• TABLE OF CONTENTS
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 Title Page
 Acknowledgement
 Table of Contents
 Abstract
 Introduction
 Simulated annealing
 The genetic algorithm
 A Markov chain model of the simple...
 Some empirical results
 The Cramer's rule formulation of...
 The zero mutation probability stationary...
 A monotonic mutation probability...
 Representation of the stationary...
 Conclusions and future directi...
 Appendix A: Discrete time finite...
 Appendix B: The Perron-Frobenius...
 Appendix C: Vandermonde determinants,...
 Appendix D: Computer listings
 References
 Biographical sketch






Title: Toward an extrapolation of the simulated annealing convergence theory onto the simple genetic algorithm
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Permanent Link: http://ufdc.ufl.edu/UF00097388/00001
 Material Information
Title: Toward an extrapolation of the simulated annealing convergence theory onto the simple genetic algorithm
Physical Description: viii, 166 leaves : ill. ; 29 cm.
Language: English
Creator: Davis, Thomas E. ( Dissertant )
Principe, Jose C. ( Thesis advisor )
Childers, Donald G. ( Reviewer )
Arroyo, Antonio A. ( Reviewer )
Rao, Murali ( Reviewer )
Chenette, Eugune R. ( Reviewer )
Phillips, Winfred M. ( Degree grantor )
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 1991
Copyright Date: 1991
 Subjects
Subjects / Keywords: Algorithms   ( lcsh )
Combinatorial optimization   ( lcsh )
Simulated annealing (Mathematics)   ( lcsh )
Electrical Engineering thesis Ph. D
Dissertations, Academic -- Electrical Engineering -- UF
Genre: bibliography   ( marcgt )
non-fiction   ( marcgt )
theses   ( marcgt )
 Notes
Abstract: Simulated annealing and the genetic algorithm are stochastic relaxation search techniques suitable for application to a wide variety of combinatorial complexity nonconvex optimization problems. Each produces a sequence of candidate solutions (or populations of candidate solutions) to the underlying optimization problem, and the purpose of both algorithms is to generate sequences biased toward solutions which optimize the objective function. The appeal of simulated annealing is that it provides asymptotic convergence to a globally optimal solution. A substantial body of knowledge exists concerning the algorithm convergence behavior. It is based upon a nonstationary Markov chain algorithm model. No genetic algorithm model comparable in scope exists in the literature. This work constitutes an attempt to provide such a model and accompanying convergence theory by extrapolating the simulated annealing results onto the genetic algorithm. A prerequisite, developed herein, is a nonstationary Markov chain genetic algorithm model. The essence of the simulated annealing theory is demonstration of (1) existence of a unique asymptotic probability distribution (stationary distribution) for the stationary Markov chain corresponding to every strictly positive constant value of an algorithm control parameter (absolute temperature), (2) existence of a stationary distribution limit as the control parameter approaches zero, (3) the desired behavior of the stationary distribution limit (i.e. optimal solution with probability one) and (4) sufficient conditions on the algorithm control parameter to ensure that the nonstationary algorithm achieves (asymptotically) the limiting distribution. With the exception of (3), this work adapts that methodology to the genetic algorithm Markov chain model employing a genetic operator parameter (mutation probability) as the algorithm control parameter. The results include a mutation probability control parameter bound analogous to (and asymptotically superior to) the conventional simulated annealing parameter bounds, and a framework for representing the genetic algorithm stationary distribution components at all consistent fixed control parameter values, including zero. The genetic algorithm stationary distribution limit has nonzero components corresponding to all solutions. Thus, the simulated annealing global optimality convergence result does not extrapolate. However, both empirical and theoretical evidence is provided which suggests that the desired limiting behavior can be approached by suitably adjusting the algorithm parameters.
Thesis: Thesis (Ph. D.)--University of Florida, 1991.
Bibliography: Includes bibliographical references (leaves 163-165).
Additional Physical Form: Also available on World Wide Web
Statement of Responsibility: by Thomas E. Davis.
General Note: Typescript.
General Note: Vita.
 Record Information
Bibliographic ID: UF00097388
Volume ID: VID00001
Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
Resource Identifier: alephbibnum - 001683775
oclc - 25046248
notis - AHZ5752

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Table of Contents
    Title Page
        Page i
        Page i-a
    Acknowledgement
        Page ii
        Page iii
    Table of Contents
        Page iv
        Page v
        Page vi
    Abstract
        Page vii
        Page viii
    Introduction
        Page 1
        Page 2
        Page 3
        Page 4
        Page 5
        Page 6
    Simulated annealing
        Page 7
        Page 8
        Page 9
        Page 10
        Page 11
        Page 12
        Page 13
        Page 14
        Page 15
        Page 16
        Page 17
        Page 18
        Page 19
    The genetic algorithm
        Page 20
        Page 21
        Page 22
        Page 23
        Page 24
        Page 25
        Page 26
        Page 27
    A Markov chain model of the simple genetic algorithm
        Page 28
        Page 29
        Page 30
        Page 31
        Page 32
        Page 33
        Page 34
        Page 35
        Page 36
        Page 37
        Page 38
        Page 39
        Page 40
        Page 41
    Some empirical results
        Page 42
        Page 43
        Page 44
        Page 45
        Page 46
        Page 47
        Page 48
        Page 49
        Page 50
        Page 51
        Page 52
        Page 53
        Page 54
        Page 55
        Page 56
        Page 57
        Page 58
        Page 59
        Page 60
        Page 61
        Page 62
        Page 63
        Page 64
        Page 65
    The Cramer's rule formulation of the stationary distribution
        Page 66
        Page 67
        Page 68
        Page 69
        Page 70
        Page 71
        Page 72
    The zero mutation probability stationary distribution limit
        Page 73
        Page 74
        Page 75
        Page 76
        Page 77
        Page 78
        Page 79
        Page 80
        Page 81
        Page 82
        Page 83
        Page 84
        Page 85
    A monotonic mutation probability ergodicity bound
        Page 86
        Page 87
        Page 88
        Page 89
        Page 90
        Page 91
    Representation of the stationary distribution solution
        Page 92
        Page 93
        Page 94
        Page 95
        Page 96
        Page 97
        Page 98
        Page 99
        Page 100
        Page 101
        Page 102
        Page 103
        Page 104
        Page 105
        Page 106
        Page 107
        Page 108
        Page 109
        Page 110
        Page 111
        Page 112
        Page 113
        Page 114
        Page 115
        Page 116
        Page 117
        Page 118
        Page 119
    Conclusions and future direction
        Page 120
        Page 121
        Page 122
        Page 123
        Page 124
        Page 125
    Appendix A: Discrete time finite state Markov chains
        Page 126
        Page 127
        Page 128
        Page 129
        Page 130
        Page 131
    Appendix B: The Perron-Frobenius theorem and stochastic matrices
        Page 132
        Page 133
        Page 134
        Page 135
        Page 136
    Appendix C: Vandermonde determinants, symmetric and alternating polynomials
        Page 137
        Page 138
        Page 139
        Page 140
        Page 141
        Page 142
        Page 143
        Page 144
    Appendix D: Computer listings
        Page 145
        Page 146
        Page 147
        Page 148
        Page 149
        Page 150
        Page 151
        Page 152
        Page 153
        Page 154
        Page 155
        Page 156
        Page 157
        Page 158
        Page 159
        Page 160
        Page 161
        Page 162
    References
        Page 163
        Page 164
        Page 165
    Biographical sketch
        Page 166
        Page 167
        Page 168
        Page 169
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