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Friday, October 21, 2011

An Introduction to Genetic Algorithms






An Introduction to Genetic Algorithms............................................................................................................1
Mitchell Melanie......................................................................................................................................1
Chapter 1: Genetic Algorithms: An Overview.................................................................................................2
Overview..................................................................................................................................................2
1.1 A BRIEF HISTORY OF EVOLUTIONARY COMPUTATION.....................................................2
1.2 THE APPEAL OF EVOLUTION.....................................................................................................4
1.3 BIOLOGICAL TERMINOLOGY.....................................................................................................5
1.4 SEARCH SPACES AND FITNESS LANDSCAPES.......................................................................6
1.5 ELEMENTS OF GENETIC ALGORITHMS...................................................................................7
Examples of Fitness Functions...................................................................................................7
GA Operators..............................................................................................................................8
1.6 A SIMPLE GENETIC ALGORITHM..............................................................................................8
1.7 GENETIC ALGORITHMS AND TRADITIONAL SEARCH METHODS..................................10
1.9 TWO BRIEF EXAMPLES..............................................................................................................12
Using GAs to Evolve Strategies for the Prisoner's Dilemma...................................................13
Hosts and Parasites: Using GAs to Evolve Sorting Networks..................................................16
1.10 HOW DO GENETIC ALGORITHMS WORK?...........................................................................21
THOUGHT EXERCISES......................................................................................................................23
COMPUTER EXERCISES...................................................................................................................24
Chapter 2: Genetic Algorithms in Problem Solving......................................................................................27
Overview................................................................................................................................................27
2.1 EVOLVING COMPUTER PROGRAMS.......................................................................................27
Evolving Lisp Programs...........................................................................................................27
Evolving Cellular Automata.....................................................................................................34
2.2 DATA ANALYSIS AND PREDICTION.......................................................................................42
Predicting Dynamical Systems.................................................................................................42
Predicting Protein Structure......................................................................................................47
2.3 EVOLVING NEURAL NETWORKS............................................................................................49
Evolving Weights in a Fixed Network.....................................................................................50
Evolving Network Architectures..............................................................................................53
Direct Encoding........................................................................................................................54
Grammatical Encoding.............................................................................................................55
Evolving a Learning Rule.........................................................................................................58
THOUGHT EXERCISES......................................................................................................................60
COMPUTER EXERCISES...................................................................................................................62
Chapter 3: Genetic Algorithms in Scientific Models.....................................................................................65
Overview................................................................................................................................................65
3.1 MODELING INTERACTIONS BETWEEN LEARNING AND EVOLUTION...........................66
The Baldwin Effect...................................................................................................................66
A Simple Model of the Baldwin Effect....................................................................................68
Evolutionary Reinforcement Learning.....................................................................................72
3.2 MODELING SEXUAL SELECTION.............................................................................................75
Simulation and Elaboration of a Mathematical Model for Sexual Selection...........................76
3.3 MODELING ECOSYSTEMS.........................................................................................................78
3.4 MEASURING EVOLUTIONARY ACTIVITY.............................................................................81
Thought Exercises..................................................................................................................................84
Computer Exercises...............................................................................................................................85
Chapter 4: Theoretical Foundations of Genetic Algorithms........................................................................87
Overview................................................................................................................................................87
4.1 SCHEMAS AND THE TWO−ARMED BANDIT PROBLEM.....................................................87
The Two−Armed Bandit Problem............................................................................................88
Sketch of a Solution..................................................................................................................89
Interpretation of the Solution....................................................................................................91
Implications for GA Performance.............................................................................................92
Deceiving a Genetic Algorithm................................................................................................93
Limitations of "Static" Schema Analysis..................................................................................93
4.2 ROYAL ROADS.............................................................................................................................94
Royal Road Functions...............................................................................................................94
Experimental Results................................................................................................................95
Steepest−ascent hill climbing (SAHC).....................................................................................96
Next−ascent hill climbing (NAHC)..........................................................................................96
Random−mutation hill climbing (RMHC)...............................................................................96
Analysis of Random−Mutation Hill Climbing.........................................................................97
Hitchhiking in the Genetic Algorithm......................................................................................98
An Idealized Genetic Algorithm...............................................................................................99
4.3 EXACT MATHEMATICAL MODELS OF SIMPLE GENETIC ALGORITHMS.....................103
Formalization of GAs.............................................................................................................103
Results of the Formalization...................................................................................................108
A Finite−Population Model....................................................................................................108
4.4 STATISTICAL−MECHANICS APPROACHES.........................................................................112
THOUGHT EXERCISES....................................................................................................................114
COMPUTER EXERCISES.................................................................................................................116
5.1 WHEN SHOULD A GENETIC ALGORITHM BE USED?........................................................116
5.2 ENCODING A PROBLEM FOR A GENETIC ALGORITHM...................................................117
Binary Encodings....................................................................................................................117
Many−Character and Real−Valued Encodings......................................................................118
Tree Encodings.......................................................................................................................118
5.3 ADAPTING THE ENCODING....................................................................................................118
Inversion.................................................................................................................................119
Evolving Crossover "Hot Spots"............................................................................................120
Messy Gas...............................................................................................................................121
5.4 SELECTION METHODS.............................................................................................................124
Fitness−Proportionate Selection with "Roulette Wheel" and "Stochastic Universal"
Sampling................................................................................................................................124
Sigma Scaling.........................................................................................................................125
Elitism.....................................................................................................................................126
Boltzmann Selection...............................................................................................................126
Rank Selection........................................................................................................................127
Tournament Selection.............................................................................................................127
Steady−State Selection...........................................................................................................128
5.5 GENETIC OPERATORS..............................................................................................................128
Crossover................................................................................................................................128
Mutation..................................................................................................................................129
Other Operators and Mating Strategies..................................................................................130
5.6 PARAMETERS FOR GENETIC ALGORITHMS.......................................................................130
THOUGHT EXERCISES....................................................................................................................132
COMPUTER EXERCISES.................................................................................................................133
Chapter 6: Conclusions and Future Directions............................................................................................135
Overview..............................................................................................................................................135
Incorporating Ecological Interactions..................................................................................................136
Incorporating New Ideas from Genetics..............................................................................................136
Incorporating Development and Learning...........................................................................................137
Adapting Encodings and Using Encodings That Permit Hierarchy and Open−Endedness.................137
Adapting Parameters............................................................................................................................137
Connections with the Mathematical Genetics Literature.....................................................................138
Extension of Statistical Mechanics Approaches..................................................................................138
Identifying and Overcoming Impediments to the Success of GAs......................................................138
Understanding the Role of Schemas in GAs........................................................................................138
Understanding the Role of Crossover..................................................................................................139
Theory of GAs With Endogenous Fitness...........................................................................................139
Appendix A: Selected General References...................................................................................................140
Appendix B: Other Resources.......................................................................................................................141
SELECTED JOURNALS PUBLISHING WORK ON GENETIC ALGORITHMS..........................141
SELECTED ANNUAL OR BIANNUAL CONFERENCES INCLUDING WORK ON
GENETIC ALGORITHMS................................................................................................................141
INTERNET MAILING LISTS, WORLD WIDE WEB SITES, AND NEWS GROUPS WITH
INFORMATION AND DISCUSSIONS ON GENETIC ALGORITHMS........................................142
Bibliography........................................................................................................................................143

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