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An Adaptive GA for Multi Objective Flexible Manufacturing Systems

A. Younes, H. Ghenniwa, S. Areibiayounes@uoguelph.ca, hgenniwa@uwo.ca 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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