
Generate random value rand.
If probability(7) > rand then: increment t and perform employed-bee
phase again.
Increment i
End While
Store the best parameters and minimum objective value to matrix Global
Parameters (GP) and Global Value (GV) respectively.
Do Scout-bee Phase
{For i = 1 to number of value in trial array
If trial (i) equal to limit then generate new parameters value randomly
and replace the old parameters value with the new one.
Calculate objective value and fitness value for current parameters.
EndFor
Find minimum value inside GV.
Find the best parameter inside GP, based on the minimum value inside GV.
Increment Iteration value.
End While
73
The details for each phases is given as the following four sections:
4.3 Initial phase
The initial phase is the first step before ABC algorithm is executed. The
purpose of this step is to initiate parameters and control variables. In this step, the
initial values of Food matrix (D x N matrix) is also generated, where D is the number
of parameters to be optimized and N is the number of food source, that is equal to
the number of employed or onlooker-bee, or equal to colony size. The food matrix is
a matrix of candidate of the best parameters. Each value in food matrix is in range
between LT and UT.
For example, assume that the food source is 10 then the food matrix for end
milling (three parameters) and AWJ (five parameters) are:
End Milling AWJ
X (l,l) X( 1,2) X(l,3) X (l,l) X(l,2) X(l,3) X(l,4) X(l,5) } Parameters pair
X(2,l) X(2,2) X(2,3) X(2,l) X(2,2) X(2,3) X(2,4) X(2,5)
X(3,l) X(3,2) X(3,3) X(3,l) X(3,2) X(3,3) X(3,4) X(3,5)
X(9,l) X(9,2) X(9,3) X(9,l) X(9,2) X(9,3) X(9,4) X(9,5)
X(10,l) X(10,2)X(10,3) X(10,l) X(10,2)X(10,3)X(10,4)X(10,5)
Where each row of the matrix is a parameters pair.
After the program initiates the food matrix, then it will begin to evaluate the
food matrix for the first time. The program calculates the objective value and the
fitness value for each pair (each row) of parameter in food matrix. Subsequently the
program “memorizes” the best one by storing the minimum objective value and the
74
best parameters value respectively in a matrix GV and GP. The program also initiates
values in trial array to 0. Trial array is an array that contains values to store how
many times unfit conditions is met during execution of ABC algorithm (if the food
source or the parameters pair cannot be optimized anymore, the program will
increment the corresponding trial value). The trial value next will be compared to a
local control variable called limit. And a variable called maxCycle is defined as a
global control variable, which determines maximum iteration that three ABC phases
(Employed-bee Phase, Onlooker-bee Phase and Scout-bee Phase) should run.
Hence, in this initial step, the program gets the first best parameters value
(that give the minimum objective value), the first minimum objective value and the
best fitness value.
4.4 Employed-bee Phase
In this phase, the program performs a mutation on each value in the food
matrix. If a pair of parameters (in which mutated value occurred) is giving the better
fitness value than the previous fitness value (before any value inside that parameters
pair is changed), then related value in this pair of parameter was changed by applying
a greedy algorithm.
The parameters pair which the value inside is being changed is called
solution. The new value is determined by using equation 5.3:
X(i,j) = X(i,j) + { (X(i,j) - X(p,j))*random } (5.3)
where p is the parameter pair index and determined randomly.
75
The next step is evaluating each parameter value inside the Solution. If the
value is below the LT then the program set the value to LT, and if the value is above
the UT then the program sets the value to UT. And then the program calculates the
objective value and the fitness value for this Solution.
i. If the fitness value of Solution is higher than the previous Fitness value
(before any value inside that parameters pair is changed), then replace the
parameters pair with the Solution. Reset the corresponding Trial value to
zero
ii. If the fitness value of Solution is lower than the previous Fitness value
(before any value inside that parameters pair is changed), then increment
the corresponding Trial value.
This process is repeated until the iteration equal to the number of food source.
When iteration is done, the program calculates the probabilities value by:
Probability (/) = Fitness (/) / sum(Fitness) (5.4)
In other words, the probability is the fitness of fitness value. This probability
value will be evaluated later in onlooker-bee phase.
4.5 Onlooker-bee Phase
In the Onlooker-bee phase, the mutation of value as in Employed-bee phase
above was repeated, but the difference is the control variables that determine what
condition the iteration should stop. The iteration will be stop if a control variable,
named T, and is equal to the number of food sources. The value of T is incremented
only if a value in probability array is higher than a random number.
76
At first time before the iteration run, T is initiated to 0. Then each probability
value is evaluated. Once the probability value P(/) (from Employed-bee phase) is
higher than a value (generated randomly), it is time to do mutation as in Employed-
bee phase and also increment T value. But if Probability P(/) value is lower the
random value, the evaluation is as follows:
i. next Probability value P(i+1), if i not equal the number of food sources
(indicates last index in Probability array)
ii. first Probability value P(z'), if i equal to the number of food source. If T is
equal to the number of food source then iteration is stopped. After the
iteration is stopped, the program will find the best of parameters value and
store in the matrix GV and GP.
4.6 Scout-bee Phase
This phase is the last step of ABC algorithm execution. In this phase, the
maximum value inside trial array was discovered. If it is bigger than limit, then the
program do initial step again for related parameter. For example, if the program find
trial (x) is bigger than limit (this means the parameter P(x) cannot be optimized
anymore) then the program will generate a new parameters pair P(£), and replace
P(x) with P(£) in food matrix, recalculate again objective and fitness value.
4.7 Experiment 1 - ABC optimization parameters for End Milling
For the experiments, a colony size of 10, 20, 50 and 100 have been tested in
the program to find the most minimum Ra value. The combination of control
variables with the bee colony size of 10 are shown in Table 4.1.
77
Table 4.1: Control variables combination with limit of 30
Colony Size Max cycles per run Limit (abandoned
food)
10 10 30
10 20 30
10 50 30
10 100 30
4.7.1 Colony size of 10 and limit of 30
The experiments initialize the control variables with a bee colony size of 10,
max cycles per run are 10 and limit is set to 30. The value of bee colony size and
max cycles per run will be increased to observe whether the minimum Ra value will
be improved.
When the program is executed, the results are depicted in Figure 4.2. The first
combination of control variables gives a minimum Ra value of 1.1719|am in the first
78
^ Artificial Bee Algorithm Program «=>'
P r o c e s s P a r a m e t e r s O p t i m i z a t i o n of S u r f a c e R o u g h n e s s i n E n d M i l l i n g a n d A b r a s i v e W a t e r j e t M a c h i n i n g
U s i n g A r t i f i c i a l B g g C o l o n y A l g o r i t h m
R a = 0.23-7 — (0.00 175 X x l ) + - (S.693 x x2) -+- (0.00159 X i3 )
Function for: End Milling
Colony S ize :
Number of Run:
Max Cycles per Run
Limit (abandoned food)
Parameters Range------
X1 X2 X3 X4 X5
Uppest Threshold:
167.03 1 0.083 14.B 120 , J }
________________Lowest Threshold :
124.53 0.025 6.2 | 60 || 0.5
All best values/run
run Num.Cycles , MinValue XI
1 10 j. 167.0301 >
2 10 0.4832 146.321:
3 10 0.2645 136.589: =
4 10 0.2080 146.3671
5 10 0.1786 167.0301
6 10 0.1932 155.552
7 10 0.1737 167.0301 -
1 1 nr j
I Sflow OlatlReady
0.9
0.8
0.7
0 . 6
0.4
0.3
0.2
0 1
Min Value, Fitnes & Mean of Fitness/Cycle
Best fitness
tMean fitness
■ Best Fitness- Mean Fitness- Min.Value
Min Ra value
3 4 5 6 7 Cycle
9 10
Figure 4.2 Results of 10 max cycles per run with limit of 30
From the results of the first control variables combinations, the set values of
process parameters that lead to the minimum values of Ra value are 167.0300 m/min
for cutting speed, 0.0250 mm/tooth for feed and 6.200 0 for radial rake angle. The
best fitness value is 0.8533. The minimum Ra value is achieved at cycle six as shown
in Table 4.2.
79
Table 4.2: The best value returned from 10 max cycles with limit of 30
Cycle Min Ra XI (v) X2 if) X3(y) Best
fitness
Mean
fitness
1 0.2232 167.0300 0.0307 7.5555 0.8175 0.6864
2 0.2230 167.0300 0.0307 7.4056 0.8177 0.7005
3 0.2230 167.0300 0.0307 7.4056 0.8177 0.7018
4 0.1738 167.0300 0.0250 7.4056 0.8519 0.7098
5 0.1738 167.0300 0.0250 7.4056 0.8519 0.7113
6 0.1719 167.0300 0.0250 6.2000 0.8533 0.7149
7 0.1719 167.0300 0.0250 6.2000 0.8533 0.7409
8 0.1719 167.0300 0.0250 6.2000 0.8533 0.7415
9 0.1719 167.0300 0.0250 6.2000 0.8533 0.7480
10 0.1719 167.0300 0.0250 6.2000 0.8533 0.7506
The second combination of control variables is tested where the number of max cycle
per run is increased to 20. The results are shown in the Figure 4.3. The minimum Ra
value achieved is 0.1719(j,m.
80
Artificial Bee Algorithm Progr; l— -i.
P r o c e s s P a r a m e t e r s O p t i m i z a t i o n of S u r f a c e R o u g h n e s s i n E n d M i l l i n g a n d A b r a s i v e W a t e r j e t M a c h i n i n g
U s i n g A r t i f i c i a l B e e C o l o n y A l g o r i t h m
R a = 0 237 — (0.00175 x icl) -+- (3 693 x x2) ■+■ (0.00 159 x tc3>
Function fo r: End Milling
Colony S ize :
Number of Run:
Max Cycles per Run:
Limit (abandoned food):
j— Parameters Range------
X1 X2 X3 X4 X5
Uppest Threshold
167.03 0.083 14 c 3.5
Lowest Threshold
124.53 0.025 6.2
All best valuesfrun
run Num.Cycles MinValue X I
1 20 0.1719 167.030( >
2 20 0.2094 148.21 S«
3 20 0.1914 160 556;
4 20 0.1719 167.0301
5 20 0.1843 159.918i
6 20 0.1741 167.030(7 r>n n i tjm ̂C7 mnr
- l i" Z] 1
Ready
Min Value, Fitnes A Mean of Fitness/Cycle
Figure 4.3 Results of 20 max cycles per run with limit of 30
In Table 4.3, the results of the second control variables combinations also
gives the best fitness value of 0.8533 at cycle six and the set values of process
parameters that lead to the minimum Ra value are 167.0300 m/min for cutting speed,
0.0250 mm/tooth for feed and 6.200 0 for radial rake angle.
81
Table 4.3: The best value returned from 20 max cycles per run with limit of 30
Cycle Min Ra XI (v) X2 if) X3(y) Best
fitness
Mean
fitness
1 0.2232 167.0300 0.0307 7.5555 0.8175 0.68642 0.2230 167.0300 0.0307 7.4056 0.8177 0.70053 0.2230 167.0300 0.0307 7.4056 0.8177 0.70184 0.1738 167.0300 0.0250 7.4056 0.8519 0.70985 0.1738 167.0300 0.0250 7.4056 0.8519 0.71136 0.1719 167.0300 0.0250 6.2000 0.8533 0.71497 0.1719 167.0300 0.0250 6.2000 0.8533 0.74098 0.1719 167.0300 0.0250 6.2000 0.8533 0.74159 0.1719 167.0300 0.0250 6.2000 0.8533 0.748010 0.1719 167.0300 0.0250 6.2000 0.8533 0.750611 0.1719 167.0300 0.0250 6.2000 0.8533 0.764212 0.1719 167.0300 0.0250 6.2000 0.8533 0.767813 0.1719 167.0300 0.0250 6.2000 0.8533 0.768814 0.1719 167.0300 0.0250 6.2000 0.8533 0.784615 0.1719 167.0300 0.0250 6.2000 0.8533 0.803216 0.1719 167.0300 0.0250 6.2000 0.8533 0.813017 0.1719 167.0300 0.0250 6.2000 0.8533 0.813018 0.1719 167.0300 0.0250 6.2000 0.8533 0.818419 0.1719 167.0300 0.0250 6.2000 0.8533 0.819320 0.1719 167.0300 0.0250 6.2000 0.8527 0.7895
Next, the value of max cycles per run is increased to 50. The results are
shown in Figure 4.4 where the minimum Ra value achieved is 0.1719|am in the first
82
S3 Artificial Bee Algorithm Progn ’ 'I---
P r o c e s s P a r a m e t e r s O p t i m i z a t i o n of S u r f a c e R o u g h n e s s in E n d M i l l i n g a n d A b r a s i v e W a t e r j e t M a c h i n i n g
U s i n g A r t i f i c i a l B e e C o l o n y A l g o r i t h m
R a = 0.237 — (0.00175 x x l ) -+- (3.693 x x2) (0.00159 X x3>
Function fo r : End Milling
Colony S ize :
Number of Run:
Max Cycles per Run
Limit (abandoned food):
I— Parameters Range------
X1 X2 X3
50
X4 X5
Uppest Threshold:
167.03 0.083 14.8 120 3.5
Lowest Threshold:
124.53 0 025 ' 6 ;
All best valuesAun
run Num.Cycles MinValue X I
1 50 0.1719 167.Q30( >
2 50 0.1719 167.Q3DI
3 50 0.1719 167.03014 50 0.1719 167.Q3DE
5 50 0.1730 166.3781
6 50 0.1719 167.030(7 m CM 7-1 0 ̂e? n n̂r
v III _1 t
| S to w Detail |
Ready
Min Value, Fitnes & Mean of Fitness/Cycle
Figure 4.4 Results of 50 max cycles per run with limit of 30
In Table 4.4, the results of the third control variables combinations also gives
the best fitness value of 0.8533 at cycle six and the set values of process parameters
that lead to the minimum Ra value are 167.0300 m/min for cutting speed, 0.0250
mm/tooth for feed and 6.200 0 for radial rake angle.
83
Table 4.4: The best value returned from 50 max cycles per run with limit of 30
Cycle Min Ra XI (v) X2 if) X3(y) Best
fitness
Mean
fitness
1 0.2232 167.0300 0.0307 7.5555 0.8175 0.68642 0.2230 167.0300 0.0307 7.4056 0.8177 0.70053 0.2230 167.0300 0.0307 7.4056 0.8177 0.70184 0.1738 167.0300 0.0250 7.4056 0.8519 0.70985 0.1738 167.0300 0.0250 7.4056 0.8519 0.71136 0.1719 167.0300 0.0250 6.2000 0.8533 0.71497 0.1719 167.0300 0.0250 6.2000 0.8533 0.74098 0.1719 167.0300 0.0250 6.2000 0.8533 0.74159 0.1719 167.0300 0.0250 6.2000 0.8533 0.748010 0.1719 167.0300 0.0250 6.2000 0.8533 0.750611 0.1719 167.0300 0.0250 6.2000 0.8533 0.764212 0.1719 167.0300 0.0250 6.2000 0.8533 0.767813 0.1719 167.0300 0.0250 6.2000 0.8533 0.768814 0.1719 167.0300 0.0250 6.2000 0.8533 0.784615 0.1719 167.0300 0.0250 6.2000 0.8533 0.803216 0.1719 167.0300 0.0250 6.2000 0.8533 0.813017 0.1719 167.0300 0.0250 6.2000 0.8533 0.813018 0.1719 167.0300 0.0250 6.2000 0.8533 0.818419 0.1719 167.0300 0.0250 6.2000 0.8533 0.819320 0.1719 167.0300 0.0250 6.2000 0.8527 0.789521 0.1719 167.0300 0.0250 6.2000 0.8527 0.792822 0.1719 167.0300 0.0250 6.2000 0.8527 0.793023 0.1719 167.0300 0.0250 6.2000 0.8527 0.798324 0.1719 167.0300 0.0250 6.2000 0.8527 0.802625 0.1719 167.0300 0.0250 6.2000 0.8527 0.813726 0.1719 167.0300 0.0250 6.2000 0.8529 0.815427 0.1719 167.0300 0.0250 6.2000 0.8533 0.821228 0.1719 167.0300 0.0250 6.2000 0.8533 0.821529 0.1719 167.0300 0.0250 6.2000 0.8533 0.8215
84
30 0.1719 167.0300 0.0250 6.2000 0.8533 0.822131 0.1719 167.0300 0.0250 6.2000 0.8533 0.822532 0.1719 167.0300 0.0250 6.2000 0.8533 0.826033 0.1719 167.0300 0.0250 6.2000 0.8533 0.829034 0.1719 167.0300 0.0250 6.2000 0.8533 0.829235 0.1719 167.0300 0.0250 6.2000 0.8533 0.829236 0.1719 167.0300 0.0250 6.2000 0.8533 0.833137 0.1719 167.0300 0.0250 6.2000 0.8533 0.833238 0.1719 167.0300 0.0250 6.2000 0.8533 0.835939 0.1719 167.0300 0.0250 6.2000 0.8533 0.839540 0.1719 167.0300 0.0250 6.2000 0.8533 0.839641 0.1719 167.0300 0.0250 6.2000 0.8533 0.841742 0.1719 167.0300 0.0250 6.2000 0.8533 0.842243 0.1719 167.0300 0.0250 6.2000 0.8533 0.803544 0.1719 167.0300 0.0250 6.2000 0.8533 0.804045 0.1719 167.0300 0.0250 6.2000 0.8533 0.809446 0.1719 167.0300 0.0250 6.2000 0.8533 0.812147 0.1719 167.0300 0.0250 6.2000 0.8533 0.812148 0.1719 167.0300 0.0250 6.2000 0.8533 0.820149 0.1719 167.0300 0.0250 6.2000 0.8533 0.822750 0.1719 167.0300 0.0250 6.2000 0.8533 0.8228
85
Finally, the number of max cycles per run is increased to 100. The results are
shown in Figure 4.5 where the minimum Ra value achieved is 0.1719|am in all 10
runs.
Artificial Bee Algorithm Progr; _____ 'P r o c e s s P a r a m e t e r s O p t i m i z a t i o n of S u r f a c e R o u g h n e s s i n E n d M i l l i n g a n d A b r a s i v e W a t e r j e t M a c h i n i n g
U s i n g A r t i f i c i a l B e e C o l o n y A l g o r i t h m
R a = 0.237 — (0.00175 x tc 1} -4- (3 693 x x2) •+■ (0.00159 x x3>
10
Function fo r: End Milling
Colony S ize :
Number of Run:
Max Cycles per Run:
Limit (abandoned food):
I— Parameters Range------
X1 X2 X3
30PUN
X4 X5
Uppest Threshold:
167 03 0.083 14 8 3.5
Lowest Threshold:
124.53 0.025 6 2 \
All best valuesAun
run Num.Cycles MinValue X I
1 100 0.1719 167.030( *
2 100 0.1719 167.0301
3 100 0.1719 167.0301
4 100 0.1719 167.030E
5 100 0.1719 167.030(
6 100 0.1719 167.030(7 inn fH71Q a err mnr
< | m Z l r
i 1 i
Ready
Min Value, Fitnes & Mean of Fitness/Cycle
Cycle
Figure 4.5 Results of 100 max cycles per run with limit of 30
The results of the last control variables combinations also gives the best
fitness value of 0.8533 at cycle six and the set values of process parameters that lead
to the minimum Ra value are 167.0300 m/min for cutting speed, 0.0250 mm/tooth for
feed and 6.200 0 for radial rake angle. This is shown in Table 4.5.
86
Table 4.5: The best value returned from 100 max cycles per run with limit of 30
Cycle Min Ra XI (v) X2 if) X3(y) Best
fitness
Mean
fitness
1 0.2232 167.0300 0.0307 7.5555 0.8175 0.68642 0.2230 167.0300 0.0307 7.4056 0.8177 0.70053 0.2230 167.0300 0.0307 7.4056 0.8177 0.70184 0.1738 167.0300 0.0250 7.4056 0.8519 0.70985 0.1738 167.0300 0.0250 7.4056 0.8519 0.71136 0.1719 167.0300 0.0250 6.2000 0.8533 0.71497 0.1719 167.0300 0.0250 6.2000 0.8533 0.74098 0.1719 167.0300 0.0250 6.2000 0.8533 0.74159 0.1719 167.0300 0.0250 6.2000 0.8533 0.748010 0.1719 167.0300 0.0250 6.2000 0.8533 0.750611 0.1719 167.0300 0.0250 6.2000 0.8533 0.764212 0.1719 167.0300 0.0250 6.2000 0.8533 0.767813 0.1719 167.0300 0.0250 6.2000 0.8533 0.768814 0.1719 167.0300 0.0250 6.2000 0.8533 0.784615 0.1719 167.0300 0.0250 6.2000 0.8533 0.803216 0.1719 167.0300 0.0250 6.2000 0.8533 0.813017 0.1719 167.0300 0.0250 6.2000 0.8533 0.813018 0.1719 167.0300 0.0250 6.2000 0.8533 0.818419 0.1719 167.0300 0.0250 6.2000 0.8533 0.819320 0.1719 167.0300 0.0250 6.2000 0.8527 0.789521 0.1719 167.0300 0.0250 6.2000 0.8527 0.792822 0.1719 167.0300 0.0250 6.2000 0.8527 0.793023 0.1719 167.0300 0.0250 6.2000 0.8527 0.798324 0.1719 167.0300 0.0250 6.2000 0.8527 0.802625 0.1719 167.0300 0.0250 6.2000 0.8527 0.813726 0.1719 167.0300 0.0250 6.2000 0.8529 0.815427 0.1719 167.0300 0.0250 6.2000 0.8533 0.821228 0.1719 167.0300 0.0250 6.2000 0.8533 0.821529 0.1719 167.0300 0.0250 6.2000 0.8533 0.8215
87
30 0.1719 167.0300 0.0250 6.2000 0.8533 0.822131 0.1719 167.0300 0.0250 6.2000 0.8533 0.822532 0.1719 167.0300 0.0250 6.2000 0.8533 0.826033 0.1719 167.0300 0.0250 6.2000 0.8533 0.829034 0.1719 167.0300 0.0250 6.2000 0.8533 0.829235 0.1719 167.0300 0.0250 6.2000 0.8533 0.829236 0.1719 167.0300 0.0250 6.2000 0.8533 0.833137 0.1719 167.0300 0.0250 6.2000 0.8533 0.833238 0.1719 167.0300 0.0250 6.2000 0.8533 0.835939 0.1719 167.0300 0.0250 6.2000 0.8533 0.839540 0.1719 167.0300 0.0250 6.2000 0.8533 0.839641 0.1719 167.0300 0.0250 6.2000 0.8533 0.841742 0.1719 167.0300 0.0250 6.2000 0.8533 0.842243 0.1719 167.0300 0.0250 6.2000 0.8533 0.803544 0.1719 167.0300 0.0250 6.2000 0.8533 0.804045 0.1719 167.0300 0.0250 6.2000 0.8533 0.809446 0.1719 167.0300 0.0250 6.2000 0.8533 0.812147 0.1719 167.0300 0.0250 6.2000 0.8533 0.812148 0.1719 167.0300 0.0250 6.2000 0.8533 0.820149 0.1719 167.0300 0.0250 6.2000 0.8533 0.822750 0.1719 167.0300 0.0250 6.2000 0.8533 0.822851 0.1719 167.0300 0.0250 6.2000 0.8533 0.824252 0.1719 167.0300 0.0250 6.2000 0.8533 0.824353 0.1719 167.0300 0.0250 6.2000 0.8533 0.824354 0.1719 167.0300 0.0250 6.2000 0.8533 0.829755 0.1719 167.0300 0.0250 6.2000 0.8533 0.830356 0.1719 167.0300 0.0250 6.2000 0.8533 0.830357 0.1719 167.0300 0.0250 6.2000 0.8533 0.809658 0.1719 167.0300 0.0250 6.2000 0.8533 0.810259 0.1719 167.0300 0.0250 6.2000 0.8533 0.810260 0.1719 167.0300 0.0250 6.2000 0.8533 0.810761 0.1719 167.0300 0.0250 6.2000 0.8533 0.780862 0.1719 167.0300 0.0250 6.2000 0.8533 0.7533
88
63 0.1719 167.0300 0.0250 6.2000 0.8533 0.756364 0.1719 167.0300 0.0250 6.2000 0.8533 0.765965 0.1719 167.0300 0.0250 6.2000 0.8533 0.767366 0.1719 167.0300 0.0250 6.2000 0.8533 0.769067 0.1719 167.0300 0.0250 6.2000 0.8533 0.769668 0.1719 167.0300 0.0250 6.2000 0.8533 0.780169 0.1719 167.0300 0.0250 6.2000 0.8533 0.789670 0.1719 167.0300 0.0250 6.2000 0.8113 0.769871 0.1719 167.0300 0.0250 6.2000 0.8186 0.761172 0.1719 167.0300 0.0250 6.2000 0.8288 0.768673 0.1719 167.0300 0.0250 6.2000 0.8288 0.774374 0.1719 167.0300 0.0250 6.2000 0.8460 0.782675 0.1719 167.0300 0.0250 6.2000 0.8481 0.783076 0.1719 167.0300 0.0250 6.2000 0.8481 0.797377 0.1719 167.0300 0.0250 6.2000 0.8483 0.805978 0.1719 167.0300 0.0250 6.2000 0.8488 0.813279 0.1719 167.0300 0.0250 6.2000 0.8488 0.813880 0.1719 167.0300 0.0250 6.2000 0.8490 0.816481 0.1719 167.0300 0.0250 6.2000 0.8511 0.817082 0.1719 167.0300 0.0250 6.2000 0.8528 0.819483 0.1719 167.0300 0.0250 6.2000 0.8528 0.820584 0.1719 167.0300 0.0250 6.2000 0.8530 0.821485 0.1719 167.0300 0.0250 6.2000 0.8530 0.825386 0.1719 167.0300 0.0250 6.2000 0.8532 0.827387 0.1719 167.0300 0.0250 6.2000 0.8533 0.827888 0.1719 167.0300 0.0250 6.2000 0.8533 0.831189 0.1719 167.0300 0.0250 6.2000 0.8533 0.834190 0.1719 167.0300 0.0250 6.2000 0.8533 0.836891 0.1719 167.0300 0.0250 6.2000 0.8533 0.838592 0.1719 167.0300 0.0250 6.2000 0.8533 0.839293 0.1719 167.0300 0.0250 6.2000 0.8533 0.839594 0.1719 167.0300 0.0250 6.2000 0.8533 0.842395 0.1719 167.0300 0.0250 6.2000 0.8533 0.8432
89
96 0.1719 167.0300 0.0250 6.2000 0.8533 0.843297 0.1719 167.0300 0.0250 6.2000 0.8533 0.845098 0.1719 167.0300 0.0250 6.2000 0.8533 0.845399 0.1719 167.0300 0.0250 6.2000 0.8533 0.8453100 0.1719 167.0300 0.0250 6.2000 0.8533 0.8455
90
4.7.2 Colony size of 20 and limit of 60
The number of bee colony size is increased to 20 with limit of 60 to
investigate whether it will give superior results from the previous size of bee colony.
The combination of control variables are given in Table 4.6 below.
Table 4.6: Control variables combination with limit of 60
Colony Size Max cycles per
run
Limit (abandoned
food)
20 10 60
20 20 60
20 50 60
20 100 60
When the program is executed using the first control variables combination,
the minimum Ra value achieved is 1.725jam. This is the minimum Ra value from the
10 runs as shown in the Figure 4.6.
91
P 3 Artificial Bee Algorithm Program
P r o c e s s P a r a m e t e r s O p t i m i z a t i o n of S u r f a c e R o u g h n e s s in E n d M i l l i n g a n d A b r a s i v e W a t e r j e t M a c h i n i n g
U s i n g A r t i f i c i a l B e e C o l o n y A l g o r i t h m
R a = 0.237 — (0.00175 x x l ) -+- (3.693 x x2) -+- (0.00159 x x3)
Function fo r : End Milling
Colony S ize : 20
Number of Run: 10
Max Cycles per Run :— RUN
Limit (abandoned food): 60
I— Parameters Range------
X1 X2 X3 X4 X5
Uppest Threshold:
167.03 0.083 I 14.8 120 || 3.5
Lowest Threshold:
| 124.53 |f 0.025 | 6.2 |
All best valuesAun
run Num. Cycles MinValue X I* * ■ . M
5 10 0.1816 167.030(
6 10 Q.1725 167.030(
7 10 0.2036 155.623: —
8 10 0.1792 163.588? =9 10 0.1781 167.0301
10 10 0.1994 151.411' -
< III □ 1
|Sftow Detail |
Ready
10
Min Value, Fitnes & Mean of Fitness/Cycle
Cycle
Figure 4.6 Results of 10 max cycles per run with limit of 60
From Table 4.7, the minimum Ra value achieved is 0.1725(j,m at cycle 10.
The best fitness value is 0.8529 and the set values of process parameters that lead to
the minimum Ra value are 167.0300 m/min for cutting speed, 0.0250 mm/tooth for
feed and 6.5963 0 for radial rake angle.
92
Table 4.7: The best value returned from 10 max cycles per run with limit of 60
Cycle Min Ra XI (v) X2 if) X3(y) Best
fitness
Mean
fitness
1 0.2132 161.4920 0.0286 6.5213 0.8242 0.75052 0.2072 153.2815 0.0250 13.2790 0.8284 0.75653 0.2011 167.0178 0.0284 6.2000 0.8326 0.76064 0.1746 167.0300 0.0250 7.9207 0.8513 0.77225 0.1746 167.0300 0.0250 7.9207 0.8513 0.77316 0.1746 167.0300 0.0250 7.9207 0.8513 0.78177 0.1745 167.0300 0.0250 7.8760 0.8514 0.78288 0.1745 167.0300 0.0250 7.8760 0.8514 0.78409 0.1739 167.0300 0.0250 7.4603 0.8519 0.785810 0.1725 167.0300 0.0250 6.5963 0.8529 0.7914
The max per cycle per run is increased to 20 and the results are better
compared to the previous control variables combination. Figure 4.7 shows that the
minimum Ra value was achieved at the seventh runs.
93
r a Artificial Bee Algorithm Progr;
P r o c e s s P a r a m e t e r s O p t i m i z a t i o n of S u r f a c e R o u g h n e s s i n E n d M i l l i n g a n d A b r a s i v e W a t e r j e t M a c h i n i n g
U s i n g A r t i f i c i a l B e e C o l o n y A l g o r i t h m
R a = 0 237 — (0.00 175 x x l ) -+- (3 693 x x2) -+- (0.00 159 x x3>
20
Function fo r: End Milling
Colony S ize :
Number of Run:
Max Cycles per Run:
Limit (abandoned food):
j— Parameters Range------
X1 X2 X3 X4 X5
Uppest Threshold
167.03 0.083 14 8 3.5
124.53 0.025 6.2
Lowest Threshold
I 0 5All best valuesAun
run Num.Cycles MinValue X IAw u ■1 “■1 1 Jl .WW 1
5 20 0.1754 165.044:
6 20 0.1806 162.073J
7 20 □ .1719 167.030(
8 20 0.1719 167.030t
9 20 0.1719 167.030(
10 20 0.1719 167.030( -< | It! 2 »
Ready
Min Value, Fitnes A Mean of Fitness/Cycle
C yc le
Figure 4.7 Results of 20 max cycles per run with limit of 60
From Table 4.8 below, the minimum Ra value is achieved at cycle 11 with the
best fitness value of 0.8533. The set values of process parameters that lead to the
minimum Ra value are 167.0300 m/min for cutting speed, 0.0250 mm/tooth for feed
and 6.200 0 for radial rake angle.
94
Table 4.8: The best value returned from 20 max cycles per run with limit of
Cycle Min Ra XI (v) X2 if) X3(y) Best
fitness
Mean
fitness
1 0.2298 137.1148 0.0250 9.6827 0.8132 0.71652 0.2298 137.1148 0.0250 9.6827 0.8132 0.72293 0.2057 150.8473 0.0250 9.6827 0.8294 0.73114 0.1806 165.2712 0.0250 9.7294 0.8470 0.74805 0.1805 165.2712 0.0250 9.7159 0.8471 0.74916 0.1805 165.2712 0.0250 9.7159 0.8471 0.75277 0.1805 165.2712 0.0250 9.7159 0.8471 0.75818 0.1781 165.2712 0.0250 8.1505 0.8489 0.76649 0.1778 165.2712 0.0250 7.9602 0.8491 0.773310 0.1775 165.2712 0.0250 7.8255 0.8492 0.775811 0.1719 167.0300 0.0250 6.2000 0.8533 0.778312 0.1719 167.0300 0.0250 6.2000 0.8533 0.782613 0.1719 167.0300 0.0250 6.2000 0.8533 0.788414 0.1719 167.0300 0.0250 6.2000 0.8533 0.795715 0.1719 167.0300 0.0250 6.2000 0.8533 0.797116 0.1719 167.0300 0.0250 6.2000 0.8533 0.798817 0.1719 167.0300 0.0250 6.2000 0.8533 0.799118 0.1719 167.0300 0.0250 6.2000 0.8533 0.800019 0.1719 167.0300 0.0250 6.2000 0.8533 0.800320 0.1719 167.0300 0.0250 6.2000 0.8533 0.8016
95
The number of max cycles per run is then increased to 50 and the results are
shown in Figure 4.8. The minimum Ra value achieved is 0.1719|am at all 10 runs.
H Artificial Bee Algorithm Progn
P r o c e s s P a r a m e t e r s O p t i m i z a t i o n of S u r f a c e R o u g h n e s s i n E n d M i l l i n g a n d A b r a s i v e W a t e r j e t M a c h i n i n g
U s i n g A r t i f i c i a l B e e C o l o n y A l g o r i t h m
R a = 0.237 — (0.00175 x x l ) > (S.693 x x2) -+- (0.00159 X x3>
Function fo r:
Colony S ize :
Number of Run:
Max Cycles per Run :
Limit (abandoned food):
p— Parameters Range —
X1 X2
End Milling
X3 X4 X5
Uppest Threshold:
167.03 0.083 14.8 3.5
Lowest Threshold
124.53 0.025 6.2
All best valuesA'un
run Num.Cycle; MinValue X I
5 50 0.1719 167.030( +
6 50 0.1719 167.03Q(
7 50 0.1719 167.030(
8 50 0.1719 167 0301
9 50 0.1719 167.030(
10 50 0.1719 167.0301 -* 1 rer 1
Ready
Min Value, Fitnes & Mean of Fitness/Cycle
Figure 5.8 Results of 50 max cycles per run with limit of 60
In Table 4.9, the minimum Ra value is achieved at cycle 10 with the best
fitness value of 0.8533. The set values of process parameters that lead to the
minimum Ra value are 167.0300 m/min for cutting speed, 0.0250 mm/tooth for feed
and 6.200 0 for radial rake angle.
96
Table 4.9: The best value returned from 50 max cycles per run with limit of 60
Cycle Min Ra XI (v) X2 if) X3(y) Best
fitness
Mean
fitness
1 0.1865 163.5834 0.0250 11.5787 0.8428 0.71902 0.1860 163.8355 0.0250 11.5787 0.8432 0.72143 0.1761 167.0300 0.0253 7.1985 0.8502 0.73624 0.1761 167.0300 0.0253 7.1985 0.8502 0.74155 0.1754 167.0300 0.0253 6.7027 0.8508 0.75006 0.1746 167.0300 0.0253 6.2000 0.8514 0.75627 0.1746 167.0300 0.0253 6.2000 0.8514 0.75698 0.1746 167.0300 0.0253 6.2000 0.8514 0.75909 0.1746 167.0300 0.0253 6.2000 0.8514 0.760810 0.1719 167.0300 0.0250 6.2000 0.8533 0.769711 0.1719 167.0300 0.0250 6.2000 0.8533 0.774212 0.1719 167.0300 0.0250 6.2000 0.8533 0.778413 0.1719 167.0300 0.0250 6.2000 0.8533 0.779014 0.1719 167.0300 0.0250 6.2000 0.8533 0.787115 0.1719 167.0300 0.0250 6.2000 0.8533 0.788816 0.1719 167.0300 0.0250 6.2000 0.8533 0.791917 0.1719 167.0300 0.0250 6.2000 0.8533 0.796418 0.1719 167.0300 0.0250 6.2000 0.8533 0.798619 0.1719 167.0300 0.0250 6.2000 0.8533 0.804420 0.1719 167.0300 0.0250 6.2000 0.8533 0.805221 0.1719 167.0300 0.0250 6.2000 0.8533 0.808822 0.1719 167.0300 0.0250 6.2000 0.8533 0.810623 0.1719 167.0300 0.0250 6.2000 0.8533 0.812824 0.1719 167.0300 0.0250 6.2000 0.8533 0.813025 0.1719 167.0300 0.0250 6.2000 0.8533 0.815926 0.1719 167.0300 0.0250 6.2000 0.8533 0.818927 0.1719 167.0300 0.0250 6.2000 0.8533 0.819928 0.1719 167.0300 0.0250 6.2000 0.8533 0.821629 0.1719 167.0300 0.0250 6.2000 0.8533 0.8217
97
30 0.1719 167.0300 0.0250 6.2000 0.8533 0.828131 0.1719 167.0300 0.0250 6.2000 0.8533 0.830332 0.1719 167.0300 0.0250 6.2000 0.8533 0.830633 0.1719 167.0300 0.0250 6.2000 0.8533 0.831634 0.1719 167.0300 0.0250 6.2000 0.8533 0.834335 0.1719 167.0300 0.0250 6.2000 0.8533 0.834436 0.1719 167.0300 0.0250 6.2000 0.8533 0.836237 0.1719 167.0300 0.0250 6.2000 0.8533 0.837838 0.1719 167.0300 0.0250 6.2000 0.8533 0.837839 0.1719 167.0300 0.0250 6.2000 0.8533 0.839240 0.1719 167.0300 0.0250 6.2000 0.8533 0.839741 0.1719 167.0300 0.0250 6.2000 0.8533 0.840442 0.1719 167.0300 0.0250 6.2000 0.8533 0.840643 0.1719 167.0300 0.0250 6.2000 0.8533 0.815144 0.1719 167.0300 0.0250 6.2000 0.8533 0.815845 0.1719 167.0300 0.0250 6.2000 0.8533 0.816446 0.1719 167.0300 0.0250 6.2000 0.8533 0.817847 0.1719 167.0300 0.0250 6.2000 0.8533 0.819848 0.1719 167.0300 0.0250 6.2000 0.8533 0.822649 0.1719 167.0300 0.0250 6.2000 0.8533 0.822950 0.1719 167.0300 0.0250 6.2000 0.8533 0.8313
98
Lastly for limit of 60, the max cycles per run is increased to 100. The results
are shown in the Figure 4.9 below. The minimum Ra value achieved is 0.1719|am at
all 10 runs.
Artific ia l Bee A lgorithm Progr<
P r o c e s s P a r a m e t e r s O p t i m i z a t i o n o f S u r f a c e R o u g h n e s s i n E n d M i l l i n g a n d A b r a s i v e W a t e r j e t M a c h i n i n g
U s i n g A r t i f i c i a l B e e C o l o n y A l g o r i t h m
Ra = 0.237 — (0.00175 x x l) -4- (3 693 x x2) + (0.00159 x tc3>
10
Function fo r: End Milling
Colony S iz e :
Number of R un:
Max Cycles per R un:
Limit (abandoned fo od):
I— Parameters Range--------
X1 X2 X3
PUN
X4 X5
Uppest Threshold:
167 03 0.083 14 8 3.5
124.53 0.025
Lowest Threshold:
1 60 I 05All best valuesAun
run N u m .C yc le s M in V a lu e X I
5 100 0.1719 167.030(*
6 100 □ .1719 167.030(
7 100 0.1719 167.030(
8 100 0.1719 167.030E T9 100 0.1719 167.0301
10 100 0.1719 167.030( -4 L Kl t
Ready
Min Value, Fitnes & Mean of Fitness/Cycle
Figure 4.9 Results of 100 max cycles per run with limit of 60
The best returned value of 100 max cycles per runs is achieved at the sixth
runs. In Table 4.10 below, the minimum Ra value of 0 .17 19|am is achieved at cycle
four with the best fitness value of 0.8532. The set values of process parameters that
lead to the minimum Ra value are 167.0300 m/min for cutting speed, 0.0250
mm/tooth for feed and 6.200 0 for radial rake angle.
99
Table 4.10: The best value returned from 100 max cycles per run with limit of 60
Cycle Min Ra XI (v) X2 if) X3(y) Best
fitness
Mean
fitness
1 0.2436 167.0300 0.0331 6.7848 0.8041 0.68902 0.1721 167.0300 0.0250 6.3459 0.8532 0.70093 0.1721 167.0300 0.0250 6.3459 0.8532 0.70564 0.1719 167.0300 0.0250 6.2000 0.8533 0.71555 0.1719 167.0300 0.0250 6.2000 0.8533 0.71876 0.1719 167.0300 0.0250 6.2000 0.8533 0.72657 0.1719 167.0300 0.0250 6.2000 0.8533 0.72818 0.1719 167.0300 0.0250 6.2000 0.8533 0.73449 0.1719 167.0300 0.0250 6.2000 0.8533 0.735310 0.1719 167.0300 0.0250 6.2000 0.8533 0.738411 0.1719 167.0300 0.0250 6.2000 0.8533 0.747512 0.1719 167.0300 0.0250 6.2000 0.8533 0.749513 0.1719 167.0300 0.0250 6.2000 0.8533 0.750714 0.1719 167.0300 0.0250 6.2000 0.8533 0.752215 0.1719 167.0300 0.0250 6.2000 0.8533 0.759316 0.1719 167.0300 0.0250 6.2000 0.8533 0.766217 0.1719 167.0300 0.0250 6.2000 0.8533 0.772418 0.1719 167.0300 0.0250 6.2000 0.8533 0.774419 0.1719 167.0300 0.0250 6.2000 0.8533 0.775220 0.1719 167.0300 0.0250 6.2000 0.8533 0.783221 0.1719 167.0300 0.0250 6.2000 0.8533 0.783722 0.1719 167.0300 0.0250 6.2000 0.8533 0.785823 0.1719 167.0300 0.0250 6.2000 0.8533 0.785824 0.1719 167.0300 0.0250 6.2000 0.8533 0.788625 0.1719 167.0300 0.0250 6.2000 0.8533 0.792426 0.1719 167.0300 0.0250 6.2000 0.8533 0.797027 0.1719 167.0300 0.0250 6.2000 0.8533 0.797628 0.1719 167.0300 0.0250 6.2000 0.8533 0.801429 0.1719 167.0300 0.0250 6.2000 0.8533 0.8040
10 0
30 0.1719 167.0300 0.0250 6.2000 0.8533 0.804231 0.1719 167.0300 0.0250 6.2000 0.8533 0.808432 0.1719 167.0300 0.0250 6.2000 0.8533 0.808833 0.1719 167.0300 0.0250 6.2000 0.8533 0.811334 0.1719 167.0300 0.0250 6.2000 0.8533 0.813435 0.1719 167.0300 0.0250 6.2000 0.8533 0.814436 0.1719 167.0300 0.0250 6.2000 0.8533 0.821337 0.1719 167.0300 0.0250 6.2000 0.8533 0.822838 0.1719 167.0300 0.0250 6.2000 0.8533 0.823639 0.1719 167.0300 0.0250 6.2000 0.8533 0.826140 0.1719 167.0300 0.0250 6.2000 0.8533 0.826941 0.1719 167.0300 0.0250 6.2000 0.8533 0.829842 0.1719 167.0300 0.0250 6.2000 0.8533 0.830143 0.1719 167.0300 0.0250 6.2000 0.8533 0.830344 0.1719 167.0300 0.0250 6.2000 0.8533 0.831145 0.1719 167.0300 0.0250 6.2000 0.8533 0.831346 0.1719 167.0300 0.0250 6.2000 0.8533 0.833147 0.1719 167.0300 0.0250 6.2000 0.8533 0.833148 0.1719 167.0300 0.0250 6.2000 0.8533 0.834649 0.1719 167.0300 0.0250 6.2000 0.8533 0.835750 0.1719 167.0300 0.0250 6.2000 0.8533 0.835851 0.1719 167.0300 0.0250 6.2000 0.8533 0.836052 0.1719 167.0300 0.0250 6.2000 0.8533 0.840353 0.1719 167.0300 0.0250 6.2000 0.8533 0.824354 0.1719 167.0300 0.0250 6.2000 0.8533 0.826755 0.1719 167.0300 0.0250 6.2000 0.8533 0.826856 0.1719 167.0300 0.0250 6.2000 0.8533 0.827357 0.1719 167.0300 0.0250 6.2000 0.8533 0.828258 0.1719 167.0300 0.0250 6.2000 0.8533 0.829959 0.1719 167.0300 0.0250 6.2000 0.8533 0.831360 0.1719 167.0300 0.0250 6.2000 0.8533 0.833961 0.1719 167.0300 0.0250 6.2000 0.8533 0.834862 0.1719 167.0300 0.0250 6.2000 0.8533 0.8350
101
63 0.1719 167.0300 0.0250 6.2000 0.8533 0.835664 0.1719 167.0300 0.0250 6.2000 0.8533 0.841065 0.1719 167.0300 0.0250 6.2000 0.8533 0.841466 0.1719 167.0300 0.0250 6.2000 0.8533 0.841567 0.1719 167.0300 0.0250 6.2000 0.8533 0.841768 0.1719 167.0300 0.0250 6.2000 0.8533 0.841869 0.1719 167.0300 0.0250 6.2000 0.8533 0.841970 0.1719 167.0300 0.0250 6.2000 0.8533 0.842171 0.1719 167.0300 0.0250 6.2000 0.8533 0.844872 0.1719 167.0300 0.0250 6.2000 0.8533 0.845173 0.1719 167.0300 0.0250 6.2000 0.8533 0.848174 0.1719 167.0300 0.0250 6.2000 0.8533 0.848475 0.1719 167.0300 0.0250 6.2000 0.8533 0.848476 0.1719 167.0300 0.0250 6.2000 0.8533 0.848677 0.1719 167.0300 0.0250 6.2000 0.8533 0.848878 0.1719 167.0300 0.0250 6.2000 0.8533 0.823379 0.1719 167.0300 0.0250 6.2000 0.8533 0.831580 0.1719 167.0300 0.0250 6.2000 0.8533 0.845881 0.1719 167.0300 0.0250 6.2000 0.8533 0.833182 0.1719 167.0300 0.0250 6.2000 0.8533 0.833683 0.1719 167.0300 0.0250 6.2000 0.8533 0.829484 0.1719 167.0300 0.0250 6.2000 0.8533 0.830185 0.1719 167.0300 0.0250 6.2000 0.8533 0.831186 0.1719 167.0300 0.0250 6.2000 0.8533 0.832187 0.1719 167.0300 0.0250 6.2000 0.8533 0.834088 0.1719 167.0300 0.0250 6.2000 0.8533 0.837389 0.1719 167.0300 0.0250 6.2000 0.8533 0.839190 0.1719 167.0300 0.0250 6.2000 0.8533 0.840191 0.1719 167.0300 0.0250 6.2000 0.8533 0.844392 0.1719 167.0300 0.0250 6.2000 0.8533 0.828793 0.1719 167.0300 0.0250 6.2000 0.8533 0.833994 0.1719 167.0300 0.0250 6.2000 0.8533 0.833995 0.1719 167.0300 0.0250 6.2000 0.8533 0.8352
10 2
96 0.1719 167.0300 0.0250 6.2000 0.8533 0.835997 0.1719 167.0300 0.0250 6.2000 0.8533 0.811098 0.1719 167.0300 0.0250 6.2000 0.8533 0.811199 0.1719 167.0300 0.0250 6.2000 0.8533 0.8128100 0.1719 167.0300 0.0250 6.2000 0.8533 0.8155
103
The bee colony size is increased to 50 with the limit of 150 to examine
whether it will improve the results from the bee colony size of 10 and 20. The control
variables combination for the experiments are shown in Table 4.11
Table 4.11: Control variables combination with limit of 150
4.7.3 Colony size of 50 and limit of 150
Colony Size Max cycles per
run
Limit (abandoned
food)
50 10 150
50 20 150
50 50 150
50 100 150
104
In Figure 4.10, the experimental results showed that the minimum Ra value achieved
is 0.1719|am in the sixth and tenth runs only.
H Artific ia l Bee A lgorithm Progn
P r o c e s s P a r a m e t e r s O p t i m i z a t i o n o f S u r f a c e R o u g h n e s s i n E n d M i l l i n g a n d A b r a s i v e W a t e r j e t M a c h i n i n g
U s i n g A r t i f i c i a l B e e C o l o n y A l g o r i t h m
Ra = 0.237 — (0.00 175 x x l) -»- (3.693 x x 2 ) ■+• (0.00 159 x x3)
Function fo r: End Milling
Colony S iz e :
Number of R un:
Max Cycles per R un:
Limit (abandoned fo od):
I— Parameters Range-------
X1 X2 X3
150
X4 X5
Uppest Threshold:
167 03 0 003 14 8 3.5
Lowest Threshold:
124.53 0.025 6 J || USAll best values/run
run N u m .C yc le ? M in V a lu e X I
1 10 0.1729 167.030( *2 10 0.1741 167.030E
3 10 0.1765 167.0301
4 10 0.1737 167.030E
5 10 0.1739 167.030(
6 10 0.1719 167.030(7 AH n 1 QCG A CQ oi ns
4 | m r
" js ih o w D e ta i l
Ready
0 9
0.8
0 7
3 0 5 a>04
0 3
02
0 1
Min Value, Fitnes & Mean of Fitness/Cycle
_l_________l_
Best fitness
Mean fitness
Min R„ value
5 6 Cycle
0
Figure 4.10 Results of 10 max cycles per run with limit of 150
From the results, the sixth runs give the best value returned from 10 max
cycles per run. The set values of process parameters that lead to the minimum Ra
value are 167.0300 m/min for cutting speed, 0.0250 mm/tooth for feed and 6.200 0
for radial rake angle. The minimum Ra value of 0.1719(_im is achieved at cycle 9 with
the best fitness value of 0.8533. This is shown in Table 4.12.
105
Table 4.12: The best value returned from 10 max cycles per run with limit of 150
Cycle Min Ra XI (v) X2 if) X3(y) Best
fitness
Mean
fitness
1 0.1730 167.0110 0.0250 6.8994 0.8525 0.73942 0.1729 167.0110 0.0250 6.8391 0.8526 0.74973 0.1729 167.0179 0.0250 6.8391 0.8526 0.75354 0.1729 167.0179 0.0250 6.8391 0.8526 0.75965 0.1728 167.0179 0.0250 6.7489 0.8527 0.76496 0.1728 167.0179 0.0250 6.7489 0.8527 0.77277 0.1723 167.0300 0.0250 6.4891 0.8530 0.77608 0.1723 167.0300 0.0250 6.4891 0.8530 0.78419 0.1719 167.0300 0.0250 6.2000 0.8533 0.788510 0.1719 167.0300 0.0250 6.2000 0.8533 0.7914
The max cycle per run is increased to 20 and the results are shown in Figure
4.11. From the experiment results, the minimum Ra value achieved is 0.1719|am in
all runs except in the second, fourth and tenth run where the minimum Ra values
achieved are 0.1720(j,m, 0.1736(j,m and 0.1770(j,m respectively.
106
n Artificial Bee Algorithm Progr;
P r o c e s s P a r a m e t e r s O p t i m i z a t i o n o f S u r f a c e R o u g h n e s s i n E n d M i l l i n g a n d A b r a s i v e W a t e r j e t M a c h i n i n g
U s i n g A r t i f i c i a l B e e C o l o n y A l g o r i t h m
Ra = 0 237 — (0.00 175 X icl) + (3 693 x x2) ■+■ (0.00 159 X tc3>
Function fo r: End Milling
Colony S iz e :
Number of R un:
Max Cycles per R un:
Limit (abandoned fo od):
j— Parameters Range---------
X1 X2 X3 X4 X5
Uppest Threshold
167.03 0.083 iro 3.5
Lowest Threshold
124.53 0.025 6.2
All best valuesA'un
run N u m .Cycles MinValue X I
5 20 0.1719 167.030( *
6 20 0.1719 167.Q30(
7 2 0 1 0 .1 71 9 1 167.030( “
8 20 0.1719 167.0301 S9 20 0.1719 167.030C
10 20 0.1770 164.121 ( -
< | ff[ □ »
jjhovv Detailj
Ready
Min Value, Fitnes A Mean of Fitness/Cycle
Figure 4.11 Results of 20 max cycles per run with limit of 150
In Table 4.13 below, the best value returned from 20 max cycles is in the
seventh run. The minimum Ra value achieved is 0.1719|am in cycle 9 with the best
fitness of 0.8533. The set values of process parameters that lead to the minimum Ra
value are 167.0300 m/min for cutting speed, 0.0250 mm/tooth for feed and 6.200 0
for radial rake angle.
107
Table 4.13: The best value returned from 20 max cycles per run with limit of 150
Cycle Min Ra XI (v) X2 if) X3(y) Best
fitness
Mean
fitness
1 0.2074 148.1252 0.0250 7.7552 0.8282 0.68952 0.2074 148.1252 0.0250 7.7552 0.8282 0.70113 0.2011 167.0300 0.0279 8.7554 0.8326 0.70824 0.2011 167.0300 0.0279 8.7554 0.8326 0.71355 0.1946 154.0561 0.0250 6.2000 0.8371 0.71866 0.1946 154.0561 0.0250 6.2000 0.8371 0.72097 0.1919 155.6038 0.0250 6.2000 0.8390 0.72518 0.1919 155.6038 0.0250 6.2000 0.8390 0.72809 0.1719 167.0300 0.0250 6.2000 0.8533 0.731410 0.1719 167.0300 0.0250 6.2000 0.8533 0.735111 0.1719 167.0300 0.0250 6.2000 0.8533 0.741412 0.1719 167.0300 0.0250 6.2000 0.8533 0.745813 0.1719 167.0300 0.0250 6.2000 0.8533 0.753114 0.1719 167.0300 0.0250 6.2000 0.8533 0.761915 0.1719 167.0300 0.0250 6.2000 0.8533 0.766616 0.1719 167.0300 0.0250 6.2000 0.8533 0.771117 0.1719 167.0300 0.0250 6.2000 0.8533 0.774818 0.1719 167.0300 0.0250 6.2000 0.8533 0.777719 0.1719 167.0300 0.0250 6.2000 0.8533 0.781920 0.1719 167.0300 0.0250 6.2000 0.8533 0.7852
Next the max cycle per run value is increased to 50 to test the performance of
ABC algorithm. The results of control variables 50 max per cycles with limit of 150
are shown in Figure 4.12 where the minimum Ra value achieved is 0.1719(_im in all
tenth runs.
108
2 Artificial Bee Algorithm Progr<
P r o c e s s P a r a m e t e r s O p t i m i z a t i o n o f S u r f a c e R o u g h n e s s i n E n d M i l l i n g a n d A b r a s i v e W a t e r j e t M a c h i n i n g
U s i n g A r t i f i c i a l B e e C o l o n y A l g o r i t h m
Ra = 0.237 — (0.00 175 X i l ) + (3 693 x + (0.00159 X x3>
Function fo r: End Milling
Colony S iz e :
Number of R un:
Max Cycles per R un:
Limit (abandoned fo od):
j— Parameters Range---------
X1 X2 X3 X4 X5
Uppest Threshold
167.03 0.083 3.5
Lowest Threshold
124.53 0.025 6.2
All best valuesfrun
run Sum .Cycles M in Value X I
5 50 0.1719 167.0300 *
6 501 a .1719 B 167.03007 50 0.1719 167.0300 —
8 50 0.1719 167.0300 m
9 50 0.1719 167.0300
10 50 0.1719 167.0300 -4 eii »
Ready
Min Value, Fitnes A Mean of Fitness/Cycle
Figure 4.12 Results of 50 max cycles per run with limit of 150
In Table 4.14 below, the results of the experiments showed that the minimum
Ra value of 1.1719|am is achieved at cycle three with the best fitness value of 0.8533.
The set values of process parameters that lead to the minimum Ra value are 167.0300
m/min for cutting speed, 0.0250 mm/tooth for feed and 6.200 0 for radial rake angle.
109
Table 4.14: The best value returned from 50 max cycles per run with limit of 150
Cycle Min Ra XI (v) X2 if) X3(y) Best
fitness
Mean
fitness
1 0.2145 162.8207 0.0291 6.2000 0.8234 0.68752 0.1792 162.8207 0.0250 6.2000 0.8480 0.69273 0.1719 167.0300 0.0250 6.2000 0.8533 0.69904 0.1719 167.0300 0.0250 6.2000 0.8533 0.70435 0.1719 167.0300 0.0250 6.2000 0.8533 0.71686 0.1719 167.0300 0.0250 6.2000 0.8533 0.72247 0.1719 167.0300 0.0250 6.2000 0.8533 0.72948 0.1719 167.0300 0.0250 6.2000 0.8533 0.73529 0.1719 167.0300 0.0250 6.2000 0.8533 0.744010 0.1719 167.0300 0.0250 6.2000 0.8533 0.746211 0.1719 167.0300 0.0250 6.2000 0.8533 0.753412 0.1719 167.0300 0.0250 6.2000 0.8533 0.756513 0.1719 167.0300 0.0250 6.2000 0.8533 0.761314 0.1719 167.0300 0.0250 6.2000 0.8533 0.763815 0.1719 167.0300 0.0250 6.2000 0.8533 0.768816 0.1719 167.0300 0.0250 6.2000 0.8533 0.775417 0.1719 167.0300 0.0250 6.2000 0.8533 0.776518 0.1719 167.0300 0.0250 6.2000 0.8533 0.777419 0.1719 167.0300 0.0250 6.2000 0.8533 0.782320 0.1719 167.0300 0.0250 6.2000 0.8533 0.787921 0.1719 167.0300 0.0250 6.2000 0.8533 0.793322 0.1719 167.0300 0.0250 6.2000 0.8533 0.794923 0.1719 167.0300 0.0250 6.2000 0.8533 0.796224 0.1719 167.0300 0.0250 6.2000 0.8533 0.796725 0.1719 167.0300 0.0250 6.2000 0.8533 0.801126 0.1719 167.0300 0.0250 6.2000 0.8533 0.802827 0.1719 167.0300 0.0250 6.2000 0.8533 0.803728 0.1719 167.0300 0.0250 6.2000 0.8533 0.806929 0.1719 167.0300 0.0250 6.2000 0.8533 0.8099
11 0
30 0.1719 167.0300 0.0250 6.2000 0.8533 0.812831 0.1719 167.0300 0.0250 6.2000 0.8533 0.814632 0.1719 167.0300 0.0250 6.2000 0.8533 0.816533 0.1719 167.0300 0.0250 6.2000 0.8533 0.817034 0.1719 167.0300 0.0250 6.2000 0.8533 0.817835 0.1719 167.0300 0.0250 6.2000 0.8533 0.818836 0.1719 167.0300 0.0250 6.2000 0.8533 0.823537 0.1719 167.0300 0.0250 6.2000 0.8533 0.823938 0.1719 167.0300 0.0250 6.2000 0.8533 0.825039 0.1719 167.0300 0.0250 6.2000 0.8533 0.826940 0.1719 167.0300 0.0250 6.2000 0.8533 0.827241 0.1719 167.0300 0.0250 6.2000 0.8533 0.828442 0.1719 167.0300 0.0250 6.2000 0.8533 0.828843 0.1719 167.0300 0.0250 6.2000 0.8533 0.829144 0.1719 167.0300 0.0250 6.2000 0.8533 0.829345 0.1719 167.0300 0.0250 6.2000 0.8533 0.832946 0.1719 167.0300 0.0250 6.2000 0.8533 0.833947 0.1719 167.0300 0.0250 6.2000 0.8533 0.835048 0.1719 167.0300 0.0250 6.2000 0.8533 0.836549 0.1719 167.0300 0.0250 6.2000 0.8533 0.838250 0.1719 167.0300 0.0250 6.2000 0.8533 0.8390
For the final combination of bee colony size of 50, the max cycles per run
value is increased to 100 with the limit of 150. The results of the experiments are
shown in Figure 4.13 where the minimum Ra value achieved is 0.1719|am in all tenth
runs.
I l l
Q Artificial Bee Algorithm Progr;
P r o c e s s P a r a m e t e r s O p t i m i z a t i o n o f S u r f a c e R o u g h n e s s i n E n d M i l l i n g a n d A b r a s i v e W a t e r j e t M a c h i n i n g
U s i n g A r t i f i c i a l B e e C o l o n y A l g o r i t h m
Ra = 0.237 — (0.00 175 X icl) + (3 693 x ■+■ (0.00 159 x tc3>
Function fo r: End Milling
Colony S iz e :
Number of R un:
Max Cycles per R un:
Limit (abandoned fo od):
j— Parameters Range---------
X1 X2 X3
100
X4 X5
Uppest Threshold
167.03 0.083 120 3.5
124.53 1 ^ 0 2 5 | 6.2 ]|
Lowest Threshold
II 0 5All best valuesA'un
run N u m .Cycles MinValue X I
1 100 0.1719 167.030( >
2 100 0.1719 167.030E
3 100| □ .1719 167.030E
4 100 0.1719 167.0301
5 100 0.1719 167.030(
6 100 0.1719 167.030(7 ̂nn ni7iQ ̂C7 mnr
< | in “ 1 r
^ o w D e ta i l j
Ready
Min Value, Fitnes A Mean of Fitness/Cycle
Figure 4.13 Results of 100 max cycles per run with limit of 150
Table 4.15 below shows the minimum Ra value 0.1719|am is achieved in
cycle two with the best fitness of 0.8533. The set values of process parameters that
lead to the minimum Ra value are 167.0300 m/min for cutting speed, 0.0250
mm/tooth for feed and 6.200° for radial rake angle.
11 2
Table 4.15: The best value returned from 100 max cycles per run with limit of
Cycle Min Ra XI (v) X2 if) X3(y) Best
fitness
Mean
fitness
1 0.1865 158.6923 0.0250 6.2000 0.8428 0.69652 0.1719 167.0300 0.0250 6.2000 0.8533 0.70263 0.1719 167.0300 0.0250 6.2000 0.8533 0.70824 0.1719 167.0300 0.0250 6.2000 0.8533 0.71135 0.1719 167.0300 0.0250 6.2000 0.8533 0.72186 0.1719 167.0300 0.0250 6.2000 0.8533 0.72727 0.1719 167.0300 0.0250 6.2000 0.8533 0.73338 0.1719 167.0300 0.0250 6.2000 0.8533 0.73879 0.1719 167.0300 0.0250 6.2000 0.8533 0.748610 0.1719 167.0300 0.0250 6.2000 0.8533 0.756011 0.1719 167.0300 0.0250 6.2000 0.8533 0.762412 0.1719 167.0300 0.0250 6.2000 0.8533 0.766713 0.1719 167.0300 0.0250 6.2000 0.8533 0.769914 0.1719 167.0300 0.0250 6.2000 0.8533 0.776215 0.1719 167.0300 0.0250 6.2000 0.8533 0.782316 0.1719 167.0300 0.0250 6.2000 0.8533 0.785617 0.1719 167.0300 0.0250 6.2000 0.8533 0.787618 0.1719 167.0300 0.0250 6.2000 0.8533 0.790519 0.1719 167.0300 0.0250 6.2000 0.8533 0.794220 0.1719 167.0300 0.0250 6.2000 0.8533 0.797721 0.1719 167.0300 0.0250 6.2000 0.8533 0.804222 0.1719 167.0300 0.0250 6.2000 0.8533 0.806223 0.1719 167.0300 0.0250 6.2000 0.8533 0.808824 0.1719 167.0300 0.0250 6.2000 0.8533 0.812425 0.1719 167.0300 0.0250 6.2000 0.8533 0.815026 0.1719 167.0300 0.0250 6.2000 0.8533 0.815527 0.1719 167.0300 0.0250 6.2000 0.8533 0.818228 0.1719 167.0300 0.0250 6.2000 0.8533 0.8202
113
29 0.1719 167.0300 0.0250 6.2000 0.8533 0.822030 0.1719 167.0300 0.0250 6.2000 0.8533 0.822631 0.1719 167.0300 0.0250 6.2000 0.8533 0.823932 0.1719 167.0300 0.0250 6.2000 0.8533 0.826133 0.1719 167.0300 0.0250 6.2000 0.8533 0.826934 0.1719 167.0300 0.0250 6.2000 0.8533 0.827535 0.1719 167.0300 0.0250 6.2000 0.8533 0.829836 0.1719 167.0300 0.0250 6.2000 0.8533 0.832137 0.1719 167.0300 0.0250 6.2000 0.8533 0.832738 0.1719 167.0300 0.0250 6.2000 0.8533 0.833339 0.1719 167.0300 0.0250 6.2000 0.8533 0.836140 0.1719 167.0300 0.0250 6.2000 0.8533 0.838141 0.1719 167.0300 0.0250 6.2000 0.8533 0.839242 0.1719 167.0300 0.0250 6.2000 0.8533 0.839943 0.1719 167.0300 0.0250 6.2000 0.8533 0.839944 0.1719 167.0300 0.0250 6.2000 0.8533 0.841445 0.1719 167.0300 0.0250 6.2000 0.8533 0.841546 0.1719 167.0300 0.0250 6.2000 0.8533 0.842847 0.1719 167.0300 0.0250 6.2000 0.8533 0.843348 0.1719 167.0300 0.0250 6.2000 0.8533 0.844749 0.1719 167.0300 0.0250 6.2000 0.8533 0.845350 0.1719 167.0300 0.0250 6.2000 0.8533 0.846151 0.1719 167.0300 0.0250 6.2000 0.8533 0.846552 0.1719 167.0300 0.0250 6.2000 0.8533 0.847253 0.1719 167.0300 0.0250 6.2000 0.8533 0.847554 0.1719 167.0300 0.0250 6.2000 0.8533 0.847955 0.1719 167.0300 0.0250 6.2000 0.8533 0.847956 0.1719 167.0300 0.0250 6.2000 0.8533 0.848057 0.1719 167.0300 0.0250 6.2000 0.8533 0.848258 0.1719 167.0300 0.0250 6.2000 0.8533 0.848859 0.1719 167.0300 0.0250 6.2000 0.8533 0.848960 0.1719 167.0300 0.0250 6.2000 0.8533 0.849761 0.1719 167.0300 0.0250 6.2000 0.8533 0.8499
114
62 0.1719 167.0300 0.0250 6.2000 0.8533 0.850163 0.1719 167.0300 0.0250 6.2000 0.8533 0.850364 0.1719 167.0300 0.0250 6.2000 0.8533 0.850565 0.1719 167.0300 0.0250 6.2000 0.8533 0.850666 0.1719 167.0300 0.0250 6.2000 0.8533 0.850767 0.1719 167.0300 0.0250 6.2000 0.8533 0.851168 0.1719 167.0300 0.0250 6.2000 0.8533 0.851569 0.1719 167.0300 0.0250 6.2000 0.8533 0.851570 0.1719 167.0300 0.0250 6.2000 0.8533 0.851771 0.1719 167.0300 0.0250 6.2000 0.8533 0.851872 0.1719 167.0300 0.0250 6.2000 0.8533 0.851973 0.1719 167.0300 0.0250 6.2000 0.8533 0.851974 0.1719 167.0300 0.0250 6.2000 0.8533 0.852175 0.1719 167.0300 0.0250 6.2000 0.8533 0.852176 0.1719 167.0300 0.0250 6.2000 0.8533 0.852177 0.1719 167.0300 0.0250 6.2000 0.8533 0.852278 0.1719 167.0300 0.0250 6.2000 0.8533 0.852479 0.1719 167.0300 0.0250 6.2000 0.8533 0.852580 0.1719 167.0300 0.0250 6.2000 0.8533 0.845781 0.1719 167.0300 0.0250 6.2000 0.8533 0.845882 0.1719 167.0300 0.0250 6.2000 0.8533 0.846083 0.1719 167.0300 0.0250 6.2000 0.8533 0.837084 0.1719 167.0300 0.0250 6.2000 0.8533 0.835985 0.1719 167.0300 0.0250 6.2000 0.8533 0.836686 0.1719 167.0300 0.0250 6.2000 0.8533 0.838487 0.1719 167.0300 0.0250 6.2000 0.8533 0.838588 0.1719 167.0300 0.0250 6.2000 0.8533 0.831689 0.1719 167.0300 0.0250 6.2000 0.8533 0.831690 0.1719 167.0300 0.0250 6.2000 0.8533 0.832491 0.1719 167.0300 0.0250 6.2000 0.8533 0.832692 0.1719 167.0300 0.0250 6.2000 0.8533 0.832293 0.1719 167.0300 0.0250 6.2000 0.8533 0.837794 0.1719 167.0300 0.0250 6.2000 0.8533 0.8384
115
95 0.1719 167.0300 0.0250 6.2000 0.8533 0.837096 0.1719 167.0300 0.0250 6.2000 0.8533 0.839597 0.1719 167.0300 0.0250 6.2000 0.8533 0.840298 0.1719 167.0300 0.0250 6.2000 0.8533 0.830699 0.1719 167.0300 0.0250 6.2000 0.8533 0.8345100 0.1719 167.0300 0.0250 6.2000 0.8533 0.8350
116
For the last control variables combination of end milling, the colony size
value is increased to 100 with the limit of 300. The control variables combinations
are described in Table 4.16.
Table 4.16: Control variables combination with limit of 300
4.7.4 Colony size of 100 and limit of 300
Colony Size Max cycles per
run
Limit (abandoned
food)
100 10 300
100 20 300
100 50 300
100 100 300
When the program is executed, the results of the first control variables
combination are shown in Figure 4.14. The minimum Ra value achieved is 0.1719|am
in the first and seventh run.
117
2 Artificial Bee Algorithm Progr<
P r o c e s s P a r a m e t e r s O p t i m i z a t i o n o f S u r f a c e R o u g h n e s s i n E n d M i l l i n g a n d A b r a s i v e W a t e r j e t M a c h i n i n g
U s i n g A r t i f i c i a l B e e C o l o n y A l g o r i t h m
Ra = 0 237 — (0.00 175 X icl) + (3 693 x ■+■ (0.00 159 x x3>
Function fo r: End Milling
Colony S iz e :
Number of R un:
Max Cycles per R un:
Limit (abandoned fo od):
j— Parameters Range---------
X1 X2 X3 X4 X5
Uppest Threshold
167.03 0.083 3.5
Lowest Threshold
124.53 0.025 6.2
All best valuesAun
run N u m .Cycles MinValue X I
5 10 0.1744 167.030( •
6 10 Q.1729 167.03Q(
7 10| 0.17 1 9 H 167.030(
8 10 0.1747 167.0301 g
9 10 0.1753 166.098:
10 10 0.1723 167.030( -
< I IB J t
i ^ o v v Detail
Ready
Min Value, Fitnes A Mean of Fitness/Cycle
Cycle
Figure 4.14 Results of 10 max cycles per run with limit of 300
The best value returned is given by the seventh run where the minimum Ra
value 0 .17 19|am can be found in cycle seven. The best fitness value is 0.8533 and the
set values of process parameters that lead to the minimum values of Ra value are
167.0300 m/min for cutting speed, 0.0250 mm/tooth for feed and 6.200 0 for radial
rake angle. This is shown in Table 4.17.
118
Table 4.17: The best value returned from 10 max cycles per run with limit of 300
Cycle Min Ra XI (v) X2 if) X3(y) Best
fitness
Mean
fitness
1 0.2212 144.5240 0.0261 6.2000 0.8189 0.69432 0.2113 144.5240 0.0250 6.2000 0.8256 0.70003 0.1884 159.2385 0.0250 7.9867 0.8415 0.70624 0.1863 160.4344 0.0250 7.9867 0.8430 0.71295 0.1841 161.1510 0.0250 7.3935 0.8445 0.71686 0.1748 166.4708 0.0250 7.3935 0.8512 0.72247 0.1719 167.0300 0.0250 6.2000 0.8533 0.73088 0.1719 167.0300 0.0250 6.2000 0.8533 0.73859 0.1719 167.0300 0.0250 6.2000 0.8533 0.742710 0.1719 167.0300 0.0250 6.2000 0.8533 0.7450
Subsequently the number of max cycle per run is increased to 20 and the
results are shown in Figure 4.15. The minimum Ra value achieved is 0.1719|am in all
tenth runs.
119
S3 Artific ial Bee A lgorithm Program \^_iP r o c e s s P a r a m e t e r s O p t i m i z a t i o n o f S u r f a c e R o u g h n e s s i n E n d M i l l i n g a n d A b r a s i v e W a t e r j e t M a c h i n i n g
U s i n g A r t i f i c i a l B e e C o l o n y A l g o r i t h m
Ra = 0 237 — (0.00 175 X i l ) + (3 693 x x 2 ) + (0.00159 x x3>
100
Function fo r: End Milling
Colony S iz e :
Number of R un:
Max Cycles per R un:
Limit (abandoned fo od):
j— Parameters Range---------
X1 X2 X3 X 4 X5
Uppest Threshold
167.03 0.083 3.5
Lowest Threshold
124.53 0.025 6.2
All best values/run
run N u m .Cycles MinValue X Iu . 1 ' 1 -■
5 20 0.1719 167.030(
6 20 0.1719 167.Q3CK
7 20 0.1719 167.030( — i8 20 0.1719 167.0301 =
9 20 0.1719 167.0301
10 20 0.1719 167.030( -
4 L HI H I »
IjS ftow b e ta i
Ready
0.9
0.8
0.7
0.6
= 0 .6
0.4
0.3
0.2
0.1
Min Value, Fitnes & Mean of Fitness/Cycle
Mean fitness
/Mill Ra value
10Cycle
15 20
Figure 4.15 Results of 20 max cycles per run with limit of 300
Table 4.18 below shows the best value returned from the fifth run with the
minimum Ra value of 0.1719 jam. This minimum Ra value is found in cycle five with
the best fitness value of 0.8533. The set values of process parameters that lead to the
minimum Ra value are 167.0300 m/min for cutting speed, 0.0250 mm/tooth for feed
and 6.200 0 for radial rake angle.
12 0
Table 4.18: The best value returned from 20 max cycles per run with limit of 300
Cycle Min Ra XI (v) X2 if) X3(y) Best
fitness
Mean
fitness
1 0.1891 165.9984 0.0267 6.4028 0.8410 0.67812 0.1875 165.9984 0.0266 6.4028 0.8421 0.68303 0.1872 165.9984 0.0266 6.2000 0.8423 0.69104 0.1854 167.0300 0.0266 6.2000 0.8436 0.69925 0.1719 167.0300 0.0250 6.2000 0.8533 0.70566 0.1719 167.0300 0.0250 6.2000 0.8533 0.71187 0.1719 167.0300 0.0250 6.2000 0.8533 0.71598 0.1719 167.0300 0.0250 6.2000 0.8533 0.72149 0.1719 167.0300 0.0250 6.2000 0.8533 0.727410 0.1719 167.0300 0.0250 6.2000 0.8533 0.735611 0.1719 167.0300 0.0250 6.2000 0.8533 0.741412 0.1719 167.0300 0.0250 6.2000 0.8533 0.747213 0.1719 167.0300 0.0250 6.2000 0.8533 0.751014 0.1719 167.0300 0.0250 6.2000 0.8533 0.756815 0.1719 167.0300 0.0250 6.2000 0.8533 0.764916 0.1719 167.0300 0.0250 6.2000 0.8533 0.771317 0.1719 167.0300 0.0250 6.2000 0.8533 0.776018 0.1719 167.0300 0.0250 6.2000 0.8533 0.780219 0.1719 167.0300 0.0250 6.2000 0.8533 0.785520 0.1719 167.0300 0.0250 6.2000 0.8533 0.7884
121
The value of max cycle per run is increased to 50 and the experimental
results are shown in Figure 4.16. From the results, the minimum Ra value achieved is
0.1719|am in all tenth runs.
H Artific ia l Bee A lgorithm Progn i--------
P r o c e s s P a r a m e t e r s O p t i m i z a t i o n o f S u r f a c e R o u g h n e s s i n E n d M i l l i n g a n d A b r a s i v e W a t e r j e t M a c h i n i n g
U s i n g A r t i f i c i a l B e e C o l o n y A l g o r i t h m
Ra = 0.237 — (0.00 175 x i l ) -1- (3 693 x ■+• (0.00159 x x3>
Function fo r: End Milling
Colony S iz e :
Number of R un:
Max Cycles per R un:
Limit (abandoned fo od):
I— Parameters Range-------
X1 X2 X3 X4 X5
Uppest Threshold:
167.03 0.083 3.5
Lowest Threshold:
124.53 0.025 6.2 60 || 0.5
All best valuesfrun
run Num .Cycles MinValue X I
5 50 0.1719 167.030(*
6 50 0.1719 167.03CH
7 50 0.1719 167.030(
8 50 0.1719 167.030t E
9 50 0.1719 167.030(
10 50 0.1719 167.030(
< | m Z i t
j S J io w D «ta il
Ready
Min Value, Fitnes & Mean of Fitness/Cycle
Figure 4.16 Results of 50 max cycles per run with limit of 300
The best value returned from 50 max cycles per run is given by the ninth runs
where the minimum Ra value is 0.1719 jam. In Table 4.19 below, the minimum Ra
value can be found in the cycle two with the best fitness value of 0.8533. The set
values of process parameters that lead to the minimum Ra value are 167.0300 m/min
for cutting speed, 0.0250 mm/tooth for feed and 6.200 0 for radial rake angle.
12 2
Table 4.19: The best value returned from 50 max cycles per run with limit of 300
Cycle Min Ra XI (v) X2 if) X3(y) Best
fitness
Mean
fitness
1 0.1755 165.1503 0.0250 6.4014 0.8507 0.68962 0.1719 167.0300 0.0250 6.2000 0.8533 0.69823 0.1719 167.0300 0.0250 6.2000 0.8533 0.70394 0.1719 167.0300 0.0250 6.2000 0.8533 0.70925 0.1719 167.0300 0.0250 6.2000 0.8533 0.71746 0.1719 167.0300 0.0250 6.2000 0.8533 0.72227 0.1719 167.0300 0.0250 6.2000 0.8533 0.72568 0.1719 167.0300 0.0250 6.2000 0.8533 0.73409 0.1719 167.0300 0.0250 6.2000 0.8533 0.740810 0.1719 167.0300 0.0250 6.2000 0.8533 0.743911 0.1719 167.0300 0.0250 6.2000 0.8533 0.748112 0.1719 167.0300 0.0250 6.2000 0.8533 0.756713 0.1719 167.0300 0.0250 6.2000 0.8533 0.759714 0.1719 167.0300 0.0250 6.2000 0.8533 0.765515 0.1719 167.0300 0.0250 6.2000 0.8533 0.770016 0.1719 167.0300 0.0250 6.2000 0.8533 0.774417 0.1719 167.0300 0.0250 6.2000 0.8533 0.779318 0.1719 167.0300 0.0250 6.2000 0.8533 0.782219 0.1719 167.0300 0.0250 6.2000 0.8533 0.786620 0.1719 167.0300 0.0250 6.2000 0.8533 0.789121 0.1719 167.0300 0.0250 6.2000 0.8533 0.793022 0.1719 167.0300 0.0250 6.2000 0.8533 0.796023 0.1719 167.0300 0.0250 6.2000 0.8533 0.800324 0.1719 167.0300 0.0250 6.2000 0.8533 0.804625 0.1719 167.0300 0.0250 6.2000 0.8533 0.807526 0.1719 167.0300 0.0250 6.2000 0.8533 0.809827 0.1719 167.0300 0.0250 6.2000 0.8533 0.812028 0.1719 167.0300 0.0250 6.2000 0.8533 0.814329 0.1719 167.0300 0.0250 6.2000 0.8533 0.8154
123
30 0.1719 167.0300 0.0250 6.2000 0.8533 0.816231 0.1719 167.0300 0.0250 6.2000 0.8533 0.817332 0.1719 167.0300 0.0250 6.2000 0.8533 0.818433 0.1719 167.0300 0.0250 6.2000 0.8533 0.820834 0.1719 167.0300 0.0250 6.2000 0.8533 0.823635 0.1719 167.0300 0.0250 6.2000 0.8533 0.824836 0.1719 167.0300 0.0250 6.2000 0.8533 0.827137 0.1719 167.0300 0.0250 6.2000 0.8533 0.827838 0.1719 167.0300 0.0250 6.2000 0.8533 0.829039 0.1719 167.0300 0.0250 6.2000 0.8533 0.830340 0.1719 167.0300 0.0250 6.2000 0.8533 0.831741 0.1719 167.0300 0.0250 6.2000 0.8533 0.832442 0.1719 167.0300 0.0250 6.2000 0.8533 0.834443 0.1719 167.0300 0.0250 6.2000 0.8533 0.835244 0.1719 167.0300 0.0250 6.2000 0.8533 0.836245 0.1719 167.0300 0.0250 6.2000 0.8533 0.837246 0.1719 167.0300 0.0250 6.2000 0.8533 0.838547 0.1719 167.0300 0.0250 6.2000 0.8533 0.838948 0.1719 167.0300 0.0250 6.2000 0.8533 0.839349 0.1719 167.0300 0.0250 6.2000 0.8533 0.840550 0.1719 167.0300 0.0250 6.2000 0.8533 0.8424
124
Finally, the value of max cycles per run is increased to 100 with the limit of
300. Figure 4.17 shows the results where the minimum Ra value discovered is
0.1719|am in all tenth runs.
P r o c e s s P a r a m e t e r s O p t i m i z a t i o n o f S u r f a c e R o u g h n e s s i n E n d M i l l i n g a n d A b r a s i v e W a t e r j e t M a c h i n i n g
U s i n g A r t i f i c i a l B e e C o l o n y A l g o r i t h m
Ra = 0 237 — (0.00 175 x i l ) -4- (S.693 x x2) + (0.00159 x x3>
10
Function fo r: End Milling
Colony S iz e :
Number of R un:
Max Cycles per R un:
Limit (abandoned fo od):
I— Parameters Range--------
X1 X2 X3
PUN
X4 X5
Uppest Threshold:
167 03 0.083 14 8 3.5
Lowest Threshold:
124.53 0.025 6 2 |
All best valuesAun
run Num .Cycles MinValue X I
3 100 0.1719 167.030( *
4 100| 0.1719H 167.030(
5 100 0.1719 167.030C
6 100 0.1719 167.030C 57 100 0.1719 167.030E —
8 100 0.1719 167.0301n Anr>
* I rtr- H I -»*'>
1
Ready
Min Value, Fitnes & Mean of Fitness/Cycle
Figure 4.17 Results of 100 max cycles per run with limit of 300
From the results in Table 4.20, the minimum Ra value of 0.1719 jam can be
found in cycle seven. The best fitness value achieved is 0.8533 and the set values of
process parameters that lead to the minimum Ra value are 167.0300 m/min for
cutting speed, 0.0250 mm/tooth for feed and 6.200 0 for radial rake angle.
125
Table 4.20: The best value returned from 100 max cycles per run with limit of
Cycle Min Ra XI (v) X2 if) X3(y) Best
fitness
Mean
fitness
1 0.1964 158.5504 0.0250 12.3068 0.8358 0.70662 0.1964 158.5504 0.0250 12.2979 0.8358 0.71143 0.1842 165.0309 0.0250 11.7750 0.8444 0.71984 0.1807 167.0300 0.0250 11.7750 0.8469 0.72695 0.1807 167.0300 0.0250 11.7750 0.8469 0.73176 0.1740 166.7493 0.0250 7.2084 0.8518 0.73557 0.1738 166.7493 0.0250 7.1150 0.8519 0.73888 0.1719 167.0300 0.0250 6.2000 0.8533 0.74489 0.1719 167.0300 0.0250 6.2000 0.8533 0.748110 0.1719 167.0300 0.0250 6.2000 0.8533 0.754211 0.1719 167.0300 0.0250 6.2000 0.8533 0.756812 0.1719 167.0300 0.0250 6.2000 0.8533 0.762013 0.1719 167.0300 0.0250 6.2000 0.8533 0.765614 0.1719 167.0300 0.0250 6.2000 0.8533 0.770415 0.1719 167.0300 0.0250 6.2000 0.8533 0.775116 0.1719 167.0300 0.0250 6.2000 0.8533 0.780817 0.1719 167.0300 0.0250 6.2000 0.8533 0.785518 0.1719 167.0300 0.0250 6.2000 0.8533 0.789619 0.1719 167.0300 0.0250 6.2000 0.8533 0.791620 0.1719 167.0300 0.0250 6.2000 0.8533 0.795021 0.1719 167.0300 0.0250 6.2000 0.8533 0.799122 0.1719 167.0300 0.0250 6.2000 0.8533 0.801123 0.1719 167.0300 0.0250 6.2000 0.8533 0.803624 0.1719 167.0300 0.0250 6.2000 0.8533 0.807225 0.1719 167.0300 0.0250 6.2000 0.8533 0.809426 0.1719 167.0300 0.0250 6.2000 0.8533 0.811627 0.1719 167.0300 0.0250 6.2000 0.8533 0.815928 0.1719 167.0300 0.0250 6.2000 0.8533 0.8176
126
29 0.1719 167.0300 0.0250 6.2000 0.8533 0.819330 0.1719 167.0300 0.0250 6.2000 0.8533 0.821131 0.1719 167.0300 0.0250 6.2000 0.8533 0.823832 0.1719 167.0300 0.0250 6.2000 0.8533 0.825833 0.1719 167.0300 0.0250 6.2000 0.8533 0.826834 0.1719 167.0300 0.0250 6.2000 0.8533 0.827835 0.1719 167.0300 0.0250 6.2000 0.8533 0.829436 0.1719 167.0300 0.0250 6.2000 0.8533 0.831437 0.1719 167.0300 0.0250 6.2000 0.8533 0.832638 0.1719 167.0300 0.0250 6.2000 0.8533 0.833939 0.1719 167.0300 0.0250 6.2000 0.8533 0.834840 0.1719 167.0300 0.0250 6.2000 0.8533 0.835341 0.1719 167.0300 0.0250 6.2000 0.8533 0.837342 0.1719 167.0300 0.0250 6.2000 0.8533 0.838543 0.1719 167.0300 0.0250 6.2000 0.8533 0.838944 0.1719 167.0300 0.0250 6.2000 0.8533 0.840245 0.1719 167.0300 0.0250 6.2000 0.8533 0.840846 0.1719 167.0300 0.0250 6.2000 0.8533 0.842147 0.1719 167.0300 0.0250 6.2000 0.8533 0.842448 0.1719 167.0300 0.0250 6.2000 0.8533 0.843149 0.1719 167.0300 0.0250 6.2000 0.8533 0.844850 0.1719 167.0300 0.0250 6.2000 0.8533 0.845251 0.1719 167.0300 0.0250 6.2000 0.8533 0.846052 0.1719 167.0300 0.0250 6.2000 0.8533 0.846553 0.1719 167.0300 0.0250 6.2000 0.8533 0.847354 0.1719 167.0300 0.0250 6.2000 0.8533 0.847855 0.1719 167.0300 0.0250 6.2000 0.8533 0.848656 0.1719 167.0300 0.0250 6.2000 0.8533 0.849057 0.1719 167.0300 0.0250 6.2000 0.8533 0.849258 0.1719 167.0300 0.0250 6.2000 0.8533 0.849459 0.1719 167.0300 0.0250 6.2000 0.8533 0.849560 0.1719 167.0300 0.0250 6.2000 0.8533 0.849661 0.1719 167.0300 0.0250 6.2000 0.8533 0.8501
127
62 0.1719 167.0300 0.0250 6.2000 0.8533 0.850463 0.1719 167.0300 0.0250 6.2000 0.8533 0.850664 0.1719 167.0300 0.0250 6.2000 0.8533 0.850965 0.1719 167.0300 0.0250 6.2000 0.8533 0.851266 0.1719 167.0300 0.0250 6.2000 0.8533 0.851467 0.1719 167.0300 0.0250 6.2000 0.8533 0.851668 0.1719 167.0300 0.0250 6.2000 0.8533 0.851769 0.1719 167.0300 0.0250 6.2000 0.8533 0.851970 0.1719 167.0300 0.0250 6.2000 0.8533 0.852071 0.1719 167.0300 0.0250 6.2000 0.8533 0.852172 0.1719 167.0300 0.0250 6.2000 0.8533 0.852273 0.1719 167.0300 0.0250 6.2000 0.8533 0.852274 0.1719 167.0300 0.0250 6.2000 0.8533 0.852375 0.1719 167.0300 0.0250 6.2000 0.8533 0.852376 0.1719 167.0300 0.0250 6.2000 0.8533 0.852477 0.1719 167.0300 0.0250 6.2000 0.8533 0.852478 0.1719 167.0300 0.0250 6.2000 0.8533 0.852579 0.1719 167.0300 0.0250 6.2000 0.8533 0.852580 0.1719 167.0300 0.0250 6.2000 0.8533 0.852581 0.1719 167.0300 0.0250 6.2000 0.8533 0.852682 0.1719 167.0300 0.0250 6.2000 0.8533 0.852783 0.1719 167.0300 0.0250 6.2000 0.8533 0.852784 0.1719 167.0300 0.0250 6.2000 0.8533 0.852885 0.1719 167.0300 0.0250 6.2000 0.8533 0.852886 0.1719 167.0300 0.0250 6.2000 0.8533 0.852887 0.1719 167.0300 0.0250 6.2000 0.8533 0.852988 0.1719 167.0300 0.0250 6.2000 0.8533 0.852989 0.1719 167.0300 0.0250 6.2000 0.8533 0.853090 0.1719 167.0300 0.0250 6.2000 0.8533 0.853091 0.1719 167.0300 0.0250 6.2000 0.8533 0.853092 0.1719 167.0300 0.0250 6.2000 0.8533 0.853193 0.1719 167.0300 0.0250 6.2000 0.8533 0.853194 0.1719 167.0300 0.0250 6.2000 0.8533 0.8531
128
95 0.1719 167.0300 0.0250 6.2000 0.8533 0.853196 0.1719 167.0300 0.0250 6.2000 0.8533 0.853197 0.1719 167.0300 0.0250 6.2000 0.8533 0.853198 0.1719 167.0300 0.0250 6.2000 0.8533 0.853199 0.1719 167.0300 0.0250 6.2000 0.8533 0.8531100 0.1719 167.0300 0.0250 6.2000 0.8533 0.8532
Using the same steps of end milling experiment, the AWJ experiment starts
with a bee colony size of 10 with the limit of 50. The control variables combinations
are shown in Table 4.21.
Table 4.21: Control variables combination with limit of 50
4.8 Experiment 2 - ABC optimization parameters for AWJ
Colony Size Max cycles per run Limit (abandoned
food)
10 10 50
10 20 50
10 50 50
10 100 50
4.8.1 Colony size of 10 and limit of 50
Using the first control variables combination, the program is executed for the
first time and the results are shown in Figure 4.18. The minimum Ra value found is
2.7090(j,m in the third run.
130
^ 3 A rtif ic ia l Bee A lg o r ith m P ro g r:
P r o c e s s P a r a m e t e r s O p t i m i z a t i o n o f S u r f a c e R o u g h n e s s i n E n d M i l l i n g a n d A b r a s i v e W a t e r j e t M a c h i n i n g
U s i n g A r t i f i c i a l B e e C o l o n y A l g o r i t h m
Ra =- 5 . 0 7 9 7 6 + ( 0 . 081*9 x s i ) + ( 0. 07912 x i 2 ) - ( 0. 34221 * x 3 ) - (0. 03661 x i 4 j - ( 0. 34866 x5) - ( 0. 00031 x i l * ) - ( 0. 00012 x i 2 s) +
( 0 , 10575 y x 3 J) + ( 0 . 0 00 4 ] x *4=) + ( 0 , 07590 * x 5 J) - ( 0. 00003 x x l x *5) - (O.OODOP x x l * x 5 ) + ( 0 . 03039 x * 3 x x 5 ) + ( 0. 00513 * x 4 x x5>
Function fo r :
Colony S iz e :
Number of R u n :
Max Cycles per Run
Limit (abandoned food)
Parameters Range---------------
X1 X2 X3
10
X4 X5
Uppest Threshold:
150 250 120 3.5
Lowest Threshold:
50 125 60 0.5
All best valuesA’un
run N u m . C yc le s M in V a lu e X I
1 10 4 4476 124.332 >
2 10 5.3259 59,417!
3 io | 2 . 7 H 9 « 73.109! £
4 10 3.1026 61.293!
5 10 3.5687 69.606!
6 10 4.3082 5i
7 10* rrr
4.6279 90.286:►
Show Detail
P.eadyCycle
10
''
Figure 4.18 Results of 10 max cycles per run with limit of 50
The results in Table 4.22 shows the minimum Ra value is achieved in cycle
eight with the best fitness value of 0.2696. The set values of process parameters that
lead to the minimum Ra value are 73.1095m/min traverse speed, 125Mpa waterjet
pressure, 1.4156mm standoff distance, 98.9371 [am abrasive gritsize and 1.0733g/s
abrasive flowrate.
131
Table 4.22 The best value returned from 10 max cycles per run with limit of 50
Cy
cle
Min Ra XI (V) X2 (P) X3 (h) X4 (a) X5
(m)
Best
fitness
Mean
fitness
1 3.5322 62.2021 154.0466 2.1971 93.6909 0.6386 0.2206 0.18272 2.8448 76.8439 125 1.2769 100.7081 1.0733 0.2601 0.19423 2.8435 76.8439 125 1.2769 98.7292 1.0733 0.2602 0.20054 2.8425 76.8439 125 1.3059 98.7292 1.0733 0.2602 0.20285 2.8130 75.9811 125 1.3059 98.7292 1.0733 0.2623 0.20336 2.8130 75.9811 125 1.3059 98.7292 1.0733 0.2623 0.20557 2.7113 73.1095 125 1.3059 98.7292 1.0733 0.2694 0.20738 2.7090 73.1095 125 1.4156 98.9371 1.0733 0.2696 0.20889 2.7090 73.1095 125 1.4156 98.9371 1.0733 0.2696 0.209710 2.7090 73.1095 125 1.4156 98.9371 1.0733 0.2696 0.2099
Next, the max cycle per run is increased to 20 and the results of the
experiment are shown in Figure 4.19. From the results, the minimum Ra value
achieved is 1.6032(j,m which is 41% better than the previous results. This value is
achieved at the seventh run.
132
H Artificial Bee Algorithm Program
P r o c e s s P a r a m e t e r s O p t i m i z a t i o n o f S u r f a c e R o u g h n e s s i n E n d M i l l i n g a n d A b r a s i v e W a t e r j e t M a c h i n i n g
U s i n g A r t i f i c i a l B e e C o l o n y A l g o r i t h m
Ra =-5.079^6 + (O .O S 1 6 9 x i l ) + (0.07911 x 12 ) - (0 .3 4 2 2 1 x e3)-(0.0& )61 x i 4 ) - (0 .3 4 S 6 6 x s 5 ) - (0.00031 x x l - ) - (0.00012 x n2?) +(0 ,1 0 5 7 5 x x 3 2) + (0 .0 0 0 4 1 x * 4 ! ) + (Q .0 7 ? 9 Q x % 5j ) - (0 .0 0 0 0 3 x * ] x x 5 ) - (Q .Q O Q 09 x x 2 x * 5 ) + (0 .0 3 0 3 9 x x 3 x * 5 } + (0 .0 0 5 1 3 x * 4 x x 5 }
Function fo r:
Colony S iz e :
Number of R un:
Max Cycles per R un:
Limit (abandoned food)
i— Parameters Range---------
X1 X2 X3
Abrasive Waterjet
1 250 r
X4 X5
Uppest Threshold
120 3.5
Lowest Threshold
50
All best valuesA'un
run N u m .Cycles M in Value X I
5 20 3.9778 5(•
6 20 3.143Q 66.269f
7 2 0 1 1.6032H 5(
8 20 1.7223 51 =E
9 20 1.8514 5(
10 20 1.8004 5( -
' 1 hi .□ 1
Ready
Cycle Min Value, Fitnes A Mean of Fitness/Cycle
25 5
Figure 4.19 Results of 20 max cycles per run with limit of 50
Table 4.23 below shows the best value returned from 20 max cycles per run
and the minimum Ra value achieved at cycle 20 with the fitness value 0.3841. The set
values of process parameters that lead to the minimum Ra value are 50/min traverse
speed, 125Mpa waterjet pressure, 2.4197mm standoff distance, 102.2916[am abrasive
gritsize and 0.5000g/s abrasive flowrate.
133
Table 4.23: The best value returned from 20 max cycle per run with limit of 50
Cycle Min Ra XI (V) X2 (P) X3 (h) X4 (a) X5
(m)
Best
fitness
Mean
fitness
1 3.2539 68.9046 125.7593 3.5708 109.3744 1.3790 0.2351 3.2539
2 3.2539 68.9046 125.7593 3.5708 109.3744 1.3790 0.2351 3.2539
3 3.1513 68.3609 125.7593 3.5708 97.0500 1.3377 0.2409 3.1513
4 3.1395 68.0617 125.7593 3.5708 97.0500 1.3377 0.2416 3.1395
5 2.9808 68.0617 125.7593 3.1873 97.0500 1.3377 0.2512 2.9808
6 2.9808 68.0617 125.7593 3.1873 97.0500 1.3377 0.2512 2.9808
7 2.8698 66.4615 125.7593 3.1873 97.0500 1.2269 0.2584 2.8698
8 2.8695 66.4615 125.7593 3.1873 98.1111 1.2269 0.2584 2.8695
9 2.7784 66.4615 125.7593 3.1873 98.1111 1.0024 0.2647 2.7784
10 2.6159 66.4615 125.7593 2.9679 98.1111 0.7601 0.2766 2.6159
11 2.5787 66.4615 125 2.9679 98.1111 0.7601 0.2794 2.5787
12 2.5787 66.4615 125 2.9679 98.1111 0.7601 0.2794 2.5787
13 2.5783 66.4615 125 2.9679 98.2622 0.7601 0.2795 2.5783
14 2.4862 66.4615 125 2.9679 102.2774 0.5000 0.2868 2.4862
15 2.2043 59.8291 125 2.9679 102.2774 0.5000 0.3121 2.2043
16 1.7364 50 125 2.9679 102.2774 0.5000 0.3654 1.7364
17 1.7364 50 125 2.9679 102.2916 0.5000 0.3654 1.7364
18 1.7364 50 125 2.9679 102.2916 0.5000 0.3654 1.7364
19 1.7364 50 125 2.9679 102.2916 0.5000 0.3654 1.7364
20 1.6032 50 125 2.4197 102.2916 0.5000 0.3841 1.6032
The value of max cycles per run is increased to 50 and the results are shown
in Figure 4.20. The minimum Ra value achieved is 1.5223 jam at the sixth run.
Compared to the previous results, the minimum Ra value is improved by 5%.
134
S3 Artific ial Bee A lgorithm Progr*
P r o c e s s P a r a m e t e r s O p t i m i z a t i o n o f S u r f a c e R o u g h n e s s i n E n d M i l l i n g a n d A b r a s i v e W a t e r j e t M a c h i n i n g
U s i n g A r t i f i c i a l B e e C o l o n y A l g o r i t h m
Ra «-5 .07976 +■ (0 .OS 169 x *1} + (0.07912 x x2) - C0.34221 x i J ) - (0 .0 S 6 6 1 - i 4 ) - (Q.34S66 * xS) - (0.00031 * x V ) - (0 .000t l x x 2 !> +< 0 ,1 0 5 7 5 x (0 .0 0 0 4 ] * * 4 = ) + (0 .0 7 5 9 0 x * 5 J) - (0 .0 0 0 0 3 s i x * 5 ) - (0 .0 0 0 0 9 x j ] x * 5 ) + (0 .0 3 0 3 9 x * 3 * s 5 ) + (0 .0 0 5 1 3 x x 4 x * 5 )
Function fo r :
Colony S iz e :
Number of Run:
Max Cycles per Run
Limit (abandoned fo od);
I— Parameters Range--------
X1 X2 X3
Abrasive Waterjet
SO
X4 X5
Uppest Threshold:
ISO 250 4 120 3.5
Lowest Threshold:
50 125 | 1 60 OS |
All best valuesAun
run Num .Cycles MinValue X I
1 50 1.5232 5( >
2 50 1.7036 St
3 50 1.6540 50.24CK =
4 50 1.5225 5t
5 50 1.6430 5(
6 50 1.5223 5(7 cn 1 C V T
v III ►
| S h o w Detail |
Ready
Min Value, Fitnes & Mean of Fitness/Cycle
Cycle
Figure 4.20 Results of 50 max cycles per run with limit of 50
In Table 4.24, the minimum Ra value is found at cycle 17 with the best fitness
value of 0.3965. The set values of process parameters that lead to the minimum Ra
value are 50/min traverse speed, 125Mpa waterjet pressure, 1.5630mm standoff
distance, 102.2855|am abrasive gritsize and 0.5000g/s abrasive flowrate.
135
Table 4.24: The best value returned from 50 max cycle per run with limit of 50
Cycle Min Ra XI (V) X2 (P) X3 (h) X4 (d) X5
(m)
Best
fitness
Mean
fitness
1 2.6148 56.9891 139.8145 1.5643 99.9421 0.6767 0.2766 0.16192 2.2761 50 139.8145 1.5643 99.9421 0.6767 0.3052 0.16953 2.2249 50 139.8145 1.5643 100.3379 0.5000 0.3101 0.17164 2.2249 50 139.8145 1.5643 100.3379 0.5000 0.3101 0.17495 1.5242 50 125 1.5643 100.3379 0.5000 0.3962 0.19296 1.5226 50 125 1.5643 101.6083 0.5000 0.3964 0.19367 1.5226 50 125 1.5630 101.6083 0.5000 0.3964 0.19368 1.5226 50 125 1.5630 101.6083 0.5000 0.3964 0.19389 1.5226 50 125 1.5630 101.6083 0.5000 0.3964 0.197810 1.5226 50 125 1.5630 101.6083 0.5000 0.3964 0.199811 1.5226 50 125 1.5630 101.6083 0.5000 0.3964 0.201912 1.5226 50 125 1.5630 101.6083 0.5000 0.3964 0.203813 1.5226 50 125 1.5630 101.6083 0.5000 0.3964 0.205014 1.5226 50 125 1.5630 101.6083 0.5000 0.3964 0.207615 1.5226 50 125 1.5630 101.6083 0.5000 0.3964 0.209716 1.5226 50 125 1.5630 101.6083 0.5000 0.3964 0.212517 1.5223 50 125 1.5630 102.2855 0.5000 0.3965 0.212518 1.5223 50 125 1.5376 102.2855 0.5000 0.3965 0.215419 1.5223 50 125 1.5376 102.2855 0.5000 0.3965 0.218520 1.5223 50 125 1.5376 102.2855 0.5000 0.3965 0.218821 1.5223 50 125 1.5376 102.2855 0.5000 0.3965 0.219122 1.5223 50 125 1.5376 102.2855 0.5000 0.3965 0.219123 1.5223 50 125 1.5376 102.2855 0.5000 0.3965 0.220024 1.5223 50 125 1.5376 102.2855 0.5000 0.3965 0.220125 1.5223 50 125 1.5376 102.2855 0.5000 0.3965 0.220926 1.5223 50 125 1.5376 102.2855 0.5000 0.3965 0.226227 1.5223 50 125 1.5376 102.4426 0.5000 0.3965 0.227228 1.5223 50 125 1.5376 102.4426 0.5000 0.3965 0.227229 1.5223 50 125 1.5376 102.4426 0.5000 0.3965 0.2317
136
30 1.5223 50 125 1.5376 102.4426 0.5000 0.3965 0.233931 1.5223 50 125 1.5376 102.4426 0.5000 0.3965 0.249032 1.5223 50 125 1.5376 102.4426 0.5000 0.3965 0.249033 1.5223 50 125 1.5405 102.4790 0.5000 0.3965 0.250234 1.5223 50 125 1.5405 102.4790 0.5000 0.3965 0.250435 1.5223 50 125 1.5405 102.4790 0.5000 0.3965 0.251536 1.5223 50 125 1.5405 102.4790 0.5000 0.3965 0.252237 1.5223 50 125 1.5405 102.4790 0.5000 0.3965 0.253938 1.5223 50 125 1.5405 102.4790 0.5000 0.3965 0.258839 1.5223 50 125 1.5405 102.4790 0.5000 0.3965 0.258840 1.5223 50 125 1.5405 102.4790 0.5000 0.3965 0.258841 1.5223 50 125 1.5405 102.4790 0.5000 0.3965 0.260942 1.5223 50 125 1.5405 102.4790 0.5000 0.3965 0.261043 1.5223 50 125 1.5405 102.4790 0.5000 0.3965 0.261344 1.5223 50 125 1.5405 102.4790 0.5000 0.3965 0.261345 1.5223 50 125 1.5405 102.4790 0.5000 0.3965 0.261346 1.5223 50 125 1.5405 102.4790 0.5000 0.3965 0.262347 1.5223 50 125 1.5405 102.4790 0.5000 0.3965 0.262348 1.5223 50 125 1.5405 102.4790 0.5000 0.3965 0.266649 1.5223 50 125 1.5405 102.4790 0.5000 0.3965 0.269850 1.5223 50 125 1.5405 102.4790 0.5000 0.3965 0.2698
Finally, for bee colony size of 10, the max cycle per run is increased to 100.
The results of the experiments are shown in Figure 4.21. From the results, the
minimum Ra value achieved is 1.5223 jam and can be found in all tenth run except at
the second, fifth, eighth and ninth run.
137
Q A r t if ic ^ l Bee A lg o r ith m P ro g ra m
P r o c e s s P a r a m e t e r s O p t i m i z a t i o n of S u r f a c e R o u g h n e s s in E n d M i l l i n g a n d A b r a s i v e W a t e r j e t M a c h i n i n g
U s i n g A r t i f i c i a l B e e C o l o n y A l g o r i t h m
Ra*-5 .079^6 + (O.OS169 x i l ) + (0.07911 x 12 ) - (0.34221 x e3)~(0.0&>61 x i4 ) - (0.34S66 x x 5 ) - (0.00031 x i l : ) - (0.00012 x i i ?) + (0.10575 x *32) + (0.90041 x jt45) + (Q.Q7?9Q x x5j) - (0.00003 * si x *5) - (0.00009 x x2 x *5) + (0.03039 x x3 x *5} + (0.00513 x *4 *
Function fo r:
Colony S iz e :
Number of R un:
Max Cycles per R un:
Limit (abandoned food)
— Parameters Range---------
X1 X2 X3
Abrasive Waterjet
100
Uppest Threshold
120 T 3.5
Lowest Threshold
50 125
All best valuesfrun
run N u m .Cycles MinValue X I
1 100 1.5223 51 >
2 100 1.5229 51
3 100 1.5223 514 100 1.5223 51
5 100 1.5234 51
6 100 1.5223 517 ̂nn 1 COOT £.(
< I Z J r
Ready
Min Value, Fitnes A Mean of Fitness/Cycle
5
Figure 4.21 Results of 100 max cycles per run with limit of 50
The minimum Ra value is given by the third run. As shown in Table 4.25, the
minimum Ra value of 1.5223 jam is found at cycle 41 with the best fitness value of
0.3965. The set values of process parameters that lead to the minimum Ra value are
50/min traverse speed, 125Mpa waterjet pressure, 1.5648mm standoff distance,
102.4940|am abrasive gritsize and 0.5000g/s abrasive flowrate.
138
Table 4.25: The best value returned from 100 max cycle per run with limit of 50
Cycle Min Ra XI (V) X2 (P) X3 (h) X4 (a) X5
(m)
Best
fitness
Mean
fitness
1 3.5188 63.6171 150.7416 1.1125 102.1060 1.0243 0.2213 0.15952 3.5188 63.6171 150.7416 1.1125 102.1060 1.0243 0.2213 0.16003 3.5188 63.6171 150.7416 1.1125 102.1060 1.0243 0.2213 0.16354 3.5188 63.6171 150.7416 1.1125 102.1060 1.0243 0.2213 0.16595 3.2269 57.5342 150.7416 1.1125 102.1060 0.9540 0.2366 0.17066 3.1124 57.5342 148.3256 1.1125 99.4207 0.9297 0.2432 0.17307 2.7307 52.5931 144.9701 1.1125 99.4207 0.9297 0.2680 0.17968 1.8802 52.5931 127.1120 1.5159 99.4207 0.9062 0.3472 0.19599 1.7771 52.5931 125 1.5159 99.4207 0.9062 0.3601 0.199410 1.6755 52.5931 125 1.5159 101.2018 0.5816 0.3738 0.202311 1.5265 50 125 1.5159 101.2018 0.5122 0.3958 0.207512 1.5265 50 125 1.5159 101.2018 0.5122 0.3958 0.211413 1.5231 50 125 1.5159 101.2018 0.5000 0.3963 0.211714 1.5231 50 125 1.5159 101.2018 0.5000 0.3963 0.214615 1.5231 50 125 1.5159 101.2018 0.5000 0.3963 0.215116 1.5231 50 125 1.5159 101.2018 0.5000 0.3963 0.218217 1.5231 50 125 1.5159 101.2018 0.5000 0.3963 0.219118 1.5231 50 125 1.5159 101.2018 0.5000 0.3963 0.221119 1.5231 50 125 1.5159 101.2018 0.5000 0.3963 0.223320 1.5231 50 125 1.5159 101.2018 0.5000 0.3963 0.223721 1.5231 50 125 1.5159 101.2018 0.5000 0.3963 0.226222 1.5231 50 125 1.5159 101.2018 0.5000 0.3963 0.233123 1.5231 50 125 1.5159 101.2018 0.5000 0.3963 0.238724 1.5231 50 125 1.5159 101.2018 0.5000 0.3963 0.241225 1.5231 50 125 1.5159 101.2018 0.5000 0.3963 0.241526 1.5224 50 125 1.5159 102.4300 0.5000 0.3965 0.246727 1.5224 50 125 1.5718 102.4300 0.5000 0.3965 0.251928 1.5224 50 125 1.5718 102.4300 0.5000 0.3965 0.252929 1.5224 50 125 1.5718 102.4300 0.5000 0.3965 0.2585
139
30 1.5224 50 125 1.5718 102.4300 0.5000 0.3965 0.268431 1.5224 50 125 1.5718 102.4300 0.5000 0.3965 0.270132 1.5224 50 125 1.5718 102.4300 0.5000 0.3965 0.272133 1.5224 50 125 1.5718 102.4300 0.5000 0.3965 0.279434 1.5224 50 125 1.5718 102.4300 0.5000 0.3965 0.290735 1.5224 50 125 1.5718 102.4300 0.5000 0.3965 0.294836 1.5224 50 125 1.5718 102.4300 0.5000 0.3965 0.299437 1.5224 50 125 1.5718 102.4300 0.5000 0.3965 0.303938 1.5224 50 125 1.5718 102.4300 0.5000 0.3965 0.304039 1.5224 50 125 1.5718 102.4300 0.5000 0.3965 0.304840 1.5224 50 125 1.5718 102.4300 0.5000 0.3965 0.309341 1.5223 50 125 1.5648 102.4940 0.5000 0.3965 0.309542 1.5223 50 125 1.5648 102.4940 0.5000 0.3965 0.324043 1.5223 50 125 1.5648 102.4940 0.5000 0.3965 0.327244 1.5223 50 125 1.5648 102.4940 0.5000 0.3965 0.328945 1.5223 50 125 1.5648 102.4940 0.5000 0.3965 0.332546 1.5223 50 125 1.5648 102.4940 0.5000 0.3965 0.332547 1.5223 50 125 1.5648 102.4940 0.5000 0.3965 0.332848 1.5223 50 125 1.5648 102.4940 0.5000 0.3965 0.333349 1.5223 50 125 1.5648 102.4940 0.5000 0.3965 0.335750 1.5223 50 125 1.5648 102.4940 0.5000 0.3965 0.335751 1.5223 50 125 1.5648 102.4940 0.5000 0.3965 0.336752 1.5223 50 125 1.5648 102.4940 0.5000 0.3965 0.337353 1.5223 50 125 1.5648 102.4940 0.5000 0.3965 0.344354 1.5223 50 125 1.5648 102.4940 0.5000 0.3965 0.348155 1.5223 50 125 1.5648 102.4940 0.5000 0.3965 0.351156 1.5223 50 125 1.5648 102.4940 0.5000 0.3965 0.352957 1.5223 50 125 1.5648 102.4940 0.5000 0.3965 0.353758 1.5223 50 125 1.5648 102.4940 0.5000 0.3965 0.353759 1.5223 50 125 1.5648 102.4940 0.5000 0.3965 0.356260 1.5223 50 125 1.5648 102.4940 0.5000 0.3965 0.356261 1.5223 50 125 1.5648 102.4940 0.5000 0.3965 0.356262 1.5223 50 125 1.5648 102.4940 0.5000 0.3965 0.3569
140
63 1.5223 50 125 1.5648 102.4940 0.5000 0.3965 0.357164 1.5223 50 125 1.5648 102.4940 0.5000 0.3965 0.357365 1.5223 50 125 1.5648 102.4940 0.5000 0.3965 0.357966 1.5223 50 125 1.5648 102.4940 0.5000 0.3964 0.312567 1.5223 50 125 1.5648 102.4940 0.5000 0.3964 0.312868 1.5223 50 125 1.5648 102.4940 0.5000 0.3964 0.315369 1.5223 50 125 1.5545 102.4443 0.5000 0.3965 0.315570 1.5223 50 125 1.5545 102.4443 0.5000 0.3965 0.318871 1.5223 50 125 1.5545 102.4443 0.5000 0.3965 0.319072 1.5223 50 125 1.5545 102.4443 0.5000 0.3965 0.319073 1.5223 50 125 1.5545 102.4443 0.5000 0.3965 0.323574 1.5223 50 125 1.5545 102.4443 0.5000 0.3965 0.326275 1.5223 50 125 1.5545 102.4443 0.5000 0.3965 0.327176 1.5223 50 125 1.5545 102.4443 0.5000 0.3965 0.327277 1.5223 50 125 1.5545 102.4443 0.5000 0.3965 0.330978 1.5223 50 125 1.5545 102.4443 0.5000 0.3965 0.332079 1.5223 50 125 1.5545 102.4443 0.5000 0.3965 0.334780 1.5223 50 125 1.5545 102.4443 0.5000 0.3965 0.335781 1.5223 50 125 1.5545 102.4443 0.5000 0.3965 0.336482 1.5223 50 125 1.5545 102.4443 0.5000 0.3965 0.337083 1.5223 50 125 1.5545 102.4443 0.5000 0.3965 0.337484 1.5223 50 125 1.5545 102.4443 0.5000 0.3965 0.338385 1.5223 50 125 1.5545 102.4443 0.5000 0.3965 0.341286 1.5223 50 125 1.5545 102.4443 0.5000 0.3965 0.341787 1.5223 50 125 1.5545 102.4443 0.5000 0.3965 0.350388 1.5223 50 125 1.5545 102.4443 0.5000 0.3965 0.351389 1.5223 50 125 1.5545 102.4443 0.5000 0.3965 0.351990 1.5223 50 125 1.5545 102.4443 0.5000 0.3965 0.352791 1.5223 50 125 1.5545 102.4443 0.5000 0.3965 0.356092 1.5223 50 125 1.5545 102.4443 0.5000 0.3965 0.304293 1.5223 50 125 1.5507 102.5797 0.5000 0.3965 0.308694 1.5223 50 125 1.5507 102.5797 0.5000 0.3965 0.308695 1.5223 50 125 1.5507 102.5797 0.5000 0.3965 0.3124
141
96 1.5223 50 125 1.5507 102.5797 0.5000 0.3965 0.312997 1.5223 50 125 1.5507 102.5797 0.5000 0.3965 0.313598 1.5223 50 125 1.5507 102.5797 0.5000 0.3965 0.313899 1.5223 50 125 1.5507 102.5797 0.5000 0.3965 0.3143100 1.5223 50 125 1.5507 102.5797 0.5000 0.3965 0.3148
142
4.8.2 Colony size of 20 and limit of 100
The bee colony is increased to 20 and the limit is set to 100. The control
variables combinations value are shown in Table 4.26 below.
Table 4.26: Control variables combination with limit of 100
Colony Size Max cycles per run Limit (abandoned
food)
20 10 100
20 20 100
20 50 100
20 100 100
The first control variables combination is tested and the results are shown in
Figure 5.22. From the results, the lowest Ra value achieved is 1,6247|am at the eighth
143
?3 Artific ia l Bee A lgorithm Pre-gram
P r o c e s s P a r a m e t e r s O p t i m i z a t i o n of S u r f a c e R o u g h n e s s in E n d M i l l i n g a n d A b r a s i v e W a t e r j e t M a c h i n i n g
U s i n g A r t i f i c i a l B e e C o l o n y A l g o r i t h m
Ra --5.07976 +■ (0.0S169 x *1) + (0-07912 x i2 ) - (4.34221 x i3) - (0.0S661 x i4 ) (Q.34S66 m i5 ) - (0.00031 « xV) - (0.000t l * x2!> +<0. 10575 x * 3 ' ) + ( 0 . 0004] * *42) + ( 0. 07590 x x 5 J) - ( 0. 00COS * s ] x *5) - ( 0. 00009 x x ] k * 5 ) + ( 0. 03039 x *3 x s 5 ) + ( 0 . 00513 x * 4 * » 5 )
Function fo r :
Colony S iz e :
Number of Run:
Max Cycles per Run
Limit (abandoned fo od):
i— Parameters Range---------
X1 X2 X3
Abrasive W ate r#
X4 X5
Uppest Threshold:
120 3.5
Lowest Threshold:
125 60
All best valuesAun
run Num .Cycles MinValue X I
• • . <n«a i — ■ — < •5 10 4.1813 114.594'
6 10 2.3855 51
7 10 3.2220 83.494
8 10 1.6247 55 £
9 10 1.6682 St
10 10 1.9432 5( -v rri t
| S t o w Detail |
Ready
Min Value, Fitnes & Mean of Fitness/Cycle
Figure 4.22 Results of 10 max cycles per run with limit of 100
Table 4.27 below shows the best value returned from the eighth run. The
minimum Ra is achieved at cycle 10 with the best fitness value of 0.3810. The set
values of process parameters that lead to the minimum values of Ra value are 50/min
traverse speed, 125Mpa waterjet pressure, 1.8195mm standoff distance, 87.3173[am
abrasive gritsize and 0.5000g/s abrasive flowrate.
144
Table 4.27: The best value returned from 10 max cycle per run with limit of 100
Cycle Min Ra XI (V) X2 (P) X3 (h) X4 (a) X5
(m)
Best
fitness
Mean
fitness
1 2.3284 61.0663 126.4985 2.0314 85.4320 0.7824 0.3004 0.17602 2.3154 61.0663 126.4985 1.8985 85.4320 0.7824 0.3016 0.17923 2.2507 61.0663 126.4985 1.8985 85.4320 0.5000 0.3076 0.18134 2.2293 61.0663 126.4985 1.8985 87.0375 0.5000 0.3097 0.18255 1.7067 50 126.4985 1.8985 87.0375 0.5000 0.3695 0.19356 1.7039 50 126.4985 1.8579 87.0375 0.5000 0.3698 0.19477 1.7039 50 126.4985 1.8579 87.0375 0.5000 0.3698 0.19598 1.6271 50 125 1.8579 87.3173 0.5000 0.3807 0.19879 1.6271 50 125 1.8579 87.3173 0.5000 0.3807 0.199810 1.6247 50 125 1.8195 87.3173 0.5000 0.3810 0.2027
To discover better results, the max cycle per run value is increased to 20. The
results are shown in Figure 4.23. The minimum Ra value achieved is 1,5229|am at the
second run.
145
Q Artificial Bee Algorithm Progr*
P r o c e s s P a r a m e t e r s O p t i m i z a t i o n of S u r f a c e R o u g h n e s s in E n d M i l l i n g a n d A b r a s i v e W a t e r j e t M a c h i n i n g
U s i n g A r t i f i c i a l B e e C o l o n y A l g o r i t h m
Ra --5.07976 +■ (0.OS 1*9 x *1} + (0.07912 x x.2) - (0.34221 x i3 )-(0 .0 S 6 6 1 - i 4 ) - (Q.34S66 x x 5 )-(0 .0 0 0 3 1 x xV) - (0.00012 x x2!> +<0,10575 x (0.0004] * *4: ) + (0.07590 x x5J) - (O.OOOOS s i x x5) - (0.00009 x j j x x5)+ (0.03039 x r f x x5) + (0.00513 * x4 * x5)
Function fo r :
Colony S iz e :
Number of Run:
Max Cycles per Run :
Limit (abandoned food)
I— Parameters Range---------
X1 X2 X3
Abrasive Waterjet
20
100
X4 X5
Uppest Threshold:
150 250 120 3.5
Lowest Threshold:
125 | 1
All best valuesAun
run N um . Cycles MinValue X I
1 20 1.9572 5( -2 20 1.5229 SI
3 20 2.1370 5I =
4 20 2.3781 51.143-
5 20 1.8040 5(
6 20 1,52GB 5(7 Tifl 1 o cm cr
V III »
I Snow Detail
Ready
Min Value, Fitnes & Mean of Fitness/Cycle
Figure 4.23 Results of 20 max cycles per run with limit of 100
The best value returned are shown in Table 4.28 below where the minimum
Ra value 1,5229|am can be found at cycle 15. The best fitness value achieved is
0.3964 and the set values of process parameters that lead to the minimum Ra value
are 50/min traverse speed, 125Mpa waterjet pressure, 1.5563mm standoff distance,
103.7480|am abrasive gritsize and 0.5000g/s abrasive flowrate.
146
Table 4.28: The best value returned from 20 max cycle per run with limit of 100
Cycle Min Ra XI (V) X2 (P) X3 (h) X4 (d) X5
(m)
Best
fitness
Mean
fitness
1 3.0108 57.2225 143.1136 1.8934 119.0669 0.9003 0.2493 0.14182 2.9986 57.2225 143.1136 1.8322 118.5863 0.9003 0.2501 0.14833 2.9986 57.2225 143.1136 1.8322 118.5863 0.9003 0.2501 0.14874 2.9129 57.2225 143.1136 1.8322 111.6937 0.9003 0.2556 0.15105 2.4408 50 140.3886 1.8322 111.6937 0.9003 0.2906 0.16106 1.7020 50 125 1.4852 111.6937 0.9003 0.3701 0.17107 1.7020 50 125 1.4852 111.6937 0.9003 0.3701 0.17658 1.5574 50 125 1.4852 111.6937 0.5000 0.3910 0.17999 1.5364 50 125 1.4852 96.7044 0.5000 0.3943 0.181410 1.5364 50 125 1.4852 96.7044 0.5000 0.3943 0.181811 1.5234 50 125 1.4852 103.8398 0.5000 0.3963 0.183112 1.5234 50 125 1.4852 103.8398 0.5000 0.3963 0.186613 1.5234 50 125 1.4852 103.8398 0.5000 0.3963 0.194114 1.5233 50 125 1.4852 103.7480 0.5000 0.3963 0.198515 1.5229 50 125 1.5563 103.7480 0.5000 0.3964 0.201416 1.5229 50 125 1.5563 103.7480 0.5000 0.3964 0.201417 1.5229 50 125 1.5563 103.7480 0.5000 0.3964 0.203518 1.5229 50 125 1.5563 103.7480 0.5000 0.3964 0.204719 1.5229 50 125 1.5563 103.7480 0.5000 0.3964 0.206020 1.5229 50 125 1.5563 103.7480 0.5000 0.3964 0.2112
Figure 4.24 below show better results are achieved when the max cycle per
run value is increased to 50. The minimum Ra value achieved is 1.5223[am at the
third, fifth, sixth and ninth run.
147
Q Artificial Bee A lgorithm Program L^j__P r o c e s s P a r a m e t e r s O p t i m i z a t i o n of S u r f a c e R o u g h n e s s in E n d M i l l i n g a n d A b r a s i v e W a t e r j e t M a c h i n i n g
U s i n g A r t i f i c i a l B e e C o l o n y A l g o r i t h m
Ra *-5.079^6 + (0.0S169 X 11) + (0.07911 x 1 2 ) - (0.34221 x E3)-(0 .0 tttfl - i4) - (0.34S66 x i 5 ) - (0.00031 x i l : ) - (0.00012 x r i * ) +(0.10575 x x33) + (0.90041 x jt45) + (0.07590 x x5J) - (0.00003 * s ] x *5) - (0.00009 x x2 x *5) + (0.03039 x x3 x 5*5} + (B.00513 x *4 x *5}
Function fo r:
Colony S iz e :
Number of R un:
Max Cycles per R un:
Limit (abandoned food)
— Parameters Range---------
X1 X2 X3
Abrasive Waterjet
20
T »
X4 X5
Uppest Threshold
120 3.5
Lowest Threshold
SO 125 1
All best valuesAun
run N u m .Cycles MinValue X I
5 50 1.5223 51•
6 50 1.5223 5(
7 50 1.5224 5( ~ |
8 50 1.5257 51
9 50 j 1.5223 H 5(
10 50 1.5226 5( -
' 1 111 □ t
^ o y v Detail
Ready
Min Value, Fitnes A Mean of Fitness/Cycle
10 20 30 40 50Cycle
5
Figure 4.24 Results of 50 max cycles per run with limit of 100
The best value returned from the ninth run is shown in Table 4.29 where the
minimum Ra value is 1.5223pm with the best fitness value 0.3965. The minimum Ra
value is found in cycle 35. The set values of process parameters that lead to the
minimum values of Ra value are 50/min traverse speed, 125Mpa waterjet pressure,
1.5295mm standoff distance, 102.3062pm abrasive gritsize and 0.5000g/s abrasive
flowrate.
148
Table 4.29: The best value returned from 50 max cycle per run with limit of 100
Cycle Min Ra XI (V) X2 (P) X3 (h) X4 (d) X5
(m)
Best
fitness
Mean
fitness
1 2.8625 57.9995 140.0170 1.3421 80.6551 0.7452 0.2589 0.17012 2.7050 57.9995 137.3707 1.3421 80.6551 0.5520 0.2699 0.17503 2.6773 57.9995 137.3707 1.3421 82.2914 0.5520 0.2719 0.17724 1.9199 50.2000 125.3663 1.3332 89.5340 1.5207 0.3425 0.19175 1.6765 50.2000 125.3663 1.3534 89.5340 0.7313 0.3736 0.19626 1.6585 50.2000 125 1.3534 89.5340 0.7313 0.3762 0.19957 1.6585 50.2000 125 1.3534 89.5340 0.7313 0.3762 0.20298 1.6480 50 125 1.6559 89.5340 0.7313 0.3776 0.20529 1.6480 50 125 1.6559 89.5340 0.7313 0.3776 0.208010 1.6480 50 125 1.6559 89.5340 0.7313 0.3776 0.214211 1.6285 50 125 1.6559 91.8201 0.7313 0.3804 0.218912 1.6281 50 125 1.6411 91.8201 0.7313 0.3805 0.223713 1.6231 50 125 1.6411 91.8201 0.7127 0.3812 0.228314 1.6001 50 125 1.6411 91.8201 0.6239 0.3846 0.231615 1.5699 50 125 1.6357 91.8201 0.5000 0.3891 0.232916 1.5699 50 125 1.6357 91.8201 0.5000 0.3891 0.237717 1.5699 50 125 1.6357 91.8201 0.5000 0.3891 0.243418 1.5683 50 125 1.6098 91.9539 0.5000 0.3894 0.245419 1.5683 50 125 1.6098 91.9539 0.5000 0.3894 0.248920 1.5683 50 125 1.6098 91.9539 0.5000 0.3894 0.254921 1.5561 50 125 1.6098 93.4747 0.5000 0.3912 0.261422 1.5561 50 125 1.6098 93.4747 0.5000 0.3912 0.263523 1.5561 50 125 1.6098 93.4747 0.5000 0.3912 0.264224 1.5446 50 125 1.6098 95.1844 0.5000 0.3930 0.266125 1.5446 50 125 1.6098 95.1844 0.5000 0.3930 0.266426 1.5255 50 125 1.6098 99.9104 0.5000 0.3960 0.268527 1.5251 50 125 1.5679 99.9104 0.5000 0.3960 0.276128 1.5251 50 125 1.5679 99.9104 0.5000 0.3960 0.277229 1.5251 50 125 1.5679 99.9104 0.5000 0.3960 0.2808
149
30 1.5250 50 125 1.5679 99.9460 0.5000 0.3960 0.282831 1.5245 50 125 1.5679 100.2020 0.5000 0.3961 0.284332 1.5245 50 125 1.5679 100.2020 0.5000 0.3961 0.287333 1.5245 50 125 1.5295 100.2020 0.5000 0.3961 0.289634 1.5245 50 125 1.5295 100.2020 0.5000 0.3961 0.290135 1.5223 50 125 1.5295 102.3062 0.5000 0.3965 0.295736 1.5223 50 125 1.5295 102.3062 0.5000 0.3965 0.296037 1.5223 50 125 1.5295 102.3062 0.5000 0.3965 0.296838 1.5223 50 125 1.5295 102.3062 0.5000 0.3965 0.307439 1.5223 50 125 1.5295 102.3062 0.5000 0.3965 0.310740 1.5223 50 125 1.5295 102.3062 0.5000 0.3965 0.313841 1.5223 50 125 1.5295 102.3062 0.5000 0.3965 0.316442 1.5223 50 125 1.5295 102.3830 0.5000 0.3965 0.318643 1.5223 50 125 1.5295 102.3830 0.5000 0.3965 0.321044 1.5223 50 125 1.5295 102.3830 0.5000 0.3965 0.321445 1.5223 50 125 1.5295 102.3830 0.5000 0.3965 0.322846 1.5223 50 125 1.5295 102.3830 0.5000 0.3965 0.323747 1.5223 50 125 1.5295 102.6003 0.5000 0.3965 0.324248 1.5223 50 125 1.5295 102.4046 0.5000 0.3965 0.325249 1.5223 50 125 1.5295 102.4046 0.5000 0.3965 0.327150 1.5223 50 125 1.5295 102.4046 0.5000 0.3965 0.3284
Lastly for limit of 100, the max cycle per run value is increased to 100. The
results are shown in Figure 4.25 where the minimum Ra value achieved is 1.5223 jam
at all 10 run.
H Artificial Bee Algorithm Progn
P r o c e s s P a r a m e t e r s O p t i m i z a t i o n of S u r f a c e R o u g h n e s s in E n d M i l l i n g a n d A b r a s i v e W a t e r j e t M a c h i n i n g
U s i n g A r t i f i c i a l B e e C o l o n y A l g o r i t h m
R* =- 5 .0 7 9 7 6 + ( 0 .0 S 1 6 9 x 1 1) + (0 .0 7 9 1 2 m i 2 ) - (0 .3 4 2 2 1 * x 3 ) - ( 0 .0 S 6 6 1 m i 4 ) - ( 0 . 3 4 S 6 6 > x S ) - (0 .0 0 0 3 1 x i l ? ) - < 0 .0 0 0 1 2 x i 2 ?> +(0.10575 x x33) ■+■ (0.00041 * xtf) + (0.07590 * x5J) - (0.00003 - * l x * 5 ) - (0.00009 *5) + (0.03059 x *3 * *5) + (0.00513 x *4 * *5}
Function fo r:
Colony S iz e :
Number of R un:
Max Cycles per Run :
Limit (abandoned fo od):
p— Parameters Range —
X1 X2
Abrasive Waterjet
X3 X4 X5
Uppest Threshold:
3.5
Lowest Threshold
125 60
All best valuesAun
run Num .Cycles MinValue X I
1 100 1.5223 5(
2 100 1.5223 si3 100 1.5223 5E
4 100 1.5223 SI
5 100 1.5223 5(
6 100 1.5223 5(7 •inn_ 1 c/
< 1 nr r
Ready
Min Value, Fitnes & Mean of Fitness/Cycle
1.5
Figure 4.25 Results of 100 max cycles per run with limit of 100
The best value returned from the third run is shown in Table 4.30. The
minimum Ra value is 1.5223[am with the best fitness value 0.3965 are found in cycle
58. The set values of process parameters that lead to the minimum values of Ra value
are 50/min traverse speed, 125Mpa waterjet pressure, 1.5333mm standoff distance,
102.7407j.im abrasive gritsize and 0.5000g/s abrasive flowrate.
151
Table 4.30: The best value returned from 100 max cycle per run with limit of 100
Cycle Min Ra XI (V) X2 (P) X3 (h) X4 (a) X5
(m)
Best
fitness
Mean
fitness
1 3.3086 50.9788 128.0358 3.3277 118.1032 2.5124 0.2321 0.14332 3.2595 50 128.0358 3.3277 118.1032 2.5124 0.2348 0.14703 3.0972 50 128.0358 3.3277 109.8899 2.5124 0.2441 0.14874 3.0972 50 128.0358 3.3277 109.8899 2.5124 0.2441 0.14915 2.9499 50 125 3.3277 109.8899 2.5124 0.2532 0.15206 2.6661 50 125 2.5274 109.8899 2.5124 0.2728 0.15627 2.6661 50 125 2.5274 109.8899 2.5124 0.2728 0.15818 2.5968 50 125 2.5274 109.8899 2.4060 0.2780 0.16099 2.5968 50 125 2.5274 109.8899 2.4060 0.2780 0.163310 2.5968 50 125 2.5274 109.8899 2.4060 0.2780 0.165711 2.5968 50 125 2.5274 109.8899 2.4060 0.2780 0.170112 2.5968 50 125 2.5274 109.8899 2.4060 0.2780 0.171613 2.5968 50 125 2.5274 109.8899 2.4060 0.2780 0.174914 2.5968 50 125 2.5274 109.8899 2.4060 0.2780 0.177015 2.5627 50 125 2.4296 109.8899 2.3917 0.2807 0.178016 2.5627 50 125 2.4296 109.8899 2.3917 0.2807 0.179917 2.0880 50 125 2.3857 109.8899 1.5851 0.3238 0.191918 1.9841 50 125 2.3857 106.8684 1.4365 0.3351 0.201819 1.9841 50 125 2.3857 106.8684 1.4365 0.3351 0.212720 1.9757 50 125 2.3442 106.8684 1.4365 0.3361 0.213521 1.9338 50 125 2.3442 95.0809 1.4365 0.3409 0.218222 1.9338 50 125 2.3442 95.0809 1.4365 0.3409 0.219523 1.7823 50 125 2.3442 95.0809 1.0425 0.3594 0.223324 1.7698 50 125 2.3442 98.2695 1.0257 0.3610 0.226525 1.7659 50 125 2.3231 98.2695 1.0257 0.3615 0.233826 1.7659 50 125 2.3231 98.2695 1.0257 0.3615 0.234927 1.7659 50 125 2.3231 98.2695 1.0257 0.3615 0.239828 1.7659 50 125 2.3231 98.2695 1.0257 0.3615 0.239929 1.7531 50 125 2.3231 98.2695 0.9905 0.3632 0.2404
152
30 1.7490 50 125 1.9125 91.1636 1.0671 0.3638 0.250231 1.7442 50 125 2.3231 100.5453 0.9667 0.3644 0.257132 1.5974 50 125 1.4825 94.6507 0.6920 0.3850 0.264833 1.5814 50 125 1.4825 99.0751 0.6920 0.3874 0.266434 1.5720 50 125 1.4825 99.0751 0.6599 0.3888 0.267835 1.5720 50 125 1.4825 99.0751 0.6599 0.3888 0.270936 1.5720 50 125 1.4825 99.0751 0.6599 0.3888 0.272937 1.5702 50 125 1.4825 100.2715 0.6599 0.3891 0.273738 1.5702 50 125 1.4825 100.2715 0.6599 0.3891 0.279339 1.5702 50 125 1.4825 100.2715 0.6599 0.3891 0.279540 1.5702 50 125 1.4825 100.2715 0.6599 0.3891 0.280141 1.5702 50 125 1.4879 100.2715 0.6599 0.3891 0.280642 1.5241 50 125 1.4879 104.3914 0.5000 0.3962 0.281543 1.5241 50 125 1.4899 104.3914 0.5000 0.3962 0.282144 1.5241 50 125 1.4899 104.3914 0.5000 0.3962 0.282845 1.5241 50 125 1.4899 104.3914 0.5000 0.3962 0.286846 1.5241 50 125 1.4899 104.3914 0.5000 0.3962 0.291347 1.5241 50 125 1.4899 104.3914 0.5000 0.3962 0.302848 1.5241 50 125 1.4899 104.3914 0.5000 0.3962 0.302949 1.5241 50 125 1.4899 104.3914 0.5000 0.3962 0.305050 1.5241 50 125 1.4899 104.3914 0.5000 0.3962 0.306051 1.5241 50 125 1.4899 104.3914 0.5000 0.3962 0.306252 1.5241 50 125 1.4899 104.3914 0.5000 0.3962 0.306853 1.5238 50 125 1.5333 104.3914 0.5000 0.3962 0.308654 1.5236 50 125 1.5333 104.2812 0.5000 0.3963 0.309755 1.5236 50 125 1.5333 104.2812 0.5000 0.3963 0.310556 1.5236 50 125 1.5333 104.2812 0.5000 0.3963 0.311357 1.5236 50 125 1.5333 104.2812 0.5000 0.3963 0.311958 1.5223 50 125 1.5333 102.7407 0.5000 0.3965 0.312259 1.5223 50 125 1.5333 102.6660 0.5000 0.3965 0.315960 1.5223 50 125 1.5333 102.6660 0.5000 0.3965 0.318361 1.5223 50 125 1.5333 102.6660 0.5000 0.3965 0.319062 1.5223 50 125 1.5333 102.6660 0.5000 0.3965 0.3208
153
63 1.5223 50 125 1.5333 102.6660 0.5000 0.3965 0.321664 1.5223 50 125 1.5333 102.3463 0.5000 0.3965 0.323265 1.5223 50 125 1.5333 102.3463 0.5000 0.3965 0.327966 1.5223 50 125 1.5371 102.3463 0.5000 0.3965 0.334167 1.5223 50 125 1.5371 102.3463 0.5000 0.3965 0.337168 1.5223 50 125 1.5380 102.3463 0.5000 0.3965 0.337369 1.5223 50 125 1.5380 102.4036 0.5000 0.3965 0.338170 1.5223 50 125 1.5383 102.4036 0.5000 0.3965 0.341271 1.5223 50 125 1.5383 102.4036 0.5000 0.3965 0.341772 1.5223 50 125 1.5383 102.4036 0.5000 0.3965 0.341973 1.5223 50 125 1.5383 102.4036 0.5000 0.3965 0.347574 1.5223 50 125 1.5383 102.4036 0.5000 0.3965 0.354275 1.5223 50 125 1.5383 102.4036 0.5000 0.3965 0.355676 1.5223 50 125 1.5383 102.4036 0.5000 0.3965 0.358077 1.5223 50 125 1.5383 102.4036 0.5000 0.3965 0.360278 1.5223 50 125 1.5383 102.4036 0.5000 0.3965 0.361979 1.5223 50 125 1.5383 102.4036 0.5000 0.3965 0.362880 1.5223 50 125 1.5383 102.4036 0.5000 0.3965 0.362981 1.5223 50 125 1.5429 102.4036 0.5000 0.3965 0.365382 1.5223 50 125 1.5429 102.4036 0.5000 0.3965 0.365883 1.5223 50 125 1.5429 102.4036 0.5000 0.3965 0.366684 1.5223 50 125 1.5429 102.4036 0.5000 0.3965 0.366785 1.5223 50 125 1.5429 102.4036 0.5000 0.3965 0.367286 1.5223 50 125 1.5429 102.4175 0.5000 0.3965 0.3674
87 1.5223 50 125 1.5429 102.4175 0.5000 0.3965 0.370088 1.5223 50 125 1.5429 102.4175 0.5000 0.3965 0.370989 1.5223 50 125 1.5429 102.4175 0.5000 0.3965 0.371190 1.5223 50 125 1.5429 102.4175 0.5000 0.3965 0.371691 1.5223 50 125 1.5429 102.4175 0.5000 0.3965 0.373392 1.5223 50 125 1.5429 102.4175 0.5000 0.3965 0.373393 1.5223 50 125 1.5429 102.4175 0.5000 0.3965 0.374394 1.5223 50 125 1.5429 102.4175 0.5000 0.3965 0.374395 1.5223 50 125 1.5429 102.4712 0.5000 0.3965 0.3764
154
96 1.5223 50 125 1.5433 102.4712 0.5000 0.3965 0.378397 1.5223 50 125 1.5433 102.4712 0.5000 0.3965 0.378398 1.5223 50 125 1.5433 102.4712 0.5000 0.3965 0.380399 1.5223 50 125 1.5433 102.4712 0.5000 0.3965 0.3803100 1.5223 50 125 1.5433 102.4712 0.5000 0.3965 0.3806
155
4.8.3 Colony size of 50 and limit of 250
The bee colony size is increased to 50 and the limit is set to 250. The control
variables combinations value are shown in Table 4.31 below.
Table 4.31: Control variables combination with limit of 250
Colony Size Max cycles per run Limit (abandoned
food)
50 10 250
50 20 250
50 50 250
50 100 250
The results of the first control variables combination with max cycles per run
of 10 is shown in Figure 4.26. From the results, the minimum Ra value achieved is
1.5769(j,m at eighth runs.
156
H Artificial Bee Algorithm Progr< ..... 1------- 1Process P a ra m e te rs O p t im iza t io n of Su rface R oughness in End M i l l in g and A b ra s iv e W a t e r j e t M a c h in in g
Using A r t i f ic ia l Bee Co lo n y A lg o r i th m
R a --5.07976 +■ (0 .OS 1*9 x *1} + (0.07912 x i2 ) - (4.34221 x i 3 ) - (0.03661 - i 4 ) - (Q.34S66 * i 5 ) -(0 .0 0 0 3 1 x x V ) - (0.00012 x x2!> +<0,10575 x (0 .0004] x x 4 ') + (0 .07590 x *5 J) - (0 .00003 s ] x *5) - (0 .00009 x *2 * x 5 ) + (0 .03039 x x3 * x 5 ) + (0 .0 0 5 1 3 x * 4 x x5)
Function f o r : A brasive W aterjet
50
10
10
250RUN
Colony S iz e :
Number of R u n :
M ax Cycles per Run :
Limit (abandoned fo o d ):
j— Parameters R ange---------
X1 X 2 X3 X 4 X5
Uppest Threshold:
150 250 120 3.5
Low est Threshold:
50 125 | I
All best valuesAun
run Num. Cycles MinValue X I
5 10 2.4953 5( *
6 10 1 .8655 5(7 10 1.6656 5(8 10 1.5769 5t =
9 10 3.8389 102.696:10 10 2.1287 5( -
< in □ r
I Snow Detad
Ready
Min Value, Fitnes & M ean of Fitness/Cycle
Figure 4.26 Results of 10 max cycles per run with limit of 250
The best value returned from the eighth run is shown in Table 4.32. The
minimum Ra value achieved is 1.5769pm with the best fitness value 0.3881 at cycle
ten. The set values of process parameters that lead to the minimum Ra value are
50/min traverse speed, 125Mpa waterjet pressure, 1.5515mm standoff distance,
92.0639pm abrasive gritsize and 0.5421g/s abrasive flowrate.
157
Table 4.32: The best value returned from 10 max cycle per run with limit of 250
Cycle Min Ra XI (V) X2 (P) X3 (h) X4 (a) X5
(m)
Best
fitness
Mean
fitness
1 2.7684 50.0163 147.1365 1.6606 80.1993 0.5703 0.2654 0.14102 2.7676 50 147.1365 1.6606 80.1993 0.5703 0.2654 0.14273 1.7402 50 125 1.6606 80.1993 0.5703 0.3649 0.15084 1.7402 50 125 1.6606 80.1993 0.5703 0.3649 0.15375 1.6202 50 125 1.6606 87.9062 0.5424 0.3817 0.15676 1.6202 50 125 1.6606 87.9062 0.5424 0.3817 0.1593
7 1.6202 50 125 1.6606 87.9062 0.5424 0.3817 0.16238 1.6202 50 125 1.6606 87.9062 0.5424 0.3817 0.16359 1.6180 50 125 1.6606 88.0939 0.5424 0.3820 0.1666
10 1.5769 50 125 1.5515 92.0639 0.5424 0.3881 0.1712
To find out better results, the max cycle per run value is increased to 20. The
results are shown in Figure 4.27. The minimum Ra value achieved is 1.5280(j,m at the
first run. This minimum Ra value is 3% much better compared to the previous Ra
value.
158
S 3 A rtific ia l Bee A lg o rith m Progr:
Process P a ra m e te r s O p t im iza t io n of Su rface R oughness in End M i l l in g and A b ra s iv e W a t e r j e t M a c h in in g
Using A r t i f ic ia l Bee Co lo n y A lg o r i th m
R a ■-5.07976 MO OS 1*9 x i l ) + (0.07912 x *2) - (4.34221 * *3) - (0.0S661 - i4 ) - (0.34S66 x x 5 )-<0.04031 x x V ) - (0.44012 >: r 2 !> +<0.10575 x i 3 ' ) + (0.0004] x x42) + (0 .0 7 5 9 0 x *5 J) - <0.00003 ■ x l x *5) - (0 ,00009 x j I k x5 ) + (0 .03039 > i 3 x »5} + (0 .0 0 5 1 3 * * 4 x *5)
Function f o r : A brasive W aterjet
501020
250RUN
Colony S iz e :
Number of R u n :
M ax Cycles per Run :
Limit (abandoned fo o d ):
j— Parameters R ange---------
X1 X 2 X3 X 4 X5
Uppest Threshold:
150 250 1 2 0 3 .5
Low est Threshold:
125 | 1
Ail best valuesAun
run Num. Cycles MinValue X I
1 20 1.5280 5(2 20 1.6384 5t3 20 1.9638 5t F
4 20 1.5735 5t
5 20 2.2999 5(6 20 1.6117 5(7 ~>n T A 11C-
* III □ r
I Snow Detail
Ready
Min Value, Fitnes & M ean of Fitness/Cycle
Figure 4.27: Results of 20 max cycles per run with limit of 250
The results in Table 4.33 show the minimum Ra value achieved at cycle 20
with the best fitness value of 0.3956. The set values of process parameters that lead
to the minimum Ra value are 50m/min traverse speed, 125Mpa waterjet pressure,
1.5283mm standoff distance, 98.7731 pm abrasive gritsize and 0.5000 g/s abrasive
flowrate.
159
Table 4.33: The best value returned from 20 max cycle per run with limit of 250
Cycle Min Ra XI (V) X2 (P) X3 (h) X4 (a) X5
(m)
Best
fitness
Mean
fitness
1 3.7331 77.8498 128.9791 3.6607 109.8497 1.2889 0.2113 0.14002 3.7331 77.8498 128.9791 3.6607 109.8497 1.2889 0.2113 0.14153 3.6606 77.8498 128.9791 3.5012 109.8497 1.2889 0.2146 0.14624 2.7072 54.3676 128.9791 3.5012 109.8497 1.2889 0.2697 0.15085 2.7072 54.3676 128.9791 3.5012 109.8497 1.2889 0.2697 0.15426 2.7072 54.3676 128.9791 3.5012 109.8497 1.2889 0.2697 0.15597 2.2724 54.3676 125 2.8457 109.8497 1.2889 0.3056 0.16218 2.0573 50 125 2.8457 109.8497 1.2889 0.3271 0.16499 2.0134 50 125 2.8457 104.1823 1.2889 0.3319 0.172610 2.0124 50 125 2.8457 104.1823 1.2867 0.3320 0.176311 1.7578 50 125 2.4134 98.5039 0.9571 0.3626 0.182312 1.6988 50 125 2.4134 98.5039 0.7878 0.3705 0.185513 1.6974 50 125 2.4134 99.6131 0.7878 0.3707 0.188914 1.6974 50 125 2.4134 99.6131 0.7878 0.3707 0.190415 1.5328 50 125 1.5031 97.4698 0.5000 0.3948 0.198916 1.5328 50 125 1.5031 97.4698 0.5000 0.3948 0.2003
17 1.5327 50 125 1.5283 97.4698 0.5000 0.3948 0.207018 1.5327 50 125 1.5283 97.4698 0.5000 0.3948 0.210119 1.5327 50 125 1.5283 97.4698 0.5000 0.3948 0.2133
20 1.5280 50 125 1.5283 98.7731 0.5000 0.3956 0.2169
The number of max cycles per run is then increased to 50 and the results are
shown in Figure 4.28. The minimum Ra value achieved is 1.5223[am at all 10 runs
except at the third, seven and ninth run.
16 0
H A rtific ia l Bee A lg o rith m Progr;
Process P a ra m e te r s O p t im iza t io n of Su rface R oug hness in End M i l l in g and A b ra s iv e W a t e r j e t M a c h in in g
Using A r t i f i c ia l Bee C o lo n y A lg o r i th m
R a =-5 .0 7 9 ^ 6 + (0.OS169 x i l ) + (0 .07911 x 12 ) - (0 .34221 x e3 )-(0 .0 & > 6 1 - i 4 ) - (0 .34S66 x i 5 ) - (0 .00031 x i V ) - (0 .00012 x r i* ) +(0 ,1 0 5 7 5 x *3 3) + (0.£)0041 x jt45) + (Q.07?9Q x x5 j) - (0 .00003 X i ] x * 5 ) - (0 .0 0 0 0 9 x x2 x * 5 ) + (0 .03039 x * 3 x *5} + (0 .00513 x * 4 x x5}
Function fo r :
Colony Size:
Number of Run:
Max Cycles per Run:
Limit (abandoned food)
i— Parameters Range-------
X1 X2 X3
Abrasive Waterjet
X4 X5
Uppest Threshold
120 3.5
Lowest Threshold
SO 125
All best valuesAunrun N u m .Cycles M in V a lu e X I
1 . ■*« **5 50 1.5223 51
6 50 1.5223 5(
7 50 1.5232 5(
8 50 1.5223 51 =
9 50 1.5226 5(
10 50 ■ ■ ■ E 2 2 E 5t -
* | nr 3 t
j^ovy Detail
Ready
Min Value, Fitnes A Mean of Fitness/Cycle
Cycle
Figure 4.28 Results of 50 max cycles per run with limit of 250
Table 4.34 below show the best value returned from 50 max cycles per run
and the minimum Ra value achieved at cycle 26 with fitness value 0.3965. The set
values of process parameters that lead to the minimum Ra value are 50/min traverse
speed, 125Mpa waterjet pressure, 1.5428 mm standoff distance, 102.5184pm
abrasive gritsize and 0.5000g/s abrasive flowrate.
f
161
Table 4.34: The best value returned from 50 max cycle per run with limit of 250
Cycle Min Ra XI (V) X2 (P) X3 (h) X4 (d) X5
(m)
Best
fitness
Mean
fitness
1 2.4406 58.4597 129.1298 1.4424 94.9639 1.4188 0.2906 0.15412 2.4406 58.4597 129.1298 1.4424 94.9639 1.4188 0.2906 0.15793 2.4348 58.4597 129.0094 1.4424 94.9639 1.4188 0.2911 0.16164 1.9686 53.4644 128.9087 2.4313 100.5644 0.5000 0.3369 0.17105 1.7108 53.4644 125 1.9248 100.5644 0.5000 0.3689 0.17486 1.7099 53.4644 125 1.9248 103.7482 0.5000 0.3690 0.17977 1.7099 53.4644 125 1.9248 103.7482 0.5000 0.3690 0.18208 1.7099 53.4644 125 1.9248 103.7482 0.5000 0.3690 0.18509 1.7099 53.4644 125 1.9248 103.7482 0.5000 0.3690 0.189110 1.7099 53.4644 125 1.9248 103.7482 0.5000 0.3690 0.193311 1.5324 50 125 1.8446 103.7482 0.5000 0.3949 0.198412 1.5324 50 125 1.8446 103.7482 0.5000 0.3949 0.201913 1.5323 50 125 1.8446 103.6489 0.5000 0.3949 0.204614 1.5323 50 125 1.8446 103.6489 0.5000 0.3949 0.206315 1.5318 50 125 1.8446 102.9040 0.5000 0.3950 0.213416 1.5267 50 125 1.7477 102.9040 0.5000 0.3958 0.2148
17 1.5267 50 125 1.7477 102.9040 0.5000 0.3958 0.216618 1.5225 50 125 1.5879 102.9040 0.5000 0.3964 0.219119 1.5225 50 125 1.5879 102.9040 0.5000 0.3964 0.221420 1.5225 50 125 1.5879 102.9040 0.5000 0.3964 0.226221 1.5225 50 125 1.5879 102.9040 0.5000 0.3964 0.228022 1.5225 50 125 1.5879 102.9040 0.5000 0.3964 0.232923 1.5225 50 125 1.5879 102.9040 0.5000 0.3964 0.234624 1.5225 50 125 1.5879 102.2331 0.5000 0.3964 0.236825 1.5225 50 125 1.5879 102.2331 0.5000 0.3964 0.2393
26 1.5223 50 125 1.5490 102.2331 0.5000 0.3965 0.241827 1.5223 50 125 1.5490 102.2331 0.5000 0.3965 0.243628 1.5223 50 125 1.5490 102.2331 0.5000 0.3965 0.245229 1.5223 50 125 1.5490 102.2331 0.5000 0.3965 0.2456
162
30 1.5223 50 125 1.5490 102.3732 0.5000 0.3965 0.247431 1.5223 50 125 1.5490 102.3732 0.5000 0.3965 0.250832 1.5223 50 125 1.5490 102.4474 0.5000 0.3965 0.253033 1.5223 50 125 1.5490 102.4474 0.5000 0.3965 0.255434 1.5223 50 125 1.5490 102.4474 0.5000 0.3965 0.257835 1.5223 50 125 1.5490 102.4474 0.5000 0.3965 0.261236 1.5223 50 125 1.5422 102.4474 0.5000 0.3965 0.262237 1.5223 50 125 1.5422 102.4474 0.5000 0.3965 0.264038 1.5223 50 125 1.5422 102.4474 0.5000 0.3965 0.2660
39 1.5223 50 125 1.5422 102.4474 0.5000 0.3965 0.267240 1.5223 50 125 1.5422 102.4474 0.5000 0.3965 0.270141 1.5223 50 125 1.5422 102.4474 0.5000 0.3965 0.273042 1.5223 50 125 1.5428 102.4474 0.5000 0.3965 0.276643 1.5223 50 125 1.5428 102.4474 0.5000 0.3965 0.278644 1.5223 50 125 1.5428 102.5184 0.5000 0.3965 0.279445 1.5223 50 125 1.5428 102.5184 0.5000 0.3965 0.284446 1.5223 50 125 1.5428 102.5184 0.5000 0.3965 0.285347 1.5223 50 125 1.5428 102.5184 0.5000 0.3965 0.286248 1.5223 50 125 1.5428 102.5184 0.5000 0.3965 0.2904
49 1.5223 50 125 1.5428 102.5184 0.5000 0.3965 0.290850 1.5223 50 125 1.5428 102.5184 0.5000 0.3965 0.2926
Lastly for limit of 250, the max cycles per run is increased to 100. The results
are shown in the Figure 4.29 below. The minimum Ra value achieved is 1,5223pm at
all 10 runs.
163
H Artificial Bee Algorithm Progr;
Process P a ra m e te r s O p t im iza t io n of Su rface R oug hness in End M i l l in g and A b ra s iv e W a t e r j e t M a c h in in g
Using A r t i f i c ia l Bee C o lo n y A lg o r i th m
R a =-5 .0 7 9 ^ 6 + (O.OS169 x i l ) + (0.07911 x 12 ) - (0 .34221 x e3 )-(0 .0 & i61 x i 4 ) - (0 .34S66 x i 5 ) - (0 .00031 m i l :) - (0 .00012 x r i s) +(0 ,1 0 5 7 5 x x3 3) + (0 .00041 x * 4 ! ) + (0 .0 7 5 9 0 x x5 J) ~ (0 .00003 X s i x x5 ) - (0 .0 0 0 0 9 x x 2 x * 5 ) + (0 .0 3 0 3 9 x x 3 x 5*5} + (0 .0 0 5 1 3 x * 4 x »5}
Function f o r :
Colony S iz e :
Number of R u n :
M ax Cycles per R u n :
Limit (abandoned food)
i— Param eters R ange---------
X1 X2 X3
Abrasive W aterjet
100
J?
X 4 X5
Uppest Threshold
120 3.5
L ow est Threshold
50 125
All best valuesAun
run N u m .Cycles M in V a lu e | X I
1 100 | 1 5 2 2 3 ® 5( >
2 100 1.5223 51
3 100 1.5223 St r
4 100 1.5223 St
5 100 1.5223 5(
6 100 1.5223 5(7 ̂nn
< | " I1 COOT
2 ----- r
^ o w Detail
Ready
Min V alue , Fitnes A Mean of Fitness/Cycle
Cycle
5
Figure 4.29 Results of 100 max cycles per run with limit of 250
The best returned value of 100 max cycles per runs is achieved at the first
runs. In Table 4.35 below, the minimum Ra value of 1.5223[am is achieved at cycle
26 with the best fitness value of 0.3965. The set values of process parameters that
lead to the minimum Ra value are 50/min traverse speed, 125Mpa waterjet pressure,
1.5522 mm standoff distance, 102.4524|am abrasive gritsize and 0.5000g/s abrasive
flowrate.
164
Table 4.35: The best value returned from 100 max cycle per run with limit of 250
Cycle Min Ra XI (V) X2 (P) X3 (h) X4 (a) X5
(m)
Best
fitness
Mean
fitness
1 3.7331 77.8498 128.9791 3.6607 109.8497 1.2889 0.2113 0.14002 3.7331 77.8498 128.9791 3.6607 109.8497 1.2889 0.2113 0.14153 3.6606 77.8498 128.9791 3.5012 109.8497 1.2889 0.2146 0.14624 2.7072 54.3676 128.9791 3.5012 109.8497 1.2889 0.2697 0.15085 2.7072 54.3676 128.9791 3.5012 109.8497 1.2889 0.2697 0.15426 2.7072 54.3676 128.9791 3.5012 109.8497 1.2889 0.2697 0.15597 2.2724 54.3676 125 2.8457 109.8497 1.2889 0.3056 0.16218 2.0573 50 125 2.8457 109.8497 1.2889 0.3271 0.16499 2.0134 50 125 2.8457 104.1823 1.2889 0.3319 0.172610 2.0124 50 125 2.8457 104.1823 1.2867 0.3320 0.176311 1.7578 50 125 2.4134 98.5039 0.9571 0.3626 0.182312 1.6988 50 125 2.4134 98.5039 0.7878 0.3705 0.185513 1.6974 50 125 2.4134 99.6131 0.7878 0.3707 0.188914 1.6974 50 125 2.4134 99.6131 0.7878 0.3707 0.190415 1.5328 50 125 1.5031 97.4698 0.5000 0.3948 0.198916 1.5328 50 125 1.5031 97.4698 0.5000 0.3948 0.2003
17 1.5327 50 125 1.5283 97.4698 0.5000 0.3948 0.207018 1.5327 50 125 1.5283 97.4698 0.5000 0.3948 0.210119 1.5327 50 125 1.5283 97.4698 0.5000 0.3948 0.213320 1.5280 50 125 1.5283 98.7731 0.5000 0.3956 0.216921 1.5280 50 125 1.5283 98.7731 0.5000 0.3956 0.219422 1.5280 50 125 1.5283 98.7731 0.5000 0.3956 0.220623 1.5280 50 125 1.5522 98.7731 0.5000 0.3956 0.223424 1.5280 50 125 1.5522 98.7731 0.5000 0.3956 0.229125 1.5273 50 125 1.5522 99.0059 0.5000 0.3957 0.2308
26 1.5223 50 125 1.5522 102.4524 0.5000 0.3965 0.233527 1.5223 50 125 1.5522 102.4524 0.5000 0.3965 0.235028 1.5223 50 125 1.5522 102.4524 0.5000 0.3965 0.237229 1.5223 50 125 1.5522 102.4524 0.5000 0.3965 0.2390
165
30 1.5223 50 125 1.5522 102.4524 0.5000 0.3965 0.243831 1.5223 50 125 1.5522 102.4524 0.5000 0.3965 0.245232 1.5223 50 125 1.5522 102.4524 0.5000 0.3965 0.246233 1.5223 50 125 1.5446 102.4524 0.5000 0.3965 0.250534 1.5223 50 125 1.5446 102.4524 0.5000 0.3965 0.251935 1.5223 50 125 1.5446 102.4524 0.5000 0.3965 0.255536 1.5223 50 125 1.5446 102.4524 0.5000 0.3965 0.257137 1.5223 50 125 1.5446 102.4524 0.5000 0.3965 0.262538 1.5223 50 125 1.5446 102.4524 0.5000 0.3965 0.2665
39 1.5223 50 125 1.5446 102.4524 0.5000 0.3965 0.270140 1.5223 50 125 1.5446 102.4524 0.5000 0.3965 0.271241 1.5223 50 125 1.5446 102.4524 0.5000 0.3965 0.272542 1.5223 50 125 1.5446 102.4524 0.5000 0.3965 0.276043 1.5223 50 125 1.5446 102.4524 0.5000 0.3965 0.280744 1.5223 50 125 1.5446 102.4524 0.5000 0.3965 0.285045 1.5223 50 125 1.5446 102.4524 0.5000 0.3965 0.287046 1.5223 50 125 1.5446 102.4524 0.5000 0.3965 0.288847 1.5223 50 125 1.5446 102.4649 0.5000 0.3965 0.291248 1.5223 50 125 1.5446 102.4649 0.5000 0.3965 0.291949 1.5223 50 125 1.5446 102.4649 0.5000 0.3965 0.295050 1.5223 50 125 1.5446 102.4649 0.5000 0.3965 0.297951 1.5223 50 125 1.5446 102.4649 0.5000 0.3965 0.300652 1.5223 50 125 1.5446 102.4649 0.5000 0.3965 0.301553 1.5223 50 125 1.5446 102.4649 0.5000 0.3965 0.303754 1.5223 50 125 1.5446 102.4649 0.5000 0.3965 0.305055 1.5223 50 125 1.5446 102.4649 0.5000 0.3965 0.306156 1.5223 50 125 1.5446 102.4649 0.5000 0.3965 0.3090
57 1.5223 50 125 1.5446 102.4649 0.5000 0.3965 0.312758 1.5223 50 125 1.5446 102.4649 0.5000 0.3965 0.3133
59 1.5223 50 125 1.5446 102.4649 0.5000 0.3965 0.315260 1.5223 50 125 1.5436 102.4880 0.5000 0.3965 0.318861 1.5223 50 125 1.5436 102.4880 0.5000 0.3965 0.322262 1.5223 50 125 1.5436 102.4880 0.5000 0.3965 0.3232
166
63 1.5223 50 125 1.5446 102.4770 0.5000 0.3965 0.324864 1.5223 50 125 1.5446 102.4770 0.5000 0.3965 0.325665 1.5223 50 125 1.5446 102.4770 0.5000 0.3965 0.327066 1.5223 50 125 1.5453 102.4770 0.5000 0.3965 0.328267 1.5223 50 125 1.5453 102.4770 0.5000 0.3965 0.329568 1.5223 50 125 1.5453 102.4770 0.5000 0.3965 0.330469 1.5223 50 125 1.5453 102.4770 0.5000 0.3965 0.332970 1.5223 50 125 1.5453 102.4825 0.5000 0.3965 0.334371 1.5223 50 125 1.5453 102.4825 0.5000 0.3965 0.336072 1.5223 50 125 1.5453 102.4825 0.5000 0.3965 0.338873 1.5223 50 125 1.5453 102.4825 0.5000 0.3965 0.340374 1.5223 50 125 1.5453 102.4825 0.5000 0.3965 0.342975 1.5223 50 125 1.5453 102.4835 0.5000 0.3965 0.344076 1.5223 50 125 1.5453 102.4835 0.5000 0.3965 0.346277 1.5223 50 125 1.5453 102.4835 0.5000 0.3965 0.349578 1.5223 50 125 1.5453 102.4835 0.5000 0.3965 0.3505
79 1.5223 50 125 1.5453 102.4835 0.5000 0.3965 0.350780 1.5223 50 125 1.5453 102.4835 0.5000 0.3965 0.352781 1.5223 50 125 1.5453 102.4835 0.5000 0.3965 0.355782 1.5223 50 125 1.5453 102.4835 0.5000 0.3965 0.357983 1.5223 50 125 1.5453 102.4835 0.5000 0.3965 0.358884 1.5223 50 125 1.5448 102.4835 0.5000 0.3965 0.358985 1.5223 50 125 1.5448 102.4835 0.5000 0.3965 0.359386 1.5223 50 125 1.5448 102.4835 0.5000 0.3965 0.3605
87 1.5223 50 125 1.5448 102.4835 0.5000 0.3965 0.361288 1.5223 50 125 1.5448 102.4835 0.5000 0.3965 0.3622
89 1.5223 50 125 1.5448 102.4835 0.5000 0.3965 0.363790 1.5223 50 125 1.5448 102.4835 0.5000 0.3965 0.364391 1.5223 50 125 1.5448 102.4835 0.5000 0.3965 0.365592 1.5223 50 125 1.5448 102.4835 0.5000 0.3965 0.366093 1.5223 50 125 1.5448 102.4835 0.5000 0.3965 0.366694 1.5223 50 125 1.5448 102.4835 0.5000 0.3965 0.368895 1.5223 50 125 1.5448 102.4835 0.5000 0.3965 0.3696
167
96 1.5223 50 125 1.5448 102.4835 0.5000 0.3965 0.370197 1.5223 50 125 1.5448 102.4835 0.5000 0.3965 0.371998 1.5223 50 125 1.5448 102.4835 0.5000 0.3965 0.372599 1.5223 50 125 1.5448 102.4835 0.5000 0.3965 0.3734100 1.5223 50 125 1.5448 102.4868 0.5000 0.3965 0.3745
168
For the final experiments of AWJ, the limit value is increased to 500 to
analyze whether it will give superior results from the prior size of bee colony. The
combination of control variables are given in Table 4.36.
4.8.4 Colony size of 100 and limit of 500
Table 4.36: Control variables combination with limit of 500
Colony Size Max cycles per run Limit (abandoned
food)
100 10 500
100 20 500
100 50 500
100 100 500
The first combination of control variables with limit of 500 gives a minimum Ra
value of 1.7025(j,m in the sixth run as shown in Figure 4.30.
169
H Artificial Bee Algorithm Progr; l—
Process P a ra m e te r s O p t im iza t io n of Su rface R oug hness in End M i l l in g and A b ra s iv e W a t e r j e t M a c h in in g
Using A r t i f i c ia l Bee C o lo n y A lg o r i th m
R a =-5 .0 7 9 ^ 6 + (O.OS169 x i l ) + (0 .07911 x 12 ) - (0 .34221 x e 3 ) - ( O .O & t f l x i 4 ) - (0 .34S66 x i 5 ) - (0 .00031 x i l : ) - (0 .00012 x r f s) +(0 ,1 0 5 7 5 x * 3 J) + (0 .90041 x j*4! ) + (0 .0 7 590 x x5j) - (0 .00003 * s i x j*5) - (0 .0 0 0 0 9 x x 2 x 5*5) + (0 .03039 x x 3 x 5*5} + (0 .00513 x * 4 x »5}
Function f o r :
Colony S iz e :
Number of R u n :
M ax Cycles per R u n :
Limit (abandoned food)
j— Param eters R ange---------
X1 X2 X3
Abrasive W aterjet
] J?
X 4 X5
Uppest Threshold
120 3.5
L ow est Threshold
SO 125
All best valuesAun
run N u m .Cycles M in V a lu e X I
1 10 2.1076 61.798; *
2 10 1.9366 51
3 10 1.8048 51 K
4 10 1.9518 55.547*
5 10 2.8528 78 .727J
6 10 1.7025 517 ̂n _ T11QO R'l 7C.C.'
< I HI r
jjhovy Detail
Ready
Min V alue , Fitnes A Mean of Fitness/Cycle
Cycle
5
Figure 4.30 Results of 10 max cycles per run with limit of 500
From the results of the first control variables combinations, the best fitness
achieved is 0.3700 and the set values of process parameters that lead to the minimum
values of Ra value were 50/min traverse speed, 125Mpa waterjet pressure, 2.1894
mm standoff distance, 105.0051 [am abrasive gritsize and 0.8849g/s abrasive flowrate.
The minimum Ra value is achieved at cycle 10. This is shown in Table 4.37.
170
Table 4.37: The best value returned from 10 max cycle per run with limit of 500
Cycle Min Ra XI (V) X2 (P) X3 (h) X4 (d) X5
(m)
Best
fitness
Mean
fitness
1 3.0485 52.3725 125 2.4067 92.6455 3.2450 0.2470 3.04852 3.0273 52.3725 125 2.4067 86.6599 3.2450 0.2483 3.02733 2.9094 50 125 2.4067 86.6599 3.2450 0.2558 2.90944 2.8429 50 125 2.1266 86.6599 3.2450 0.2602 2.84295 2.7381 50 141.2298 3.0432 113.3087 0.8982 0.2675 2.73816 2.4477 50.7560 125 2.8223 91.0909 2.1794 0.2901 2.44777 1.9679 50 125 3.0432 113.3087 0.8849 0.3369 1.96798 1.8787 50 125 2.7427 113.3087 0.8849 0.3474 0.16649 1.8768 50 125 2.7424 113.1437 0.8849 0.3476 0.1694
10 1.7025 50 125 2.1894 105.0051 0.8849 0.3700 0.1733
Next, the number of max cycle per run is increased to 50. The results are
shown at Figure 4.31 where the minimum Ra value achieved is 1.5223[am at the fifth
171
P 3 Artificial Bee Algorithm Progn
Process P a ra m e te rs O p t im iza t io n of Su rface R oughness in End M i l l in g and A b ra s iv e W a t e r j e t M a c h in in g
Using A r t i f ic ia l Bee Co lo n y A lg o r i th m
R a is-5.07976 +■ (0.0S169 x i l ) + (0.07912 x i2 ) - (0.34221 x i 3 ) - (0.03661 - i4 ) - (Q.34S66 * x5)-(0.00031 x x V ) - (0.00012 x x2!> +<0.10575 x (0 .0004] * *42) + (0 .07590 x *5 J) - (0 .00003 s i x *5) - (0 .00009 x j j x x 5 )+ (0 .03039 x i 3 * s 5 ) + (0 .0 0 5 1 3 x x 4 * *5)
Abf asjve Waterjet
100Function f o r :
Colony S iz e :
Number of R u n :
M ax Cycles per Run :
Limit (abandoned fo o d ):
I— Parameters R ange---------
X1 X 2 X3 X 4 X5
Uppest Threshold:
500
150 250 120 3.5
Low est Threshold:
50 125 | 1
All best valuesAun
run N u m . Cycles M in V a lu e X I
3 20 1.5290 5( *
4 20 1 .9526 51
5 20 1.5223 5( B
6 2Q 1.8499 5t I7 20 1 .7774 5(
8 20 1.5753 5( -
< IK □ r
! Snow Detail
Ready
Min Value, Fitnes & M ean of Fitness/Cycle
50 0.5
Figure 4.31 Results of 20 max cycles per run with limit of 500
Table 4.38 below shows the best value returned from 20 max cycles per run
and the minimum Ra value is achieved at cycle 19 with fitness value 0.3965. The set
values of process parameters that lead to the minimum Ra value are 50/min traverse
speed, 125Mpa waterjet pressure, 1.5359 mm standoff distance, 102.3683|am
abrasive gritsize and 0.5000g/s abrasive flowrate.
172
Table 4.38: The best value returned from 20 max cycle per run with limit of 500
Cycle Min Ra XI (V) X2 (P) X3 (h) X4 (a) X5
(m)
Best
fitness
Mean
fitness
1 2.6782 57.2655 125 2.7471 67.8716 1.2845 0.2719 0.14812 2.6782 57.2655 125 2.7471 67.8716 1.2845 0.2719 0.15073 2.6013 57.2655 125 2.4336 67.8716 1.2845 0.2777 0.15464 2.6013 57.2655 125 2.4336 67.8716 1.2845 0.2777 0.15855 2.5975 57.2655 125 2.4154 67.8716 1.2845 0.2780 0.16086 2.5415 57.2655 125 2.0943 67.8716 1.2845 0.2824 0.1632
7 2.0984 50 125 2.0943 67.8716 0.8484 0.3227 0.16708 2.0096 50 125 2.0943 70.0319 0.6581 0.3323 0.16949 2.0096 50 125 2.0943 70.0319 0.6581 0.3323 0.174310 2.0096 50 125 2.0943 70.0319 0.6581 0.3323 0.176411 2.0096 50 125 2.0943 70.0319 0.6581 0.3323 0.178312 2.0096 50 125 2.0943 70.0319 0.6581 0.3323 0.180613 1.9585 57.7059 125 1.9942 100.7599 0.6390 0.3380 0.183314 1.9557 57.7059 125 1.9942 100.7599 0.6298 0.3383 0.185315 1.7787 50 125 2.0943 79.0936 0.5000 0.3599 0.187516 1.7787 50 125 2.0943 79.0936 0.5000 0.3599 0.1902
17 1.7431 50 125 2.0943 81.0289 0.5000 0.3646 0.192918 1.5436 50 125 1.9942 102.3683 0.5000 0.3931 0.1966
19 1.5223 50 125 1.5359 102.3683 0.5000 0.3965 0.199920 1.5223 50 125 1.5359 102.3895 0.5000 0.3965 0.2027
The number of max cycles per run is then increased to 50 and the results are
shown in Figure 4.32. The minimum Ra value achieved is 1.5223[am at all 10 runs
except at the second and eighth run.
173
H A rtific ia l Bee A lg o rith m Progr; Id - - !■£$■!Process P a ra m e te r s O p t im iza t io n of Su rface R oug hness in End M i l l in g and A b ra s iv e W a t e r j e t M a c h in in g
Using A r t i f i c ia l Bee C o lo n y A lg o r i th m
R a =-5 .0 7 9 ^ 6 + (0 .0 5 1 6 9 x i l ) + (0 .07911 x 12 ) - (0 .34221 x x 3 ) ~ ( 0 .0 t t t f l x i4) - (0 .34S66 x i 5 ) - (0 .00031 x i V ) - (0 .00012 x x2 ?) +(0 ,1 0 5 7 5 x x3 3) + (0.£)0041 x jt45) + (0 .07590 x x5 J) - (0 .00003 x s i x x5) - (0 .0 0 0 0 9 x x 2 x *5 ) + (0 .03039 x * 3 x *5} + (0 .00513 x * 4 * *5}
Function f o r :
Colony S iz e :
Number of R u n :
M ax Cycles per R u n :
Limit (abandoned food)
i— Param eters R ange---------
X1 X2 X3
Abrasive W aterjet
T »
X 4 X5
Uppest Threshold
120 3.5
L ow est Threshold
SO 1 25 1
All best valuesAun
run N u m .Cycles M in V a lu e X I
1 50 1.5223 5( >
2 50 1.5227 51
3 50 1.5223 5[ r
4 50 1.5223. 5t
5 50 1.5223 5(
6 50 1.5223 5(7 cn 1 COOT
< | rtr 3 r
jShow Petal
Ready
Min V alue , Fitnes A Mean of Fitness/Cycle
Cycle
Figure 4.32 Results of 50 max cycles per run with limit of 500
In Table 4.39 below, the minimum Ra value of 1.5223[am is achieved at cycle
15 with the best fitness value of 0.3965. The set values of process parameters that
lead to the minimum Ra value are 50/min traverse speed, 125Mpa waterjet pressure,
1.5479 mm standoff distance, 102.521 ljam abrasive gritsize and 0.5000g/s abrasive
flowrate.
5
174
Table 4.39: The best value returned from 50 max cycle per run with limit of 500
Cycle Min Ra XI (V) X 2(P ) X3 (h) X4 (d) X5
(m)
Best
fitness
Mean
fitness
1 2.8657 58.0213 145.3158 1.3389 100.4561 0.5129 0.2587 0.14372 2.8657 58.0213 145.3158 1.3389 100.4561 0.5129 0.2587 0.14713 2.7811 50 139.0474 1.3128 71.4895 1.4976 0.2645 0.15044 2.7811 50 139.0474 1.3128 71.4895 1.4976 0.2645 0.15415 2.7811 50 139.0474 1.3128 71.4895 1.4976 0.2645 0.15566 2.5200 58.0213 137.7459 1.6673 102.1511 0.5129 0.2841 0.15777 2.3723 58.0213 134.5636 1.6673 102.1511 0.5129 0.2965 0.15998 1.9129 58.0213 125 1.6186 102.1511 0.5129 0.3433 0.16279 1.5266 50 125 1.6186 102.1511 0.5129 0.3958 0.165610 1.5266 50 125 1.6186 102.1511 0.5129 0.3958 0.168611 1.5266 50 125 1.6186 102.1511 0.5129 0.3958 0.171912 1.5229 50 125 1.6186 102.1511 0.5000 0.3964 0.176313 1.5229 50 125 1.6186 102.1511 0.5000 0.3964 0.178714 1.5229 50 125 1.6186 102.1511 0.5000 0.3964 0.1813
15 1.5223 50 125 1.5479 102.1511 0.5000 0.3965 0.184316 1.5223 50 125 1.5479 102.6075 0.5000 0.3965 0.186917 1.5223 50 125 1.5479 102.4509 0.5000 0.3965 0.190918 1.5223 50 125 1.5479 102.4509 0.5000 0.3965 0.192819 1.5223 50 125 1.5479 102.4509 0.5000 0.3965 0.195120 1.5223 50 125 1.5479 102.4509 0.5000 0.3965 0.198221 1.5223 50 125 1.5479 102.4509 0.5000 0.3965 0.200522 1.5223 50 125 1.5479 102.4509 0.5000 0.3965 0.204223 1.5223 50 125 1.5479 102.4509 0.5000 0.3965 0.206724 1.5223 50 125 1.5479 102.4509 0.5000 0.3965 0.209125 1.5223 50 125 1.5479 102.4509 0.5000 0.3965 0.213226 1.5223 50 125 1.5479 102.4509 0.5000 0.3965 0.214727 1.5223 50 125 1.5479 102.4509 0.5000 0.3965 0.217128 1.5223 50 125 1.5450 102.5492 0.5000 0.3965 0.219329 1.5223 50 125 1.5450 102.5492 0.5000 0.3965 0.2243
175
30 1.5223 50 125 1.5450 102.5492 0.5000 0.3965 0.227531 1.5223 50 125 1.5450 102.5492 0.5000 0.3965 0.231032 1.5223 50 125 1.5450 102.5492 0.5000 0.3965 0.233233 1.5223 50 125 1.5450 102.5492 0.5000 0.3965 0.235334 1.5223 50 125 1.5450 102.5492 0.5000 0.3965 0.240435 1.5223 50 125 1.5450 102.5492 0.5000 0.3965 0.241836 1.5223 50 125 1.5450 102.5492 0.5000 0.3965 0.244837 1.5223 50 125 1.5450 102.5492 0.5000 0.3965 0.249838 1.5223 50 125 1.5450 102.5492 0.5000 0.3965 0.2540
39 1.5223 50 125 1.5450 102.5492 0.5000 0.3965 0.258240 1.5223 50 125 1.5450 102.5342 0.5000 0.3965 0.261641 1.5223 50 125 1.5450 102.5342 0.5000 0.3965 0.264242 1.5223 50 125 1.5450 102.5342 0.5000 0.3965 0.267643 1.5223 50 125 1.5450 102.5331 0.5000 0.3965 0.269844 1.5223 50 125 1.5450 102.4594 0.5000 0.3965 0.272745 1.5223 50 125 1.5450 102.4594 0.5000 0.3965 0.273746 1.5223 50 125 1.5450 102.4594 0.5000 0.3965 0.277247 1.5223 50 125 1.5450 102.4594 0.5000 0.3965 0.278448 1.5223 50 125 1.5454 102.5045 0.5000 0.3965 0.2823
49 1.5223 50 125 1.5454 102.5045 0.5000 0.3965 0.286050 1.5223 50 125 1.5454 102.5045 0.5000 0.3965 0.2904
Finally, for limit of 500, the max cycles per run is increased to 100. The
results are shown in the Figure 4.33 below. The minimum Ra value achieved is
1.5223 jam at all 10 runs.
176
H Artificial Bee Algorithm Progr;
Process P a ra m e te r s O p t im iza t io n of Su rface R oug hness in End M i l l in g and A b ra s iv e W a t e r j e t M a c h in in g
Using A r t i f i c ia l Bee C o lo n y A lg o r i th m
R a =-5 .0 7 9 ^ 6 + (0 .0 5 1 6 9 x i l ) + (0 .07911 x 12 ) - (0 .34221 x e 3 )- (0 .0 & > 6 1 - i 4 ) - (0 .34S66 x s5 ) - (0 .00031 x i l 3) - (0 .00012 x r i * ) +(0 ,1 0 5 7 5 x * 3 3) + (0 .EJ0041 x jt45) + (0 .0 7 590 * %5J) - (0 .00003 * x l x * 5 ) - (0 .00009 x x 2 x * 5 ) + (0 .0 3 0 3 9 x x 3 x 5*5} + (0 .0 0 5 1 3 x * 4 x *5 }
Function f o r :
Colony S iz e :
Number of R u n :
M ax Cycles per R u n :
Limit (abandoned food)
i— Param eters R ange---------
X1 X2 X3
Abrasive W aterjet
100
X 4 X5
Uppest Threshold
130 3.5
L ow est Threshold
SO 1 25 1
All best valuesAun
run N u m .Cycles M in V alue X I
5 100 1.5223 5(•
6 100 1.5223 5(
7 100 1.5223 5( ~ 1
8 100 1.5223 51 =
9 103 1.5223 ■ 5(
10 100 1.5223 5( -
' I Hi □ r
i Show Detail
Ready
Min V alue , Fitnes A Mean of Fitness/Cycle
5
Figure 4.33 Results of 100 max cycles per run with limit of 500
The best returned value of 100 max cycles per runs is achieved at the ninth
runs. In Table 4.40 below, the minimum Ra value of 1.5223[am achieved at cycle
eight with the best fitness value of 0.3965. The set values of process parameters that
lead to the minimum Ra value are 50/min traverse speed, 125Mpa waterjet pressure,
1.5504 mm standoff distance, 102.5213[am abrasive gritsize and 0.5000g/s abrasive
flowrate.
177
Table 4.40: The best value returned from 100 max cycle per run with limit of 500
Cycle Min Ra XI (V) X2 (P) X3 (h) X4 (a) X5
(m)
Best
fitness
Mean
fitness
1 2.2441 61.6679 125 1.1142 105.8174 0.9604 0.3083 0.13982 2.2441 61.6679 125 1.1142 105.8174 0.9604 0.3083 0.14193 2.2131 61.6679 125 1.3407 105.8174 0.9078 0.3112 0.14404 1.6647 50 125 1.3407 105.8174 0.9078 0.3753 0.15025 1.6647 50 125 1.3407 105.8174 0.9078 0.3753 0.15216 1.6629 50 125 1.5504 105.8174 0.9078 0.3755 0.1576
7 1.5695 50 125 1.6020 93.3007 0.5501 0.3892 0.1601
8 1.5223 50 125 1.5504 102.5213 0.5000 0.3965 0.16389 1.5223 50 125 1.5504 102.5213 0.5000 0.3965 0.166110 1.5223 50 125 1.5504 102.5213 0.5000 0.3965 0.169011 1.5223 50 125 1.5504 102.5213 0.5000 0.3965 0.171812 1.5223 50 125 1.5504 102.5213 0.5000 0.3965 0.174713 1.5223 50 125 1.5504 102.5213 0.5000 0.3965 0.178714 1.5223 50 125 1.5504 102.5213 0.5000 0.3965 0.180815 1.5223 50 125 1.5504 102.5213 0.5000 0.3965 0.187016 1.5223 50 125 1.5450 102.5213 0.5000 0.3965 0.1915
17 1.5223 50 125 1.5450 102.5213 0.5000 0.3965 0.192718 1.5223 50 125 1.5450 102.5213 0.5000 0.3965 0.197819 1.5223 50 125 1.5450 102.5213 0.5000 0.3965 0.201020 1.5223 50 125 1.5450 102.5213 0.5000 0.3965 0.204221 1.5223 50 125 1.5450 102.5213 0.5000 0.3965 0.207322 1.5223 50 125 1.5450 102.5213 0.5000 0.3965 0.210323 1.5223 50 125 1.5450 102.5213 0.5000 0.3965 0.213724 1.5223 50 125 1.5450 102.5050 0.5000 0.3965 0.217725 1.5223 50 125 1.5450 102.5050 0.5000 0.3965 0.220126 1.5223 50 125 1.5450 102.5050 0.5000 0.3965 0.2226
27 1.5223 50 125 1.5450 102.5050 0.5000 0.3965 0.226528 1.5223 50 125 1.5450 102.5050 0.5000 0.3965 0.229629 1.5223 50 125 1.5450 102.5050 0.5000 0.3965 0.2319
178
30 1.5223 50 125 1.5450 102.5050 0.5000 0.3965 0.234231 1.5223 50 125 1.5450 102.5050 0.5000 0.3965 0.239732 1.5223 50 125 1.5450 102.5050 0.5000 0.3965 0.241833 1.5223 50 125 1.5450 102.5050 0.5000 0.3965 0.245834 1.5223 50 125 1.5450 102.5050 0.5000 0.3965 0.250635 1.5223 50 125 1.5450 102.5050 0.5000 0.3965 0.253136 1.5223 50 125 1.5450 102.5050 0.5000 0.3965 0.255537 1.5223 50 125 1.5450 102.5050 0.5000 0.3965 0.258138 1.5223 50 125 1.5450 102.5050 0.5000 0.3965 0.2651
39 1.5223 50 125 1.5450 102.5050 0.5000 0.3965 0.268940 1.5223 50 125 1.5450 102.5050 0.5000 0.3965 0.270241 1.5223 50 125 1.5450 102.5050 0.5000 0.3965 0.272942 1.5223 50 125 1.5450 102.5050 0.5000 0.3965 0.278443 1.5223 50 125 1.5450 102.5050 0.5000 0.3965 0.282144 1.5223 50 125 1.5450 102.5050 0.5000 0.3965 0.285445 1.5223 50 125 1.5450 102.5050 0.5000 0.3965 0.287246 1.5223 50 125 1.5450 102.5050 0.5000 0.3965 0.290047 1.5223 50 125 1.5450 102.5050 0.5000 0.3965 0.292148 1.5223 50 125 1.5450 102.5050 0.5000 0.3965 0.2946
49 1.5223 50 125 1.5450 102.5050 0.5000 0.3965 0.296650 1.5223 50 125 1.5450 102.5050 0.5000 0.3965 0.298351 1.5223 50 125 1.5450 102.5050 0.5000 0.3965 0.301052 1.5223 50 125 1.5450 102.5050 0.5000 0.3965 0.302753 1.5223 50 125 1.5450 102.5050 0.5000 0.3965 0.306254 1.5223 50 125 1.5450 102.5050 0.5000 0.3965 0.307455 1.5223 50 125 1.5450 102.5050 0.5000 0.3965 0.310456 1.5223 50 125 1.5450 102.5050 0.5000 0.3965 0.3128
57 1.5223 50 125 1.5450 102.5050 0.5000 0.3965 0.314558 1.5223 50 125 1.5450 102.5050 0.5000 0.3965 0.3166
59 1.5223 50 125 1.5450 102.5050 0.5000 0.3965 0.318160 1.5223 50 125 1.5450 102.5050 0.5000 0.3965 0.320661 1.5223 50 125 1.5450 102.5050 0.5000 0.3965 0.322262 1.5223 50 125 1.5450 102.5050 0.5000 0.3965 0.3228
179
63 1.5223 50 125 1.5450 102.5050 0.5000 0.3965 0.324364 1.5223 50 125 1.5450 102.5050 0.5000 0.3965 0.325365 1.5223 50 125 1.5450 102.5050 0.5000 0.3965 0.326666 1.5223 50 125 1.5450 102.5050 0.5000 0.3965 0.327367 1.5223 50 125 1.5450 102.5050 0.5000 0.3965 0.330068 1.5223 50 125 1.5450 102.5050 0.5000 0.3965 0.331769 1.5223 50 125 1.5450 102.5050 0.5000 0.3965 0.332870 1.5223 50 125 1.5450 102.5050 0.5000 0.3965 0.334171 1.5223 50 125 1.5450 102.5050 0.5000 0.3965 0.336572 1.5223 50 125 1.5450 102.5050 0.5000 0.3965 0.338073 1.5223 50 125 1.5450 102.5050 0.5000 0.3965 0.340574 1.5223 50 125 1.5450 102.5050 0.5000 0.3965 0.342275 1.5223 50 125 1.5450 102.5050 0.5000 0.3965 0.344976 1.5223 50 125 1.5450 102.5050 0.5000 0.3965 0.345477 1.5223 50 125 1.5450 102.5050 0.5000 0.3965 0.346278 1.5223 50 125 1.5450 102.5050 0.5000 0.3965 0.347979 1.5223 50 125 1.5450 102.5002 0.5000 0.3965 0.348880 1.5223 50 125 1.5450 102.5002 0.5000 0.3965 0.349581 1.5223 50 125 1.5450 102.5002 0.5000 0.3965 0.353282 1.5223 50 125 1.5450 102.5002 0.5000 0.3965 0.355883 1.5223 50 125 1.5450 102.5002 0.5000 0.3965 0.360584 1.5223 50 125 1.5450 102.5002 0.5000 0.3965 0.362785 1.5223 50 125 1.5450 102.5002 0.5000 0.3965 0.363086 1.5223 50 125 1.5450 102.5002 0.5000 0.3965 0.3645
87 1.5223 50 125 1.5450 102.5002 0.5000 0.3965 0.365888 1.5223 50 125 1.5450 102.5002 0.5000 0.3965 0.3663
89 1.5223 50 125 1.5450 102.5002 0.5000 0.3965 0.366590 1.5223 50 125 1.5450 102.5002 0.5000 0.3965 0.366791 1.5223 50 125 1.5450 102.5002 0.5000 0.3965 0.368692 1.5223 50 125 1.5450 102.4978 0.5000 0.3965 0.369593 1.5223 50 125 1.5450 102.4978 0.5000 0.3965 0.370194 1.5223 50 125 1.5450 102.4978 0.5000 0.3965 0.371295 1.5223 50 125 1.5450 102.4978 0.5000 0.3965 0.3717
180
96 1.5223 50 125 1.5450 102.4978 0.5000 0.3965 0.371797 1.5223 50 125 1.5450 102.4978 0.5000 0.3965 0.372598 1.5223 50 125 1.5450 102.4978 0.5000 0.3965 0.373199 1.5223 50 125 1.5450 102.4978 0.5000 0.3965 0.3736100 1.5223 50 125 1.5450 102.4978 0.5000 0.3965 0.3742
4.9 Summary of end milling experimental results
181
A number of 10, 20, 50 and 100 colony sizes have been tested and the
algorithm has been run 10 times for each of the population size. From the experiment
it can be observed that the lowest value of Ra can be achieved by using the smallest
bee colony size of 10. The bee colony size of 10 gives a minimal Ra value of
0.1719|am even though the value of bee colony size is increased to 100. All control
variables combination with the bee colony size of 10 gives a minimal Ra value of
1.1719(j,m in first runs. In bee colony size of 20, the first control variables
combination gives a minimal Ra value of 0.1725|am. This Ra value is improved by
0.3% when the max cycles per run are increased to 20, 50 and 100.
0.05
20
Colony Size 10
Colony Size 20
Colony Size 50
Colony Size 100
40 60
Cycles
80 100 120
Figure 4.34 Comparison of the effect of colony size in end milling experiment
When the bee colony size is increased to 50 and 100, all control variables
combinations also give good results where the minimal Ra value found is 0.1719|am.
From the experiment, we found out that a minimum of max per cycle 10 with 10 runs
is sufficient to get a minimum value of Ra. Even if we increased the number of runs
182
and max per cycles value, the results did not give any significant differences. The
average minimal Ra value of 0.1719(j,m is achieved on the sixth runs. Figure 4.34
shows the comparison of effect of population size in end milling machining. Table
4.42 shows the summary of ABC optimization results using different colony size and
limit in end milling.
Table 4.41: Summary of ABC optimization results using different colony size
and limit in end milling
Colony Size Max cycles per run Limit Min Ra (|im)
10 10 30
0.1719
10 20 30
10 50 30
10 100 30
20 10 60 0.1725
20 20 60
0.171920 50 60
20 100 60
50 10 150
0.1719
50 20 150
50 50 150
50 100 150
100 10 300
0.1719
100 20 300
100 50 300
100 100 300
4.10 Summary of AWJ experimental results
183
In Experiment 2 of AWJ, the same control parameter setting of end milling
experiment was employed. The experiment shows that a smaller number of bee
colony sizes, 10 also give an optimal Ra value. For bee colony size of 10, the first
control variables combinations give a minimum Ra value of 2.7090. The value of Ra
is improved by 41% when the max cycles per run value increased to 20. The minimal
Ra value found is 1.6032|am.
Next, when the max cycles per run are increased to 50 and 100, the minimal
Ra value found is 1.5223[am. This minimal Ra value is enhanced by 44% and 5%
compared to the first and second control variables combinations respectively. When
the bee colony size is increased to 20, the minimal Ra value achieved is 1.6247|am.
When the max cycle per run is increases to 20, the minimal Ra value achieved is
1,5229|am which is less by 6% compared to the first control variable combinations of
bee colony size 20. The minimal Ra of 1.5223[am is achieved when the max cycle per
run was increased to 50 and 100. This minimal Ra value is less by 6% and 0.04%
compared to the first and second control variable combinations. Subsequently, the
bee colony size is increased to 50. The first control variables combinations give a
minimal Ra value of 1.5769|am. This minimal Ra value is improved further by 3%
where a minimal Ra value of 1.5280 is found in the second control variables
combinations. When the max cycles per run are increased to 50 and 100, the minimal
Ra value achieved is 1.5223(j,m.
184
3.5
2.5OJc
_cdarjocr:O!
DCO
1.5
0.5
t
\
V ' I __
• • ColonySize 10
“ “ ColonySize 20
ColonySize 50
—■ColonySize 100
20 40 60
Cycles
SO 100 120
Figure 4.35 Comparison of the effect of colony size in AWJ experiment
For the last experiments, the bee colony size is increased to 100. The first
control variables combinations give a minimal Ra value of 1.7025(j,m. However this
minimal Ra value was further improved by 10% in the second, third and fourth
control variables combinations where a minimal Ra value of 1.5223[am is found. In
AWJ machining experiment, we found out that to get a minimal Ra value of
1.5223jam, a minimum 50 max cycle per and 10 runs is adequate. A max cycle value
of 10 and 20 did not give a good result in all bee colony sizes. The average minimal
Ra value of 0.15223[am is achieved on the sixth runs. Figure 4.35 shows the
comparison of the effect of colony size in AWJ. Table 4.44 shows the summary of
ABC optimization results using different colony size and limit in AWJ.
and limit in AWJ
Table 4.42: Summary of ABC optimization results using different colony
Colony Size Max cycles per run Limit Min Ra (|im)
10 10 50 2.7090
10 20 50 1.6032
10 50 50 1.5223
10 100 50
20 10 100 1.6247
20 20 100 1.5229
20 50 100
1.522320 100 100
50 10 250 1.5769
50 20 250 1.5280
50 50 250
1.522350 100 250
100 10 500 1.7025
100 20 500
1.5223100 50 500
100 100 500
CHAPTER 5
ANALYSIS OF RESULTS
1.1 Introduction
The objective of this chapter is to validate and evaluate the results of ABC
optimization. Validation is performed to determine whether the results of ABC
optimization technique are acceptable to describe the problem investigated.
Evaluation process is conducted to investigate how significance of results from ABC
optimization technique for the problem investigated. In the previous chapter, the
main phases of ABC optimization was described in details and the experimental
results also have been presented.
187
The validation process of ABC optimization results is given as follows:
i. For end milling and AWJ, the equation 4.1 and 4.2 are used to
validate the results respectively.
The evaluation processes of ABC optimization results are given as follows:
i. Analyse the predicted Ra value estimated by ABC optimization.
ii. Analyse optimal process parameters estimated by ABC optimization.
5.2 Analysis of results
5.2.1 Validation and evaluation of ABC for end milling
The best results of end milling are shown in Figure 5.2 where the set values
of process parameters that lead to the minimum Ra value for ABC are 167.0300
m/min for cutting speed, 0.0250 mm/tooth for feed rate and 6.200° for radial rake
angle. Based on equation 4.1, the calculation for validating the ABC result for end
milling is given as follows:
Ra= 0.237 - 0.00175 (167.0300) + 8.693 (0.0250) + 0.00159 (6.200)
= 0.17185 ~0.1719(am
188
As a result, evaluations of the Ra for ABC optimization results for end milling are
given as follows:
(i) Evaluation of the Ra for ABC in end milling
(a) Experimental data vs. ABC
With Ra = 0.1719|am for ABC and Ra = 0.190[am for experimental data, it can
be stated that ABC has given a lower minimum value of the predicted Ra by
about 0.0181 jam.
(b) Regression vs ABC
With Ra = 0.1719|am for ABC and Ra = 0.187jam for regression, it can be
stated that ABC has given a lower minimum value of the predicted Ra by
about 0.0151 jam.
(c) GA vs ABC
GA performance is much better than ABC by giving a minimal value of the
predicted by about 0.0334|am where Ra = 0.1719|am for ABC and Ra =
0.1385|am for GA.
(d) SA vs. ABC
SA performance is much better than ABC by giving a minimal value of the
predicted by about 0.0334|am where Ra = 0.1719|am for ABC and Ra =
0.1385(j,m for SA.
189
In order to evaluate the optimal process parameters of ABC for end milling,
the values of the process parameters level of the end milling experimental design,
noted as -1.4142, -1, 0, +1 and +1.4142 as given in Table 2.6 are classified as the
lowest, lower, medium, high, highest scales. With xi = optimal cutting conditions of
AWJ, Table 5.1 shows the conditions used to define the scale of the levels for the
three optimal process parameters.
Table 5.1: Conditions to define the scale for optimal process parameters of end
milling
(ii) Evaluation of the optimal process parameters for ABC in end milling
Decision Independent variables
v (m/min) / (mm/tooth) y(°)
Lowest 124.53 < xi < 133.03 0.025 < xi < 0.036 6.20 < xi < 7.92
Low 133.03 < xi < 141.53 0.036 < xi < 0.048 7.92 < xi < 9.64
Medium 141.53 < xi < 150.03 0.048 < xi < 0.059 9.64 < xi < 11.36
High 150.03 < xi < 158.53 0.059 < xi < 0.071 11.36 < xi < 13.08
Highest 158.53 < xi < 167.03 0.071 < xi< 0.083 13.08 < xi < 14.80
The set values of optimal process parameters that lead to the minimum Ra
value are 167.0300 m/mm for cutting speed, 0.0250 mm/tooth for feed rate and
6.200° for radial rake angle. Considering the conditions given in Table 5.2, it could
be stated that optimal process parameters that lead to minimum predicted Ra value
are highest cutting speed, lowest feed rate and lowest radial rake angle. Table 5.3
below shows the comparison of the optimal process parameters in end milling using
three optimization techniques such as GA, SA and ABC.
Table 5.2: Comparison of the optimal process parameters in end milling
Technique Cutting Speed (v) Feed rate if) Radial rake
angle (y)
The best
predicted
value of Ra
GA 167.029 0.025 14.769 0.138
SA 167.03 0.025 14.797 0.1385
ABC 167.0300 0.0250 6.200 0.1719
5.2.2 Validation and evaluation of ABC for AWJ
Figure 5.3 shows the optimal solution of the ABC are 50 mm/min for cutting
speed, 125 Mpa for waterjet pressure, 1.5504 mm for standoff distance, 102.5213(j,m
for abrasive grit size and 0.5 g/s for abrasive flow rate. Considering Equation 4.2, the
calculation for validating the AWJ is given as follows:
Ra = -5.07976 + 0.08169 (50)+ 0.07912 (125) - 0.34221 (1.5504) - 0.08661
(102.5213) - 0.34866 (0.5) - 0.00031 (50)2 - 0.00012 (125)2 + 0.10575 (1.5504)2 +
0.00041 (102.5213)2 + 0.07590 (0.5)2 - 0.00008 (50) (0.5)- 0.00009 (125) (0.5) +
0.03089 (1.5504) (0.5) + 0.00513 (102.5213) (0.5)
= 1.52227 ~ 1.5223(j,m
191
As a result, evaluations of the Ra for ABC optimization results for end milling are
given as follows:
(i) Evaluation of the Ra for ABC in AWJ
(a) Experimental data vs. ABC
With Ra = 1.5223[am for ABC and Ra = 2.124(j,m for experimental data, it can
be stated that ABC has given a lower minimum value of the predicted Ra by
about 0.6017|jm.
(b) Regression vs ABC
With Ra = 1.5223|am for ABC and Ra = 2.62195(j,m for regression, it can be
stated that ABC has given a lower minimum value of the predicted Ra by
about 0.10685|jm.
(c) GA vs ABC
With Ra = 1.5223 [am for ABC and Ra = 1,5549|am for GA, it can be stated
that ABC performance is much better than GA by giving a minimal value of
the predicted by about 0.0326(j,m.
(d) SA vs. ABC
With Ra = 1.5223[am for ABC and Ra = 1,5355|am for ABC, it can be stated
that ABC performance is much better than SA by giving a minimal value of
the predicted by about 0.0132|am.
192
In order to evaluate the optimal process parameters of ABC for AWJ, the
values of the cutting condition level noted as 1, 2 and 3 as given in Table 2.9, are
classified as the lowest, lower, medium, high, highest scales. With xi = optimal
cutting conditions of AWJ, Table 5.3 shows the conditions used to define the scale of
the levels for the five optimal process parameters.
Table 5.3: Conditions to define the scale for optimal process parameters of AWJ
(ii) Evaluation of the optimal process parameters for ABC in AWJ
Decision Independent variables
V (mm/min) P (Mpa) h (mm) d (jam) m (g/s)Lowest 50 < xi< 70 125 <xi< 150 1.0 <xi< 1.6 60 <xi< 72 0.5 <xi< 1.1
Low 70 < xi< 90 150 <xi< 175 1.6 <xi< 2.2 72 <xi< 84 1.1 <xi< 1.7
Medium 90 <xi< 110 175 <xi< 200 2.2 <xi< 2.8 84 <xi< 96 1.7 <xi< 2.3
High 110 <xi < 130 200 <xi < 225 2.8 <xi< 3.4 96 <xi< 108
2.3 < xi< 2.9
Highest 130 <xi \ <
150225 <xi < 250 3.4 <xi< 4.0 108 <xi<
1202.9 <xi< 3.5
The set values of optimal process parameters that lead to the minimum Ra
value are 50 mm/min for traverse speed, 125 MPa for waterjet pressure, 1.5504 mm
for standoff distance, 102.5213 jam for abrasive grit size and 0.500 g/s for abrasive
flow rate. Considering the conditions given in Table 5.3, it could be stated that
optimal process parameters that lead to minimum predicted Ra value lowest cutting
speed, lowest waterjet pressure, lowest standoff distance, high abrasive grit size and
lowest abrasive flow rate. Table 5.4 below shows the comparison of the optimal
process parameters in end milling using three optimization techniques such as GA,
SA and ABC,
193
Table 5.4: Comparison of the optimal process parameters in AWJ
Technique Traverse
cutting
speed (V)
Waterjet
pressure
(P)
Standoff
distance
(h)
Abrasive
grit size
{d)
Abrasive
flow rate
(m)
The best
predicted
value of
Ra
GA 50.024 125.018 1.636 94.73 0.525 1.5549
SA 50.003 125.029 1.486 107.737 0.500 1.5335
ABC 50 125 1.5504 102.5213 0.500 1.5223
In Table 5.5, a minimal Ra of 0.1719(j,m was found using ABC and it is clear
that ABC algorithm outperforms experimental and regression results in optimizing
process parameters of end milling machining. However, compared to GA and SA,
both techniques performed better than ABC where the Ra value achieved was much
lower compared to ABC. There are a few possibilities that can clarify these
outcomes such as:
i. The regression model that was employed in end milling in equation
3.4 was a simple regression model compared to AWJ where the
regression model used in equation 3.10 was developed using second
order polynomial regression.
ii. In end milling, the optimal process parameters setting that lead to
minimum predicted Ra value of 0.1719|am are highest cutting speed,
lowest feed rate and lowest radial rake angle. Compared to GA and
SA optimization, both have the same setting of highest cutting speed
and lowest feed rate. However for the third process parameters, the
setting of radial rake angle is highest in GA and SA.
194
Table 5.5: Comparison of minimum Ra in end milling and AWJ machining
Technique Min Ra in Experiment 1 -
(End milling)
Min Ra in Experiment 2 -(AWJ)
Experimental 0.190 2.124
Regression 0.187 2.62915
GA 0.139 1.5549
SA 0.1385 1.5355
ABC 0.1719 1.5223
In AWJ, a minimum Ra value of 1.5223[am was achieved and when compared
to experimental, regression, GA and SA, it has been found that ABC technique
decrease the Ra value which are about, 28%, 42%, 2% and 0.9% respectively. In
optimizing the process parameters of AWJ, the performance of ABC is superior
compared to experimental, regression, GA and SA.
195
This chapter has discussed the validation and evaluation of results of the
ABC optimization that was proposed in this study. From the results, the proposed
technique was successfully found minimum Ra value in both end milling and AWJ.
In end milling, the ABC performance is better compared to the experimental and
regression but not GA and SA. However the performance of ABC is better in AWJ
where the minimal Ra found was lower compared to experimental, regression, GA
and SA.
5.3 Summary
CHAPTER 6
CONCLUSION AND FUTURE WORK
6.1 Introduction
This chapter discusses the work that has been done or overall conclusion to
complete this study. Basically, the aim of this study is to study the optimal effect of
process parameters of end milling and AWJ machining in influencing the minimum
Ra value. In this study, experiments design for Ra measurement based on the work of
(Mohruni, 2008) for end milling machining and (Caydas and Hascalik, 2008) for
AWJ machining have been referred. The regression modeling was developed and
ABC optimization algorithm was employed to find the minimum Ra value. The
performance of ABC technique was evaluated and has been compared to the results
of experimental, regression, GA and SA techniques.
197
In doing this research, the work had been done according to the steps outlined
in the project methodology. The experiments that have been done and the summary
of work in this research are listed below:
i. Assessment of real experimental data based on effort
attempted by Mohruni (2008) and also (Caydas and Hascalik,
2008).
ii. Regression modeling development
iii. ABC algorithm for optimization of process parameters
a) Formulation of optimization solution
b) Find the combination of the optimal process parameters.
c) Find the minimum Ra value.
iv. Validation and evaluation of results
a) The minimum Ra value of ABC was compared to the result
of experimental sample data, regression modeling, GA and
SA.
6.1 Summary of Work
198
Based on the experiment that has been done on this study, the summary of the
experiments are as follows:
i. From Table 6.1, the minimum Ra value in end milling found was
0.1719|am by using ABC optimization algorithm. When compared to
other techniques such as experimental and regression, the Ra value
using the proposed technique was much lower by 10% and 8%
respectively. However when compared to other optimization
technique such as GA and SA, both techniques give minimum Ra
value compared to ABC. In GA and SA, the minimum Ra value found
was 0.139|am.
Table 6.1: Reduction percentage of minimum surface roughness in end milling
6.2 Research summary and conclusion
Data type Technique % of reduction
End milling ABC vs. experimental 10%
ABC vs. regression 8%
ABC vs. GA -23.6%
ABC vs. SA -23.6%
ii. In optimizing process parameters of AWJ machining, the minimum Ra
value found was 1.5223jj,m. This Ra value was the lowest compared to
other technique like experimental, regression, GA and SA. In
experimental the minimum Ra value was 2.124|am and in regression
the minimum Ra value was 2.62915[am. ABC optimization technique
successfully minimized the Ra value by 28% and 42% from
experimental and regression.
199
When compared to GA and SA, ABC also gives better results where
the Ra value was much lower in GA and SA by 2% and 0.9%
respectively. This is shown in Table 6.2.
Table 6.2: Reduction percentage of minimum surface roughness in AWJ
Data type Technique % of reduction
AWJ ABC vs. experimental 28%
ABC vs. regression 42%
ABC vs. GA 2%
ABC vs. SA 0.9%
iii. Referring to Table 6.3, it can be pointed out that a smaller number of
bee colony sizes were adequate to find the most minimum Ra value in
both end milling and AWJ. In end milling experiments, a bee colony
size of 10 was sufficient to find the minimal Ra value of 0.1719|am
with a maximum number of cycles of 10. When the bee colony size
was increased to 20, 50 and 100, the results remained the same. This
is also happened in AWJ experiments where the minimum Ra value of
1.5223 pm can be found using a smaller number of bee colony size of
10 with a maximum number of cycles of 50. In order to get the best
results, it is mostly determined by the control variable of max cycles
per run. As the value of max cycle per run was increased, the
performance of ABC was also improved. In both end milling and
AWJ experiments, the value 50 and 100 of max cycles per run gives a
better performance. In both machining experiment, an average of sixth
runs is needed to get the best minimal Ra value. When the number of
runs is increased, it does not give any major differences to the result.
200
Table 6.3: Summary of minimum bee colony size and max number of cycles
Data type Bee colony
size
Max number
of cycles
Average
number of
runs
Min Ra (|im)
End milling 10 10 6 0.1719
AWJ 10 50 6 1.5223
iv. By using ABC optimization, the dominant factors that affects for
giving a minimum Ra value in end milling is feed rate if). In ABC, the
minimum Ra value is higher compared to minimum Ra value in GA
and SA. This might be influenced by a lowest level of radial rake
angle (y) as shown in Table 6.4. For AWJ, it was found out that
traverse speed (v) and waterjet pressure ip) are the dominant factors
that influence for giving a minimum Ra value. The level of process
parameters for giving minimum Ra value are the same in SA and GA
approach which are lowest traverse speed ( V), lowest waterjet
pressure (P), lowest standoff distance (h), high abrasive grit size id)
and lowest abrasive flow rate (m). The summary of level of thr
optimal process parameters is shown in Table 6.4.
201
Table 6.4: Summary of level of the optimal process parameters
Technique Level of process parameters
End milling AWJV / y V P h d m
Experimental Hgst Lwst High Lwst Lwst Lwst Lwst Lwst
Regression Med Lwst Low Lwst Lwst Lwst Lwst Med
GA Hgst Lwst Hgst Lwst Lwst Low Med Lwst
SA Hgst Lwst Hgst Lwst Lwst Lwst High Lwst
ABC Hgst Lwst Lwst Lwst Lwst Lwst High Lwst
Indicator of level: Lwst = Lowest, Med = Medium, Hgst = E ighest
6.3 Suggestion for Future Work
In summary, the experimental result have been achieved and evaluated in this
study. However, there are several suggestions for the future works to improve the
performance of this project that can be done later.
i. Currently, the hybrid optimization technique has become a trend
among researchers. By hybridizing the proposed techniques with other
optimization techniques such as GA, SA, PSO or AIS the results
could be improved.
ii. In this study, only a several process parameters have been considered
in order to find a minimum Ra value. In the future, more process
parameters can be considered as well for the machining performances
not just limited to find Ra value. Other machining performances that
can be considered are MRR, production time, production cost, tool
wear, tool geometry and etc.
202
iii. There are two type of machining processes focused in this study
which are end milling (traditional machining) and abrasive waterjet
machining (modem machining). In the future, trial are suggested for
different kind of machining processes especially on other traditional
machining processes such as turning and also modem machining such
as electrical discharge machining (EDM), Wire-cut electro discharge
machining (WEDM).
6.5 Summary
This chapter has discussed and concluded the aim of this study. The results of
the study were presented and evaluated. The three objectives of the study were
achieved and lastly recommendations of future works were suggested.
203
REFERENCES
Abu-Mouti, F. S., & El-Hawary, M. E. (2009). Modified Artificial Bee Colony
Algorithm for Optimal Distributed Generation Sizing and Allocation in
Distribution Systems. 2009 IEEE Electrical Power & Energy Conference , 1-9.
Adil Baykasoglu, Lale Ozbakir and Pinar Tapkan (2007). Artificial Bee Colony
Algorithm and Its Application to Generalized Assignment Problem, Swarm
Intelligence, Focus on Ant and Particle Swarm Optimization, Felix T.S. Chan
and Manoj Kumar Tiwari (Ed.), ISBN: 978-3-902613-09-7, I-Tech Education
and Publishing.
Aderhold, A., Diwold, K., Scheidler, A., & Middendorf, M. (2010). Artificial Bee
Colony Optimization: A New Selection Scheme and Its Performance. NICSO
2 0 1 0 ,283-294.
Akay, B., & Karaboga, D. (2010). Artificial bee colony algorithm for large-scale
problems and engineering design optimization. Journal o f Intelligent
Manufacturing.
Ansalam Raj, T. G., & Narayanan Namboothiri, V. N. (2010). An improved genetic
algorithm for the prediction of surface finish in dry turning of SS 420 materials.
International Journal of Advanced Manufacturing Technology, 47(1-4), 313
324.
Azmir, M. A., & Ahsan, A. K. (2008). Investigation on glass/epoxy composite
surfaces machined by abrasive water jet machining. Journal of Materials
Processing Technology, 198(1-3), 122-128.
Bahamish, H., Abdullah, R., & Salam, R. (2009). Protein Tertiary Structure
Prediction Using Artificial Bee Colony Algorithm. Modelling & Simulation,
2009. AM S '09. Third Asia International Conference , 256-263.
Benala, T., Jampala, S., Villa, S., & Konathala, B. (2009). A novel approach to
image edge enhancement using Artificial Bee Colony optimization algorithm for
hybridized smoothening filters. Nature & Biologically Inspired Computing,
2009. NaBIC 2009. World Congress , 1071-1076.
204
Benitez, C-., & Lopes, H. (2010). Parallel Artificial Bee Colony Algorithm
Approaches for Protein Structure Prediction Using the 3DHP-SC Model.
Intelligent Distributed Computing I V , 255-264.
Bharathi Raja, S., & Baskar, N. (2010). Particle swarm optimization technique for
determining optimal machining parameters of different work piece materials in
turning operation. International Journal of Advanced Manufacturing
Technology,, 1-19.
Bodi, C-., & Yingjian, L. (2009). Optimization of Multi-pass Turning of Slender Bar
usingArtificial Neural Networks and Genetic Algorithm. Industrial Electronics
and Applications, 2009. ICIEA 2009. 4th IEEE Conference , 1246-1249.
Caydas,U .,& Hascalik, A. (2008) A study on surface roughness in abrasive waterjet
machining process using artificial neural networks and regression analysis
method. J Mater Process Technol 202:574-582.
Chen, H. -., Lin, J. -., Yang, Y. -., & Tsai, C, -. (2010). Optimization of wire
electrical discharge machining for pure tungsten using a neural network
integrated simulated annealing approach. Expert Systems with Applications
Chen, Y. -., Lin, Y. -., Lin, Y. -., Chen, S. -., & Hsu, L. -. (2010). Optimization of
electrodischarge machining parameters on Zr02 ceramic using the taguchi
method. Proceedings of the Institution of Mechanical Engineers, Part B: Journal
of Engineering Manufacture, 224(2), 195-205.
Echert, D., McDonald, M., & Monserud, D. (1989). Underwater Cutting By
Abrasive-Waterjet. OCEANS '89. Proceedings , 1562 - 1566.
Escamilla, I., Perez, P., Torres, L., Zambrano, P., & Gonzalez, B. (2009).
Optimization using neural network modeling and swarm intelligence in the
machining of titanium (ti 6al 4v) alloy. Paper presented at the 8th Mexican
International Conference on Artificial Intelligence - Proceedings of the Special
Session, MICAI 2009, 33-38.
Gao, X. B., Tao, H., Zhang, P. P., Qiu, H. J. (2008). Optimisation of Machining
Parameters for NC Milling Ultrahigh Strength Steel. Advanced Design and
Manufacture to Gain a Competitive Edge, 451-461.
Guo, D., Chen, J., & Cheng, Y. (2006). Laser cutting parameters optimization based
on artificial neural network. Paper presented at the IEEE International
Conference on Neural Networks - Conference Proceedings, 1106-1 111.
205
Hashish, M. (1991). Optimization factors in abrasive-waterjet machining. Journal of
Engineering for Industry, 113(1), 29-37.
Haq, A. N., Marimuthu, P., & Jeyapaul, R. (2008). Multi response optimization of
machining parameters of drilling Al/SiC metal matrix composite using grey
relational analysis in the taguchi method. International Journal of Advanced
Manufacturing Technology, 37(3-4), 250-255.
Ho, Y., & D.L, P. (2002). Simple Explanation of the No Free Lunch Theorem of
Optimization. Journal Cybernetics and Systems Analysis Volume 38 Issue 2 .
Hossain, M. I., Amin, A. N , & Patwari, A. U. (2008). Development of an Artificial
Neural Network Algorithm for Predicting theSurface Roughness in End Milling
of Inconel 718 Alloy. Proceedings o f the International Conference on Computer
and Communication Engineering 2008 (pp. 1321-1324). Kuala Lumpur: IEEE.
K.Kadirgamaa, M.M.Noora, N.M.Zuki.N.M, Rahmana, M., Rejaba, M., R.Daud, et
al. (2008). Optimization of Surface Roughness in End Milling on Mould
Aluminium Alloys (AA6061-T6) Using Response Surface Method and Radian
Basis Function Network. Jordan Journal o f Mechanical and Industrial
Engineering , 2(4), 209- 214.
Kalpakjian, S., & Schmid, S. (2009). Manufacturing Engineering and Technology.
Prentice Hall.
Kanagarajan, D., Karthikeyan, R., Palanikumar, K , & Davim, J. P. (2008).
Optimization of electrical discharge machining characteristics of WC/Co
composites using non-dominated sorting genetic algorithm (NSGA-II).
International Journal of Advanced Manufacturing Technology, 36(11-12), 1124
1132.
Karaboga, D. (2005). An idea based on honey bee swarm for numerical optimization.
Technical Report TR06, Erciyes University, Engineering Faculty, Computer
Engineering Department, 2005.
Karaboga, D., & Akay, B. (2009). A comparative study of Artificial Bee Colony
algorithm. Applied Mathematics and Computation , 214, 108-132.
Karaboga, D., & Basturk, B. (2008). On the performance of artificial bee colony
(ABC) algorithm. Applied Soft Computing , 8, 687-697.
Karaboga, D., Okdem, S., & Ozturk, C. (2010). Cluster based wireless sensor
network routings using Artificial Bee Colony Algorithm. Autonomous and
Intelligent Systems (AIS), 2010 International Conference , 1-5.
206
Karaboga, N. (2009). A newdesign method based on artificial bee colony algorithm
for digital HR filters. Journal oftheFranklinlnstitute , 346, 328-348.
Kilickap, E., Huseyinoglu, M., & Yardimeden, A. (2011). Optimization of drilling
parameters on surface roughness in drilling of AISI 1045 using response surface
methodology and genetic algorithm. International Journal of Advanced
Manufacturing Technology, 52(1-4), 79-88.
Kolahan, F., & Hamid, K. i. (2009). Modeling and Optimization of Abrasive
Waterjet Parameters using Regression Analysis. World Academy o f Science,
Engineering and Technology 59 2009 , 488-493.
Kolahan, F., & Khajavi, A. H. (2009). A statistical approach for predicting and
optimizing depth of cut in AWJ machining for 6063-T6 al alloy. Proceedings of
World Academy of Science, Engineering and Technology, 59, 142-145
Krishnanand, K , Panigrahi, B., Nayak, S., & Rout, P. (2009). Comparative Study of
Five Bio-Inspired Evolutionary Optimization Techniques. 2009 World Congress
on Nature & Biologically Inspired Computing (NaBIC 2009) , 1231-1236.
Kurban, T., & Besdok, E. (2009). A Comparison of RBF Neural Network Training
Algorithms for Inertial Sensor Based Terrain Classification. Sensor 2009 , 6312
6329.
Lin, Y. -., Wang, A. -., Wang, D. -., & Chen, C, -. (2009). Machining performance
and optimizing machining parameters of al 203-tic ceramics using edm based on
the taguchi method. Materials and Manufacturing Processes, 24(6), 667-674.
Markopoulos, A., Vaxevanidis, N. M., Petropoulos, G., & Manolakos, D. E. (2006).
Artificial neural networks modeling of surface finish in electro-discharge
machining of tool steels. Paper presented at the Proceedings of 8th Biennial
ASME Conference on Engineering Systems Design and Analysis, ESDA2006, ,
2006
Manna, A., & Salodkar, S. (2008). Optimization of machining conditions for
effective turning of E0300 alloy steel. Journal of Materials Processing
Technology, 203(1-3), 147-153.
M.Dorigo, V.Maniezzo, & A.Colomi. (1996). Ant sytem: optimization by a colony
of cooperating agents. IEEE Trans.Systems,Man, Cybernet, Part B 26(1), 29-41.
Mike, S., Joseph, C-., & Caleb, M. (1998). Surface Roughness Prediction Technique
For CNC End-Milling. Journal o f Industrial Technology , 15, 2-6.
207
Mohammadi, A., Fadaei Tehrani, A., Emanian, E., & Karimi, D. (2008). A new
approach to surface roughness and roundness improvement in wire electrical
discharge turning based on statistical analyses. International Journal of
Advanced Manufacturing Technology, 39(1-2), 64-73.
Mohruni, A. S. (2008). Performance evaluation of uncoated and coated carbide tools
when end milling of titanium alloy using response surface methodology. Thesis
for Doctor of Philosophy, Universiti Teknologi Malaysia, Skudai, Johor,
Malaysia.
Motorcu, A. R. (2010). The optimization of machining parameters using the taguchi
method for surface roughness of an AISI 8660 hardened alloy steel. Strojniski
Vestnik/Joumal of Mechanical Engineering, 56(6)
Murthy, K. S., & Rajendran, I. (2010). A study on optimisation of cutting parameters
and prediction of surface roughness in end milling of aluminium under MQL
machining. International Journal of Machining and Machinability of Materials,
7(1-2), 112-128.
Oktem, H. (2009). An integrated study of surface roughness for modelling and
optimization of cutting parameters during end milling operation. International
Journal of Advanced Manufacturing Technology, 43(9-10), 852-861.
Palanikumar, K. (2006). Cutting parameters optimization for surface roughness in
machining of GFRP composites using taguchi's method. Journal of Reinforced
Plastics and Composites, 25(16), 1739-1751
Pansuwan, P., Rukwong, N., & Pongcharoen, P. (2010). Identifying optimum
Artificial Bee Colony (ABC) algorithm’s parameters for scheduling the
manufacture and assembly of complex products. Second International
Conference on Computer and Network Technology. IEEE.
Pasam, V. K., Battula, S. B., Valli, P. M., & Swapna, M. (2010). Optimizing surface
finish in WEDM using the taguchi parameter design method. Journal of the
Brazilian Society of Mechanical Sciences and Engineering, 32(2), 107-113.
Pei, W., Jeng, S., Bin, Y., & Shu, C. (2009). Enhanced Artificial Bee Colony
Optimization. International Journal o f Innovative Computing, Information and
Control Volume 5, Number 12 , 1-12.
Rao, R. S., Narasimham, S., & Ramalingaraju, M. (2008). Optimization of
Distribution Network Configuration for Loss Reduction Using Artificial Bee
208
Colony Algorithm. World Academy o f Science, Engineering and Technology 45
2008 , 708-714.
Rao, R., & Pawar, P. (2010). Parameter optimization of a multi-pass milling process
using non-traditional optimization algorithm. Applied Soft Computing , 10, 445
456.
Rao, R. V., Pawar, P. J., & Davim, J. P. (2010). Parameter optimization of ultrasonic
machining process using nontraditional optimization algorithms. Materials and
Manufacturing Processes, 25(10), 1120-1130.
Ramakrishnan, R., & Karunamoorthy, L. (2006). Multi response optimization of wire
EDM operations using robust design of experiments. International Journal of
Advanced Manufacturing Technology, 29(1-2), 105-112.
Razfar, M. R., & Zadeh, M. R. Z. (2009). Optimum damage and surface roughness
prediction in end milling glass fibre-reinforced plastics, using neural network
and genetic algorithm. Proceedings of the Institution of Mechanical Engineers,
Part B: Journal of Engineering Manufacture, 223(6), 653-664.
Saab, S. M., El-Omari, N. K., & Owaied, H. H. (2009). Developing Optimization
Algorithm.
Saeedi, S., Samadzadegan, F., & El-Sheimy, N. (2009). Object Extraction From
Lidar Data Using An Artificial Swarm Bee Colony Clustering Algorithm.
CMRT09. IAPRS, Vol. XXXVIII, Part 3/W4 , 133-138.
Saha, P., Singha, A., Pal, S. K., & Saha, P. (2008). Soft computing models based
prediction of cutting speed and surface roughness in wire electro-discharge
machining of tungsten carbide cobalt composite. International Journal of
Advanced Manufacturing Technology, 39(1-2), 74-84
Sahoo, P., Routara, B. C-., & Bandyopadhyay, A. (2009). Roughness modelling and
optimisation in EDM using response surface method for different work piece
materials. International Journal of Machining and Machinability of Materials,
5(2-3), 321-346.
Samanta, B., Erevelles, W., & Omurtag, Y. (2008). Prediction of workpiece surface
roughness using soft computing. Proceedings of the Institution of Mechanical
Engineers, Part B: Journal of Engineering Manufacture, 222(10), 1221-1232.
Samanta, B. (2009). Surface roughness prediction in machining using soft
computing. International Journal of Computer Integrated Manufacturing, 22(3),
257-266.
209
Sarkar, S., Mitra, S., & Bhattacharyya, B. (2005). Wire electrical discharge
machining of gamma titanium aluminide for optimum process criteria yield in
single pass cutting operation. International Journal of Manufacturing
Technology and Management, 7(2-4), 207-223.
Sayuti, M., Sarhan, A. A. D., & Hamdi, M. (2011). Optimizing the machining
parameters in glass grinding operation on the CNC milling machine for best
surface roughness
Senthilkumar, C., Ganesan, G., & Karthikeyan, R. (2010). Bi-performance
optimization of electrochemical machining characteristics of Al/20%SiCp
composites using NSGA-II. Proceedings of the Institution of Mechanical
Engineers, Part B: Journal of Engineering Manufacture, 224(9), 1399-1407.
Somashekhar, K. P., Ramachandran, N., & Mathew, J. (2009). Modeling and
optimization of process parameters in micro wire EDM by genetic algorithm
Retrieved from www.scopus.com
Ting, T., Lee, T., & Htay, T. (2005). Performance Analysis of Grinding Process via
Particle Swarm Optimization. Computational Intelligence and Multimedia
Applications, 2005. Sixth International Conference , 92-97.
V. Tereshko, “Reaction-diffusion model of a honey bee colony's foraging behavior,”
M. Schoenauer et al, Eds., Parallel Problem Solving from Nature VI (Lecture
Note in Computer Science, Vol. 1917) Springer-Verlag: Berlin, pp.807-816,
2000 .
Wang, J., Gong, Y., Shi, J., & Abbay, G. (2009). Surface roughness prediction in
micromilling using neural networks and taguchi's design of experiments. Paper
presented at the Proceedings of the IEEE International Conference on Industrial
Technology
Wang, Z., Yuan, J., Hu, X., & W., D. (2009). Surface Roughness Prediction and
Cutting Parameters Optimization in High-Speed Milling A M nlCu Using
Regression and Genetic Algorithm. 2009 International Conference on
Measuring Technology andMechatronics Automation , 334-337
Wolpert, D.H., Macready, W.G. (1997), "No Free Lunch Theorems for
Optimization,"IEEE Transactions on Evolutionary Computation 1, 67.
Wolpert, D.H., and Macready, W.G. (2005) "Coevolutionary free lunches," IEEE
Transactions on Evolutionary Computation, 9(6): 721-735.
210
Xiaojin, F. (2006). The study of influence factors about work ability in Metal-cutting
Processing. Proceedings o f the Sixth International Conference on Intelligent
Systems Design and Applications (ISDA'06) (pp. 0-7695-2528-8). IEEE.
Yanda, H., Ghani, J. A., Rodzi, M. N. A. M., Othman, K., & Haron, C, H. C, (2010).
Optimization of material removal rate, surface roughness and tool life on
conventional dry turning of FCD700. International Journal of Mechanical and
Materials Engineering, 5(2), 182-190.
Zain, A. M., Haron, H., & Sharif, S. (2010a). Application of GA to optimize cutting
conditions for minimizing surface roughness in end milling machining process.
Expert System with Applications , 37, 4650-4659.
Zain, A. M., Haron, H., & Sharif, S. (2010b). Simulated Annealing To Estimate The
Optimal Cutting Conditions For Minimizing Surface Roughness In End Milling
Ti-6A1-4V. Machining Science and Technology , 14, 43-62.
Zain, A. M., Haron, H., & Sharif, S. (2010c). Genetic Algorithm and Simulated
Annealing to estimate optimal process parameters of the abrasive waterjet
machining. Engineering with Computers .
Zhang, J. Z., Chen, J. C-., & Kirby, E. D. (2007). Surface roughness optimization in
an end-milling operation using the taguchi design method. Journal of Materials
Processing Technology, 184(1-3), 233-239.
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