ORIGINAL ARTICLE

ISSN No : 2230-7850

International MultidisciplinaryResearch Journal

Indian Streams

Research Journal

Executive EditorAshok Yakkaldevi

Editor-in-ChiefH.N.Jagtap

Vol 4 Issue 4 May 2014

Mohammad HailatDept. of Mathematical Sciences, University of South Carolina Aiken

Abdullah SabbaghEngineering Studies, Sydney

Catalina NeculaiUniversity of Coventry, UK

Ecaterina PatrascuSpiru Haret University, Bucharest

Loredana BoscaSpiru Haret University, Romania

Fabricio Moraes de AlmeidaFederal University of Rondonia, Brazil

George - Calin SERITANFaculty of Philosophy and Socio-Political Sciences Al. I. Cuza University, Iasi

Hasan BaktirEnglish Language and Literature Department, Kayseri

Ghayoor Abbas ChotanaDept of Chemistry, Lahore University of Management Sciences[PK]

Anna Maria ConstantinoviciAL. I. Cuza University, Romania

Horia PatrascuSpiru Haret University,Bucharest,Romania

Ilie Pintea,Spiru Haret University, Romania

Xiaohua YangPhD, USA

......More

Flávio de São Pedro FilhoFederal University of Rondonia, Brazil

Kamani PereraRegional Center For Strategic Studies, Sri Lanka

Janaki SinnasamyLibrarian, University of Malaya

Romona MihailaSpiru Haret University, Romania

Delia SerbescuSpiru Haret University, Bucharest, Romania

Anurag MisraDBS College, Kanpur

Titus PopPhD, Partium Christian University, Oradea,Romania

Pratap Vyamktrao NaikwadeASP College Devrukh,Ratnagiri,MS India

R. R. PatilHead Geology Department Solapur University,Solapur

Rama BhosalePrin. and Jt. Director Higher Education, Panvel

Salve R. N.Department of Sociology, Shivaji University,Kolhapur

Govind P. ShindeBharati Vidyapeeth School of Distance Education Center, Navi Mumbai

Chakane Sanjay DnyaneshwarArts, Science & Commerce College, Indapur, Pune

Awadhesh Kumar ShirotriyaSecretary,Play India Play,Meerut(U.P.)

Iresh SwamiEx - VC. Solapur University, Solapur

N.S. DhaygudeEx. Prin. Dayanand College, Solapur

Narendra KaduJt. Director Higher Education, Pune

K. M. BhandarkarPraful Patel College of Education, Gondia

Sonal SinghVikram University, Ujjain

G. P. PatankarS. D. M. Degree College, Honavar, Karnataka

Maj. S. Bakhtiar ChoudharyDirector,Hyderabad AP India.

S.Parvathi DeviPh.D.-University of Allahabad

Sonal Singh,Vikram University, Ujjain

Rajendra ShendgeDirector, B.C.U.D. Solapur University, Solapur

R. R. YalikarDirector Managment Institute, Solapur

Umesh RajderkarHead Humanities & Social Science YCMOU,Nashik

S. R. PandyaHead Education Dept. Mumbai University, Mumbai

Alka Darshan ShrivastavaShaskiya Snatkottar Mahavidyalaya, Dhar

Rahul Shriram SudkeDevi Ahilya Vishwavidyalaya, Indore

S.KANNANAnnamalai University,TN

Satish Kumar KalhotraMaulana Azad National Urdu University

Editorial Board

International Advisory Board

Welcome to ISRJISSN No.2230-7850

Indian Streams Research Journal is a multidisciplinary research journal, published monthly in English, Hindi & Marathi Language. All research papers submitted to the journal will be double - blind peer reviewed referred by members of the editorial board.Readers will include investigator in universities, research institutes government and industry with research interest in the general subjects.

RNI MAHMUL/2011/38595

Address:-Ashok Yakkaldevi 258/34, Raviwar Peth, Solapur - 413 005 Maharashtra, IndiaCell : 9595 359 435, Ph No: 02172372010 Email: ayisrj@yahoo.in Website: www.isrj.net

Indian Streams Research Journal ISSN 2230-7850Volume-4 | Issue-4 | May-2014Available online at www.isrj.net

OPTIMIZATION OF WATER DISTRIBUTION PIPE NETWORK BY GENETIC ALGORITHM

Abstract:-Water is the most essential commodity required to maintain life. Water supplies in general and water distribution networks in particular have been a part of the modern living. Out of the total expenditure incurred on different facilities of water supply system, the expenditure incurred on the distribution network is maximum. Therefore, it is necessary to optimize the water distribution network. Optimization involves the tradeoff between the performance and cost of the network. There are several approaches for optimization of water distribution network. Many researchers have applied genetic algorithm for the optimization of water distribution networks which has proven to be efficient over the traditional optimization techniques.

Genetic algorithm search begins with a set of potential solutions and changing them during several iterations. The Genetic Algorithm tends to converge on the most 'fit' solutions. The process begins with a set of potential solutions or chromosomes (usually in the form of bit strings of binary numbers) that are randomly generated or selected. The entire set of these chromosomes comprises a population. The chromosomes evolve during several iterations or generations. New generations (offspring) are generated using the crossover and mutation techniques. Crossover involves splitting two chromosomes and then combining or exchanging randomly selected bits of one chromosome with the other in a pair. Mutation involves flipping a single bit of a chromosome. The chromosomes are then evaluated using a certain fitness criteria and the best ones are kept while others are discarded. This process repeats until one chromosome has the best fitness and thus taken as the best solution of the problem.

In the present paper, the genetic algorithm model was developed in C#.net to find out optimum cost of the water distributing network. The applicability of the developed genetic algorithm model is discussed in this paper with a case study on water distribution network of Jaragnagar area of Kolhapur city, Maharashtra.

Keywords:-Water distribution network, pipe network analysis, Genetic algorithm.

INTRODUCTION

Next to air, water is the most essential commodity required to maintain life. The present uses of water are varied and may be classified as domestic, public, commercial and industrial. Water is provided to many communities through water distribution pipe networks. Thus, water distribution networks have been a part of the modern living. Out of the total expenditure incurred on different facilities of water supply system, the expenditure incurred on the distribution network is maximum. Therefore, it is necessary to design the water distribution network properly and optimize the water distribution network.

Several researchers have reported conventional algorithms for optimizing the cost through the application of mathematical techniques, such as linear, non-linear or dynamic programming. The major limitations of these techniques are rigidity, difficulties in representing the heterogeneous systems and their computational in-efficiency when number of variables

V.P. Patil and S.D. Gorantiwar ,“OPTIMIZATION OF WATER DISTRIBUTION PIPE NETWORK BY GENETIC ALGORITHM” Indian

Streams Research Journal | Volume 4 | Issue 4 | May 2014 | Online & Print

1 2V.P. Patil and S.D. Gorantiwar

1Assistant Professor of Mathematics, Department of Farm Structures and Electrification, Dr.A.S. College of Agril.Engg.,Mahatma Phule Krishi Vidhyapeeth,Rahuri, Dist: Ahmednagar (MS)

2Professor of Irrigation and Drainage Engineering, Department of IDE, Dr.A.S. College of Agril.Engg.,Mahatma Phule Krishi Vidhyapeeth,Rahuri, Dist: Ahmednagar (MS)

1

.

is more. Also, many conventional optimization techniques result in a local optimum which is dependent on the starting point in the search process. Hence, there is a need to develop appropriate optimization technique which would be applicable for pipe distribution network. Genetic algorithms (GA) are nature based stochastic computational techniques. The major advantages of these algorithms are their broad applicability, flexibility and their ability to find optimal or near optimal solutions with relatively modest computational requirements. Genetic algorithms, pioneered by Holland (1975), have proven useful in a variety of search and optimization problems in engineering, science and commerce (Goldberg, 1989). Simpson et.al. (1994) presented a methodology for optimizing pipe networks using genetic algorithms. They found that the genetic algorithm technique finds the global optimum in relatively few evaluations compared to the size of the search space. Chen (1997) investigated the improvement in conventional genetic algorithms for the task of irrigation optimization by introducing two cross over approaches: sequence crossover and homo-crossover for the Shijing Irrigation Networks which is located in China. Gupta et.al. (1998) developed the methodology based on genetic algorithm for lower cost design of new and augmentation of existing water distribution networks. Dandy et.al.(1996) developed an improved GA formulation for pipe network optimization. The case study results indicated that the improved GA performs significantly better than the simple GA. Wardlaw and Sharif (1999) demonstrated that GAs provide robust and acceptable solutions to the four-reservoir deterministic finite-horizon problem, and can reproduce the known global optimum. Stewart et.al.(2004) developed special purpose genetic algorithm for the class of spatial planning problems in which different land uses have to be allocated across a geographical region, subject to a variety of constraints and conflicting management objectives. Ting-chao et al.(2005) developed macroscopic nodal pressure model and the model of relationship between supply flow and water source head by using genetic algorithm. Thus, the GAs have wide applications in obtaining the optimum solutions in water related problems.

MATERIALS AND METHODS

Genetic algorithms are a stochastic heuristic search method whose mechanisms are based upon simplification of evolutionary processes observed in nature as proposed by in Darwin's theory of evolution. Genetic algorithms operate on a population of solutions rather than a single solution. Since, they operate on more than one solution at once; genetic algorithms are typically good at both the exploration and exploitation of the search space.

Genetic algorithm search begins with a set of potential solutions and changing them during several iterations. The Genetic algorithm hopes to converge on the most 'fit' solution. The process begins with a set of potential solutions or chromosomes (usually in the form of bit strings of binary numbers) that are randomly generated or selected. The entire set of these chromosomes comprises a population. The chromosomes evolve during several iterations or generations. New generations (offspring) are generated using the crossover and mutation techniques. Crossover involves splitting two chromosomes and then combining randomly selected bits of one chromosome with the other in a pair. Mutation involves flipping a single bit of a chromosome. The chromosomes are then evaluated using a certain fitness criteria and the best ones are kept while others are discarded. This process repeats until one chromosome has the best fitness and thus taken as the best solution of the problem. This process is illustrated in the Figure 1 below.

Optimization Of Water Distribution Pipe Network By Genetic Algorithm

2Indian Streams Research Journal | Volume 4 | Issue 4 | May 2014

Initialize the population

Select individuals for mating

Mate individuals to produce off spring

Mutate offspring

Insert offspring into population

Evaluate the population for

fittnes

Stop

No Are stooping criteria satisfied?

Yes

.

Fig 1. Flowchart for optimization by GA

CASE STUDY

The genetic algorithm model was developed in C#.net to find out optimum cost of the water distributing sub-network of Jaragnagar area of Kolhapur city(Figure 2). The data of this sub-network are presented in Tables 1 to 3 and the network is presented in the Figure 2. Nodal details are given in Table 4.This network consists of 15 pipes and 12 nodes. Constraint on minimum nodal pressure is 10m. Water is supplied through a over head water tank of 15m height at node No.1. The coefficient of roughness for the pipes is 0.005. The population size of the solutions used for the GA based algorithm is 20. The pipe diameters are the decision variables and form the bits of the string. They have been generated randomly within the range 0.05 to 0.5m. The pipe details of the best solutions obtained through GA technique are presented in Table 5.

Table 1.The pipe network details for loop '0’

Table 2. The pipe network details for loop '1' and '2’

Table 3.The pipe network details for loop '3'

3Indian Streams Research Journal | Volume 4 | Issue 4 | May 2014

Loop.

No.

Pipe No. Peak Flow

(lps)

Length of the

pipe(m)

Loop. No. Pipe No. Peak Flow

(lps)

Length of the

pipe(m)

0

1- 2 92.52 160

0

3 -1 0 31.5

2 -10 3.618 31.5

10 -3 3.618 150.5

Loop.

No.

Pipe No. Peak Flow

(lps)

Length of the

pipe(m)

Loop. No. Pipe No. Peak Flow

(lps)

Length of the

pipe(m)

1

2 - 4 179.952 65

2

5 - 6 15.894 77

4 - 5 17.952 30 6 -7 15.894 31

5 - 9 1.674 35 7- 8 0 21

9 -10 0.384 30 8 - 9 0.84 65

10 -2 3.618 31.5 9 - 5 1.674 35

Loop.

No.

Pipe No. Peak Flow

(lps)

Length of the

pipe(m)

Loop.

No.

Pipe No. Peak Flow

(lps)

Length of

the

pipe(m)

3

9-8 0.840 65

3

12 -11 0 56

8 -7 0 21 11- 3 0 168

7- 12 15.894 378 3 - 10 3.618 130.5

10 - 9 0.384 30

Optimization Of Water Distribution Pipe Network By Genetic Algorithm

.

Table 4. Node elevations for the pipe network

Fig 2. Network map

RESULTS AND DISCUSSIONS

The genetic algorithm model developed in C#.net was used to find out optimum cost of the water distributing sub-network of Jaragnagar area of Kolhapur city, Maharashtra. Sensitivity analysis was performed by varying generation number, cross-over probability and mutation probability as below.

Generation numbers: 500 - 1000Cross-over probability: 0.5 - 0.8Mutation probability: 0.008 - 0.03

The developed model was run for this network using these parameters.The results of the sensitivity analysis are presented in Figures 6 to 8.

Fig 3. The variation of the average costs of the network over generations for different crossover probabilities for mutation probability 0.008

4Indian Streams Research Journal | Volume 4 | Issue 4 | May 2014

Node

No.

Elevation

(m)

Node No. Elevation (m) Node No. Elevation (m)

1. 593.00 6 583.34 11 596.55

2. 591.30 7 584.57 12 597.59

3. 593.46 8 589.50

4. 589.30 9 589.80

5. 589.21 10 590.60

1 2

1

3

1

5

1

6

1 7

1

8

9

1

10

I II

III IV

4

12

11

Optimization Of Water Distribution Pipe Network By Genetic Algorithm

.

Fig 4. The variation of the average costs of the network over generations for different crossover probabilities for mutation probability 0.01

Fig 5. The variation of the average costs the network over generations different crossover for mutation probability 0.03

Fig 6. The average costs vs GA iterations for Cross over probability 0.08 and mutation probability 0.008

It was observed that the optimum solution is obtained for cross over probability of 0.08 and mutation probability

5Indian Streams Research Journal | Volume 4 | Issue 4 | May 2014

Optimization Of Water Distribution Pipe Network By Genetic Algorithm

.

0.008. Therefore, this combination was tested for the 1000 iterations of GA. The time required to converge the genetic algorithm model after 1000th iterations was 01.07 hrs. After 1000th generation the optimum solution obtained is presented in Table 5. It was also observed that the model generates desired results for the other sub-networks of the Jaragnagar area of Kolhapur city. It was also observed from the results shown in figures that the average cost decreases as cross over probability increases. The average cost also decreases with the mutation probability.

Table 1 Optimal solution

CONCLUSION

The genetic algorithm model developed in C#.net generates the optimum cost of the water distribution network of the Jaragnagar area of Kolhapur city for cross over probability of 0.08 and mutation probability 0.008. The model can also be used to find the optimal pipe network for other distribution networks.

REFERENCES

1.Chen Y.M.(1997) Management of water resources using improved genetic algorithms, Computers and Electronics in Agriculture,18: 117-1272.Dandy G. C.,.Simpson, A. R and Murphy L. J. (1996) , An improved genetic algorithm for pipe network optimization, Journal of Water Resources Planning and Management, 32(2): 449-458.3.Goldberg D.E. (1989) Genetic Algorithms in Search, Optimization and Machine Learning. Addison-Westley Press. 4.Gupta I., Gupta A. and Khanna, P. (1999) Genetic algorithm for optimization of water distribution systems. Environment, Modelling and Software 14437-446 5.Holland J. H. (1992) Adaptation in Natural and Artificial Systems (2nd edn.) Univ. of Michigan Press. 6.Stewart T.J. and Janssen, R. (2004) A genetic algorithm approach to multiobjective land use planning, Computers and Operations Research, 31: 2293-23137.Ting-chao YU and Zhang, Tu-giao (2005) Optimal operation of water supply systems with tanks based on genetic algorithms, Journal of Zhejiang University Science 2005,6A(8): 886-893.8.Wardlaw R. and Sharif M.(1999) Evaluation of genetic algorithms for optimal reservoir system operation. Journal of Water Resources Planning and Management. 125 (1) 25-33.

6Indian Streams Research Journal | Volume 4 | Issue 4 | May 2014

Optimum Cost(Rs.)

Diameters(m)

Rs.84706209.46

0.06, 0.08, 0.105, 0.12, 0.15, 0.17, 0.205, 0.225, 0.08, 0.075, 0.075, 0.075, 0.075,

0.205, 0.075, 0.075, 0.085, 0.19, 0.085, 0.105, 0.225

Optimization Of Water Distribution Pipe Network By Genetic Algorithm

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