18651215 Parallel Niching Genetic Algorithms a Crowding Perspective

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    PARALLEL NICHING GENETIC ALGORITHMS:

    A CROWDING PERSPECTIVE

    BY

    JASON BROWNLEE

    B.A.S., Swinburne University of Technology, 2002

    MINOR THESIS

    Submitted in partial fulfilment of the requirements for the degree of Master ofInformation Technology

    Centre for Intelligent Systems and Complex Processes

    School of Information TechnologySwinburne University of Technology

    2004

    Victoria, Australia

    Copyright by

    Jason Brownlee2004

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    AbstractGenetic algorithms are a class of global search algorithm inspired by biological evolution

    that return approximate solutions to difficult search problems. Parallel niching geneticalgorithms are a specialised type of genetic algorithm that search for and maintain

    multiple approximate solutions by grouping subpopulations of candidate solutions aroundareas of interest in the search space. Crowding is one way of achieving a niching effect

    based on the concept of localised competition for limited resources where similarcandidate solutions are matched together and compete for survival based on solution

    usefulness. An abstract conceptual model called the generalised crowding model is

    provided to describe discussed traditional crowding algorithms. It provides a template forexisting crowding algorithms and a framework for crowding algorithm based analysis and

    development. A simple crowding algorithm is proposed that has no forced biases or

    similarity approximations and is shown to be an embodiment of the generalised crowdingmodel and the redefined crowding principle of localised generational competition. The

    simple crowding algorithm is analysed using crowding centric measures, revealing

    insights into unbiased parental pairing, candidate solution matching and actualreplacement behaviour. Analysis of common crowding functionalities on the simplecrowding algorithm and comparison between the proposed algorithm and other crowding

    techniques reveals a practical trade-off between decreased time until convergence at the

    cost of decreased niche stability.

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    Table of Contents

    ABSTRACT........................................................................................................................I

    TABLE OF CONTENTS ................................................................................................ II

    LIST OF FIGURES ........................................................................................................ IV

    LIST OF TABLES ............................................................................................................V

    LIST OF EQUATIONS....................................................................................................V

    INTRODUCTION............................................................................................................. 1

    CANONICAL GENETIC ALGORITHM .................................................................................. 2NICHING GENETIC ALGORITHM ....................................................................................... 7

    METHODS ...................................................................................................................... 12

    METHODOLOGY ............................................................................................................. 12

    TEST PROBLEMS............................................................................................................. 14MEASURES ..................................................................................................................... 16

    PREVIOUS RESEARCH............................................................................................... 18

    CROWDING FACTORMODEL .......................................................................................... 18

    DETERMINISTIC CROWDING ........................................................................................... 20

    RESTRICTED TOURNAMENT SELECTION......................................................................... 23MULTI-NICHE CROWDING ............................................................................................. 25

    PROBABILISTIC CROWDING............................................................................................ 27

    DISCUSSION ................................................................................................................... 29

    QUINTESSENTIAL CROWDING............................................................................... 31

    CROWDING..................................................................................................................... 31GENERALISED CROWDING MODEL................................................................................. 32

    DISCUSSION ................................................................................................................... 36

    QUINTESSENTIAL CROWDING INVESTIGATED............................................... 39

    SIMPLE CROWDING ALGORITHM.................................................................................... 39

    NATURE OF REPLACEMENTS .......................................................................................... 44HYBRIDS ANDNORMALS IN SEARCH.............................................................................. 47

    REPLACEMENT WASTE AND REPLACEMENT ERROR....................................................... 49

    DISCUSSION ................................................................................................................... 53

    AUGMENTED SIMPLE CROWDING ....................................................................... 56BIAS IN UPFRONT SELECTION ........................................................................................ 56SAMPLING IN LOCALISED SELECTION ............................................................................ 60

    ALTERNATIVE REPLACEMENT STRATEGIES ................................................................... 63

    DISCUSSION ................................................................................................................... 65

    SIMPLE CROWDING COMPARED .......................................................................... 68

    MAINTENANCE OF DIVERSITY........................................................................................ 68

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    PROMOTION OF USEFUL DIVERSITY ............................................................................... 70

    TIME UNTIL CONVERGENCE ........................................................................................... 71

    LOCALISATION MATCHING BEHAVIOUR........................................................................ 72REPLACEMENTS BEHAVIOUR......................................................................................... 73

    REPLACEMENT ERRORBEHAVIOUR............................................................................... 74

    DISCUSSION ................................................................................................................... 74CONCLUSION ............................................................................................................... 76

    SUMMARY...................................................................................................................... 76FUTURE RESEARCH........................................................................................................ 77

    CONCLUSIONS................................................................................................................ 83

    BIBLIOGRAPHY........................................................................................................... 85

    APPENDIX A TEST FUNCTIONS ........................................................................... 87

    F1-SINE FUNCTION -5PEAKS OF EQUAL HEIGHT.......................................................... 87F2-SINE FUNCTION -5PEAKS OF DIFFERING HEIGHT.................................................... 87

    F3-SCALED SIX-HUMP CAMEL BACK FUNCTION ............................................................ 88F4-HIMMELBAUS FUNCTION ....................................................................................... 89F5-SCHWEFELS FUNCTION .......................................................................................... 90

    APPENDIX B TEST RESULTS................................................................................. 91

    INVESTIGATION INTO QUINTESSENTIAL CROWDING....................................................... 91

    AUGMENTED SIMPLE CROWDING................................................................................... 91

    SIMPLE CROWDING COMPARED ..................................................................................... 91

    APPENDIX C GENERALISED CROWDING MODEL ........................................ 93

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    List of FiguresFIGURE 1-PSEUDO CODE LISTING OF THE CANONICAL GENETIC ALGORITHM ...................... 4

    FIGURE 2-PSEUDO CODE LISTING OF THE CROWDING FACTOR MODEL .............................. 19FIGURE 3-PSEUDO CODE LISTING OF THE DETERMINISTIC CROWDING TECHNIQUE............ 21

    FIGURE 4-PSEUDO CODE LISTI