Parameter selection for genetic algorithm-based simulation optimization

PARAMETER SELECTION FOR GENETIC ALGORITHM (GA)-BASED SIMULATION OPTIMIZATION

A THESIS

SUBMITTED TO THE DEPARTMENT OF INDUSTRIAL ENGINEERING

AND THE INSTITUTE OF ENGINEERING AND SCIENCES OF BILKENT UNIVERSITY

IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF

MASTER OF SCIENCE

By

Onur Boyabatlı August, 2001

I certify that I have read this thesis and in my opinion it is fully adequate, in scope and in quality, as a thesis for the degree of Master of Science.

Assoc. Prof. İhsan Sabuncuoğlu (Principal Advisor)

I certify that I have read this thesis and in my opinion it is fully adequate, in scope and in quality, as a thesis for the degree of Master of Science.

Assoc. Prof. M. Selim Aktürk

I certify that I have read this thesis and in my opinion it is fully adequate, in scope and in quality, as a thesis for the degree of Master of Science.

Assist. Prof. Doğan Serel

Approved for the Institute of Engineering and Sciences:

Prof. Mehmet Baray

ABSTRACT

PARAMETER SELECTION FOR GENETIC ALGORITHM (GA)-BASED SIMULATION OPTIMIZATION

Onur Boyabatlı

M.S. in Industrial Engineering Supervisor: Assoc. Prof. İhsan Sabuncuoğlu

August, 2001

Improvements on heuristic techniques with the availability of faster PC’s increase the importance of simulation-optimization (sim/opt) applications. Sim/opt methodologies use computer simulation integrated with an optimization sub-routine to optimize the problems of interest. The main contribution of these methods is to make simulation as a prescriptive tool rather than a descriptive tool, which has been widely used as the descriptive tool for estimating the performance of complex stochastic systems. Sim/opt methodologies have been applied on various combinatorial optimization problems, and the current trend in sim/opt area is the use of heuristic techniques. Genetic Algorithm (GA) is the well known meta-heuristic, which is a global search algorithm taking its inspiration from natural genetics. GA has several parameters affecting its performance. Even for the GA with same structural parameters (coding scheme, operator types, stopping criterion), the different combinations of numerical parameters (initial population type, population size, maximum generation number and the crossover and mutation probabilities) may lead to drastic changes in the performance of the algorithm. This study examines the effects of numerical parameters of GA on its performance in terms of both fitness and CPU time; and proposes guidelines for appropriate parameter selection. A test problem of a serial assembly line taken from the literature is used for the GA-based simulation-optimization application. A genetic algorithm coded in C is integrated with a simulation model developed using SIMAN simulation language. Modifications on the test problem are made to analyze the behavior of GA parameters under different experimental conditions. The computational results reveal that in the case of a dominant set of decision variables, for rapid convergent GA applications high mutation rates are more useful, whereas the crossover operator does not have any significant impact on GA performance.

ÖZET

GENETIK ALGORITMALARA BAĞLI BENZETİM-ENİYİLEME UYGULAMALARINDA PARAMETRE SEÇİMİ

Onur Boyabatlı

Endüstri Mühendisliği Bölümü Yüksek Lisans Tez Yöneticisi: Doç. Dr. İhsan Sabuncuoğlu

Ağustos, 2001

Daha hızlı kişisel bilgisayarların varlığı, bulgusal tekniklerdeki ilerlemelerle birlikte benzetim-eniyileme uygulamalarının önemini arttırmıştır. Benzetim-eniyileme metodları ilgili problemleri eniyilemek için, bilgisayar benzetimini bir eniyileme alt-rutini ile tümleyerek kullanırlar. Bu metodların ana katkısı, kompleks rassal sistemlerin performanslarını kestirirken tasfir edici bir araç olarak yaygınca kullanılan benzetimi, hükmedici bir araç haline getirmektir. Benzetim-eniyileme metodları birçok birleşi eniyileme problemleri üzerinde uygulanmıştır, ve benzetim-eniyileme içindeki şu anki trend meta-bulgusal tekniklerin kullanılmasıdır. Genetik algoritma en yaygın meta-bulgusal teknik olup, ilhamını doğal genetikten alan tümel arama algoritmasıdır. Genetik algoritmaların performansını etkileyen birçok parametresi vardır. Aynı yapısal parametredeki (kodlama yapısı, işlemci çeşitleri, sonlanma kriteri)genetik algoritmalarda bile, sayısal parametrelerin ( populasyon büyüklüğü, en yüksek cenerasyon sayısı, değişim ve eşeyleme olasılıkları, başlangıç popülasyonu çeşidi) değişik birleşimi, algoritmanın performansında şiddetli değişikliklere meydan verebilir. Bu çalışma sayısal parametrelerin genetik algoritmanın kabiliyet ve ana işlemci zamanına dayanan performansı üzerindeki etkilerini inceler. Uygun parametre seçimleri için rehberlik önerir. Literatürden alınan bir seri montaj hattı, test problemi olarak genetik algoritmalara dayanan benzetim-eniyileme uygulamasında kullanılıyor. C dilinde kodlanan genetik algoritma, SIMAN kullanılarak geliştirilen benzetim modeline tümlenmiştir. Test problemi üzerinde değişiklikler yapılarak genetic algoritmanın parametrelerinin değişik deneysel koşullrdaki davranışları incelenmiştir. Hesaplanan sonuçlar ortaya çıkarmıştır ki; karar değişkenlerinin üstün bir seti olduğu durumda, hızlı yakınsak genetik algoritmalar için yüksek değişim olasılığı daha kullanışlıyken, eşeyleme işlemcisinin genetik algoritmanın performansı üzerinde belirleyici bir etkisi olmamaktadır.

ACKNOWLEDGEMENT

I would like to express my deep gratitude to Assoc. Prof. İhsan Sabuncuoğlu for his guidance, attention, motivation, suggestions, and patience throughout this work.

I am grateful to Assoc. Prof Selim Aktürk and Assist. Prof. Doğan Serel for their valuable comments and kindness.

I would like to express my special thanks to Güneş Erdoğan for his deep understanding, and his sincere help throughout the work.

Special thanks to Deniz Orhon, for her deep motivation and encouragement, and the reminding when I forgot myself. It is precious to know there is someone who really believes in me.

And my family, many thanks to you for your moral support and great encouragement all the time.

I cannot fully express my dear gratitude for my other colleagues, and professors for their both academic and moral support and encouragement. Many thanks, especially for your patience and understanding.

CONTENTS

1 Introduction 1 2 Literature Review 6 2.1 Simulation-Optimization Literature 6 2.2 GA Literature 10 3 Genetic Algorithms 19 3.1 Introduction 19 3.2 Conceptual Framework 20 3.3 Mathematical Background 24 4 Proposed Study 27 4.1 Study Objective 27 4.1.1 Structural Parameters 27 4.1.2 Numerical Parameters 29 4.2 Test Problem 32 4.3 Simulation Model 34 4.4 GA Model 35 4.5 Validation of Models 40 4.6 Design of Experiments 41 4.5.1 2k _{Factorial Design 42} 4.5.2 Diagnostic Checking 47

5 Experimental Results 48

5.1 Original Test Problem 49

5.1.1 Model Adequacy Checking 49

5.1.2 Fitness Response 52

5.1.3 CPU Time Response 64

5.1.4 Conclusion 71

6 Further Analyses 78

6.1 Modification of Objective Function Parameters 78

6.1.1 Model Adequacy Checking 80

6.1.2 Fitness Response 82

6.1.2.1 Original Case 82

6.1.2.2 1000 Case 84

6.1.2.3 Buffer Case 87

6.1.3 CPU Time Response 89

6.1.3.1 Original Case 89

6.1.3.2 1000 and Buffer Cases 91

6.1.4 Conclusion 97

6.2 Constrained Version of Test Problem 99

6.2.1 Model Adequacy Checking 100

6.2.2 Fitness Response 100

6.2.3 CPU Time Response 103

6.2.4 Conclusion 106

6.3 Modification of Crossover Operator 107

6.3.2 CPU Time Response 112

6.3.3 Conclusion 114

7 Discussion 115

A Simulation Code of the Model B Genetic Algorithm Code

LIST OF FIGURES

1 Flowchart of Simulation-Optimization Techniques 2

2 Flowchart of Simple Genetic Algorithm 20

3 The serial assembly line modeled in test problem (Law et al., 2000) 33

4 Flowchart of GA Model 39

5 Behavior of Fitness According to Generation Number in Proposed GA 41 6.a Best fitness obtained versus maximum generation number graph 45 6.b Difference of Fitness versus Maximum Generation Number Graph 45 6.c CPU Time versus Maximum Generation Number Graph 46

7.a Residual Plot of Fitness Response 52

7.b Residual Plot of CPU Time Response 52

8 Normal Probability Plot of Effects for Fitness Response 54 9.a Population Type Main Effect Graph on Fitness 57 9.b Population Size Main Effect Graph on Fitness 57 9.c Maximum Generation Number Main Effect on Fitness 57 9.d Mutation Probability Main Effect on Fitness 58

9.e All Factors Main Effects on Fitness 58

9.f Population Type-Mutation Probability Interaction Effect on Fitness 58 10 Normal Probability of Effects for CPU Time Response 65

11.a Population Size Main Effect On CPU Time 67

11.b Maximum generation Number Main Effect on CPU Time 67 11.c Mutation Probability Main Effect on CPU Time 67

11.d All Factors’ Main Effects on CPU Time 68

11.e Maximum Generation Number-Population Size Interaction Effect on CPU Time 68 12.a Best Fitness with Different Levels of Crossover Probability 72 12.b CPU Time with Different Levels of Crossover Probability 73 13.a Best Fitness with Different Levels of Mutation Probability 74 13.b CPU Time with Different Levels of Mutation Probability 74 14.a Population Type Main Effect on Fitness of Original Case 83 14.b All Factors’ Main Effects on Fitness of Original Case 83

15.a Crossover Probability Main Effect on Fitness of the 1000 Case 86 15.b Mutation Probability Main Effect on Fitness of the 1000 Case 86 15.c All Factors’ Main Effects on Fitness of the 1000 Case 86 16 All Factors’ Main Effects on Fitness of Buffer Case 88 17.a Population Type Main Effect on CPU Time of Original Case 90 17.b Mutation Probability Main Effect on CPU Time of Original Case 90 17.c All Factors’ Main Effects on CPU Time of Original Case 90 18.a Population Type Main Effect on CPU Time of 1000 Case 92 18.b Mutation Probability Main Effect on CPU Time of 1000 Case 93 18.c All Factors’ Main Effects on CPU Time of 1000 Case 93 18.d Population Type-Mutation Probability Interaction Effect on CPU of 1000 Case 93 19.a Population Type Main Effect on CPU Time of Buffer Case 94 19.b Mutation Probability Main Effect on CPU Time of Buffer Case 94 19.c All Factors’ Main Effects on CPU Time of Buffer Case 94 19.d Population Type-Mutation Probability Interaction Effect on CPU of Buffer Case 95 20 All Factors’ Main Effects on Fitness of Constrained Case 102 21.a Population Type Main Effect on CPU Time of Constrained Case 104 21.b Mutation Probability Main Effect on CPU Time of Constrained Case 104 21.c All Factors’ Main Effects on CPU Time of Constrained Case 105 21.d Population Type-Mutation Probability Interaction Effect on 105

CPU of Constrained Case

22.a Population Type Main Effect on Fitness of Crossover Case 110 22.b Mutation Probability Main Effect on Fitness of Crossover Case 110 22.c All Factors’ Main Effects on Fitness of Crossover Case 110 23.a Population Type Main Effect on CPU Time of Crossover Case 112 23.b Mutation Probability Main Effect on CPU Time of Crossover Case 113 23.c All Factors’ Main Effects on CPU Time of Crossover Case 113 23.d Population Type-Mutation Probability Interaction Effect on 113

LIST OF TABLES

1 Summary of Simulation-Optimization Algorithms 9 2 Summary of Theoretical Studies on Genetic Algorithms 13 3 Summary of GA-based Simulation-Optimization Case Studies 15

4 Processing Times of Machines in Workstations 33

5 Structural Parameters of GA Covered in the Analysis 35 6 Comparison of Simulation Results of Original Model and Proposed Model 40

7 Factors and Levels for Factorial Design 46

8.a GA Results for Fitness Response 50

8.b GA Results for CPU Time Response 51

9 ANOVA Results For Fitness Response 53

10 ANOVA Results For CPU Time Response 64

11 Results of Factorial Design Analysis 72

12 Percentage Change in Responses According to Changes in Factor Levels 76

13 Final Result of Analysis 77

14.a GA Results for Fitness Response of Original Case 80 14.b GA Results for Fitness Response of 1000 Case 80 14.c GA Results for Fitness Response of Buffer Case 81 15.a GA Results for CPU Time Response of Original Case 81 15.b GA Results for CPU Time Response of 1000 Case 81 15.c GA Results for CPU Time Response of Buffer Case 82 16 ANOVA Results For Fitness Response for Original Case 82 17 ANOVA Results For Fitness Response for 1000 Case 84 18 ANOVA Results For Fitness Response for Buffer Case 87 19 ANOVA Results For CPU Time for Original Case 89 20.a ANOVA Results For CPU Time Response for 1000 Case 91 20.b ANOVA Results For CPU Time Response for Buffer Case 92 21 Results of Factorial Design Analysis for Modified Objective Function Parameters 98 22 Percentage Change in Responses According to Change in Population Type 98 23.a GA Results for Fitness Response of Constrained Case 100

23.b GA Results for CPU Time Response of Constrained Case 100 24 ANOVA Results For Fitness Response for Constrained Case 101 25 ANOVA Results For CPU Time Response for Constrained Case 103 26 Results of Factorial Design Analysis for Constrained Case 106 27.a GA Results for Fitness Response of Constrained Case 109 27.b GA Results for Fitness Response of Constrained Case 109 28 ANOVA Results For Fitness Response for Crossover Case 109 29 ANOVA Results For CPU Time for Crossover Case 112 30 Summary of Results of Analyses for All Cases 116 31 Percentage Change in Responses According to Population Type for All Cases 116



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