1 an adaptive ga for multi objective flexible manufacturing systems a. younes, h. ghenniwa, s....
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An Adaptive GA for Multi Objective Flexible Manufacturing Systems
A. Younes, H. Ghenniwa, S. [email protected], [email protected] sareibi @
uoguelph.ca
July 2002
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Outline
Introduction Background (Flexible Manufacturing Systems) Motivation/Contributions Example Mathematical Formulation Genetic Algorithm Implementation Numerical Testing and Comparison. Conclusions & Future Work.
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Introduction
Flexible Manufacturing Systems consist of multiple heterogenous machines (robots/computers).
Ultimate goal: is to maximize the FMS throughput. Several problems such as part type partitioning,
assignment and sequencing must be solved before this goal can be achieved.
This work is an initial investigation for the suitability of Genetic Algorithms to solve Dynamic Optimization problems associated with scheduling/sequencing in FMS systems.
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Background
The goodness of an assignment is measured in terms of minimizing part transfer (primary) and balancing the work-load of the machines (secondary).
The aim is to facilitate the creation of machine cells with minimum part transfer while maximizing the utilization of machines.
While minimizing part transfer tends to favor the assignment of the whole of a part to a single machine, balancing work-load tries to make the work-load distribution even among the machines.
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Motivation
A large number of combinatorial problems are associated with Manufacturing Optimization.
Many short comings from current techniques used for dynamic optimization problems.
This work is used as foundation for future work in the area of dynamic scheduling/sequencing of Flexible Manufacturing Systems.
Techniques developed for such problems can be easily adapted for other type of problems that are dynamic in nature.
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Contribution
One of the main contribution of this work is developing an automated technique to generate benchmarks for Flexible Manufacturing Systems (both Static and Dynamic Benchmarks)
Several crossover techniques have been developed and tested for Flexible Manufacturing Systems.
Not too much work has been done in the literature on solving dynamic optimization problems for Flexible Manufacturing Systems.
This work lays the foundation for Evolutionary dynamic optimization strategy for scheduling/sequencing of FMS.
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Mathematical Formulation F1: Minimization of part transfer (by minimizing the number
of machines required to process the part) F2: Minimization of the number of necessary operations
required from each machine over the possible processing choices.
F3: Load balancing by minimizing the cardinality distance between the workload of any pair of machines.
Over multi-objective mathematical model of FMS is to solve for F1, F2, F3 Subject to a part being processed by a single machine.
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FMS Example
M1 O1 O2 O3 O5
M2 O2 O3 O5
M3 O4 O5
P1 O1 O2 O3 O5
P2 O2 O3 O5
P1 P2
Four operations needed to process P1
Three operations needed to process P2M1 can perform Four operations
Two part types & Three Machines
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M2 can perform three operations
M3 can perform two operations
This choice tries to minimize part transfer
between machines
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FMS Example
M1 O1 O2 O3 O5
M2 O2 O3 O5
M3 O4 O5
P1 P2Two part types & Three Machines
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This choice tries to distribute workload (operations) evenly between machines
P1 O1 O2 O3 O5
P2 O2 O3 O5
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A GA Algorithm for FMS Genetic Algorithms are well suited for multiple-objective
optimization problems. The basic feature of GA is multiple directional and global
search through maintaining a population of potential solutions from generation to generation.
In our implementation we have combined a Pareto-based approach with an adaptive weighted sum technique for tackling the multi-objective flexible manufacturing systems problem.
One of the main issues is determining the fitness value of individuals according to multiple objectives.
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GA Main Componenets
Representation Fitness Function
Selection &
Deletion
TransformationFunctions
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Chromosome Representation
M1 O5
P1 P2
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P1 O1 O2 O3 O5
P2 O2 O3 O5
M1 M1 M2 M3 M1 M2 M3
Chromosome
O2O1 O3
O3O2 O5
O5O4
M2
M3
P1 P2
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PTF
Fitness Function
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j
parts
jPT transferf
1
machines
iiBAL Nopf
1
2
normalized
BALF
normalized
The weights determine which of the two objectives is favored
Two objectives are considered
BALPT FWFWScore 21
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Crossover
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PARENT 1M1
M2
M4
M3
M2
M4
M5
PARENT 2M3
M3
M4
M5
M1
M2
M4
PART1 PART2
CHILD 1M1
M2
M4
M3
M1
M2
M4
`
CHILD 2M3
M3
M4
M5
M2
M4
M5
Simple Crossover
Cut points set at
the part delimiter
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Crossover
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PARENT 1M1
M2
M4
M3
M2
M4
M5
PARENT 2M3
M3
M4
M5
M1
M2
M4
PART1 PART2
CHILD 1M1
M3
M4
M5
M2
M2
M5
CHILD 2M3
M2
M4
M3
M1
M4
M4
Uniform Crossover
A Cut point for
each gene delimiter
` ` ```
`
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Crossover
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PARENT 1M1
M2
M4
M3
M2
M4
M5
PARENT 2M3
M3
M4
M5
M1
M2
M4
PART1 PART2
CHILD 1M1
M2
M4
M5
M1
M2
M4
`
CHILD 2M3
M3
M4
M3
M2
M4
M5
Structured Crossover
Cut points Randomly
set in the string
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GA Algorithm
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initialize pop. ;
evaluate initial pop. ;
while not stopping condition
{
select fittest parents for reproduction;
apply crossover & mutation;
evaluate pop.;
}
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Benchmarks
Several Benchmarks used to evaluate the performance of the GA for FMS.
Randomly generated with different M/P/O.
The Generator can be used for both Dynamic & Static optimization solvers.
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Benchmarks (Statistics)
0
20
40
Benchmarks for FMS
Machines 3 2 5 5 5 6 7 10 11 15
Parts 1 2 2 5 10 6 7 15 20 30
Operations 5 5 7 6 8 10 7 9 9 12
B1 B2 B3 B4 B5 B6 B7 B8 B9 B10
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Results & Discussion
The Genetic Algorithm code was developed on a Sun Sparc Ultra 10 Workstation running Solaris 8.
The Code was written in C and compiled using GNU g++ version 2.95.2.
Results obtained were first run using the Genetic Algorithm by optimizing each objective function separately.
The Genetic Algorithm was then run by optimizing both objective functions together.
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GA Convergence
Convergence Rate
0
10
20
30
40
Generation
OF1/O
F2
10M15P 11M20P
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Crossover Operator
Convergence Rate
0
0.2
0.4
0.6
0.8
Generation
OF1(P
art
Tra
nsf
er)
Simple Xover Uniform Xover
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Machines Involved
0123456
Mach
ines
3M1P5O 3M2P5O 5M2P7O
Benchmarks
Small Size Benchmarks
PT BAL FWA AWA
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Cont .. Machines Involved
0
5
10
15
20
25
Mach
ines
5M5P6O 5M10P8O 6M6P10O 7M7P7O
Benchmarks
Medium Sized Benchmarks
PT BAL FWA AWA
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Cont .. Machines Involved
020406080
100120
Mach
ines
10M15P9 11M20P9O 15M30P12O
Benchmarks
Large Sized Benchmarks
PT BAL FWA AWA
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Operations Per Machine
0246
Mac
hin
es
PT
FWA
Benchmarks
3M-1P-5O
PT BAL FWA AWA
PT 2 2 0
BAL 2 1 1
FWA 2 2 0
AWA 2 2 0
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Operations Per Machine
0246
Mac
hin
es
PT
FWA
Benchmarks
3M-2P-5O
PT BAL FWA AWA
PT 4 2 1
BAL 3 2 2
FWA 3 2 2
AWA 3 2 0
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Operations Per Machine
0
2
4
6
Mac
hin
es
PT
FWA
Benchmarks
5M-2P-7O
PT BAL FWA AWA
PT 1 0 1 2 3
BAL 1 1 1 2 2
FWA 1 0 2 2 2
AWA 1 0 2 2 2
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Conclusions
In this paper we introduced an adaptive Genetic Algorithm for Flexible Manufacturing Systems.
A random benchmark generator was developed for both static and dynamic problems.
Results obtained indicate that our Genetic Algorithm implementation achieves excellent results with respect to part transfer and balancing the work among the machines.
Currently we are testing the Genetic Algorithm on a Dynamic version for Flexible Manufacturing where one or more machines may fail during optimization.
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Future Work
Compare this Genetic Algorithm implementation with other advanced search techniques (Tabu Search, GRASP) for both static and dynamic problems.
Incorporate local search with the Genetic Algorithm to create a Memetic Algorithm
Include sequencing constraints and tools costs in the objective function.
Integrating Multi Agent Systems with Genetic Algorithms for complex dynamic optimization approaches.
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All Source Code is Available at the following web site:http://www.uoguelph.ca/~sareibi
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