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E-raamat: Representations for Genetic and Evolutionary Algorithms

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Representations for Genetic and Evolutionary AlgorithmsSuurem pilt
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In the field of genetic and evolutionary algorithms (GEAs), much theory and empirical study has been heaped upon operators and test problems, but problem representation has often been taken as given. This monograph breaks with this tradition and studies a number of critical elements of a theory of representations for GEAs and applies them to the empirical study of various important idealized test functions and problems of commercial import. The book considers basic concepts of representations, such as redundancy, scaling and locality and describes how GEAs'performance is influenced. Using the developed theory representations can be analyzed and designed in a theory-guided manner. The theoretical concepts are used as examples for efficiently solving integer optimization problems and network design problems. The results show that proper representations are crucial for GEAs'success.

Introduction
1(8)
Purpose
2(2)
Organization
4(5)
Representations for Genetic and Evolutionary Algorithms
9(22)
Genetic Representations
10(5)
Genotypes and Phenotypes
10(1)
Decomposition of the Fitness Function
11(2)
Types of Representations
13(2)
Genetic and Evolutionary Algorithms
15(7)
Principles
15(1)
Functionality
16(3)
Schema Theorem and Building Block Hypothesis
19(3)
Problem Difficulty
22(6)
Reasons for Problem Difficulty
22(3)
Measurements of Problem Difficulty
25(3)
Existing Recommendations for the Design of Efficient Representations for Genetic and Evolutionary Algorithms
28(3)
Goldberg's Meaningful Building Blocks and Minimal Alphabets
29(1)
Palmer's Tree Encoding Issues
29(1)
Ronald's Representational Redundancy
30(1)
Three Elements of a Theory of Genetic and Evolutionary Representations
31(46)
Redundancy
33(12)
Definitions and Background
33(3)
Decomposing Redundancy
36(1)
Population Sizing
37(2)
Run Duration and Overall Problem Complexity
39(1)
Empirical Results
40(4)
Conclusions, Restrictions and Further Research
44(1)
Building Block-Scaling
45(12)
Background
46(1)
Domino Model without, Genetic Drift
47(3)
Population Sizing for Domino Model and Genetic Drift
50(3)
Empirical Results
53(3)
Conclusions
56(1)
Distance Distortion
57(16)
Influence of Representations on Problem Difficulty
59(2)
Locality and Distance Distortion
61(2)
Modifying BB-Complexity for the One-Max problem
63(4)
Empirical Results
67(4)
Conclusions
71(2)
Summary and Conclusions
73(4)
Time-Quality Framework for a Theory-Based Analysis and Design of Representations
77(22)
Solution Quality and Time to Convergence
78(1)
Elements of the Framework
79(5)
Redundancy
79(1)
Scaling
80(1)
Distance Distortion
81(3)
The Framework
84(5)
Uniformly Scaled Representations
85(1)
Exponentially Scaled Representations
86(3)
Implications for the Design of Representations
89(7)
Uniformly Redundant Representations Are Robust
90(2)
Exponentially Scaled Representations Are Fast, but Inaccurate
92(2)
BB-Modifying Representations Are Difficult to Predict
94(2)
Summary and Conclusions
96(3)
Analysis of Binary Representations of Integers
99(20)
Two Integer Optimization Problems
100(1)
Binary String Representations
101(4)
A Theoretical Comparison
105(6)
Redundancy and the Unary Encoding
105(2)
Scaling, Modification of Problem Difficulty, and the Binary Encoding
107(1)
Modification of Problem Difficulty and the Gray Encoding
108(3)
Empirical Results
111(5)
Conclusions
116(3)
Analysis of Tree Representations
119(58)
The Tree Design Problem
120(10)
Definition
120(2)
Metrics and Distances
122(1)
Tree Structures
123(1)
Schema Analysis for Graphs
124(1)
Scalable Test Problems for Graphs
125(3)
Tree Encoding Issues
128(2)
Prufer Numbers
130(19)
Historical Review
130(2)
Construction
132(2)
Properties
134(2)
The Low Locality of the Prufer Number Encoding
136(12)
Summary and Conclusions
148(1)
The Link and Node Biased Encoding
149(17)
Introduction
150(1)
Motivation and Functionality
151(2)
Biased Initial Populations and Non-Uniformly Redundant Encodings
153(2)
The Node-Biased Encoding
155(4)
The Link-and-Node-Biased Encoding
159(3)
Empirical Results
162(3)
Conclusions
165(1)
The Characteristic Vector Encoding
166(8)
Encoding Trees with the Characteristic Vector
167(1)
Repairing Invalid Solutions
168(1)
Bias and Stealth Mutation
169(4)
Summary
173(1)
Conclusions
174(3)
Design of Tree Representations
177(22)
Network Random Keys (NetKeys)
178(12)
Motivation
178(1)
Functionality
179(4)
Advantages
183(2)
Bias
185(2)
Population Sizing and Run Duration for the One-Max Tree Problem
187(2)
Conclusions
189(1)
A Direct Tree Representation (NetDir)
190(9)
Historical Review
191(1)
Properties of Direct Representations
191(2)
Operators for NetDir
193(3)
Summary
196(3)
Performance of Genetic and Evolutionary Algorithms on Tree Problems
199(38)
GEA Performance on Scalable Test Tree Problems
200(15)
Analysis of Representations
200(2)
One-Max Tree Problem
202(8)
Deceptive Tree Problem
210(5)
GEA Performance on the Optimal Communication Spanning Tree Problem
215(20)
Problem Definition
216(1)
Theoretical Predictions
216(1)
Palmer's Test Instances
217(4)
Raidl's Test Instances
221(4)
Test Instances from Berry, Murtagh, and McMahon (1995)
225(4)
Selected Real-World Test Instances
229(6)
Summary
235(2)
Summary, Conclusions and Future Work
237(8)
Summary
237(2)
Conclusions
239(3)
Future Work
242(3)
A. Optimal Communication Spanning Tree Test Instances 245(18)
Palmer's Test Instances
245(5)
Raidl's Test Instances
250(4)
Berry's Test Instances
254(2)
Real World Problems
256(7)
References 263(18)
List of Symbols 281(4)
List of Acronyms 285(2)
Index 287


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