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E-book: Biologically Inspired Optimization Methods

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(Wessex Institut of Technology)
  • Format: 240 pages
  • Pub. Date: 14-Aug-2008
  • Publisher: WIT Press
  • ISBN-13: 9781845643447
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Biologically Inspired Optimization MethodsLarger Image
  • Format: 240 pages
  • Pub. Date: 14-Aug-2008
  • Publisher: WIT Press
  • ISBN-13: 9781845643447
Other books in subject:

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Wahde (Chalmers U. of Technology, Sweden) presents a textbook for an introductory course in stochastic optimization algorithms for upper-level engineering students with a background in analysis, algebra, and probability theory and some knowledge of computer programming. He uses ant colonies, particle swarms, and neural networks as his main models, but mentions other biological systems as well. The US office of WIT Press is Computational Mechanics. Annotation ©2008 Book News, Inc., Portland, OR (booknews.com)

Biologically inspired optimization methods constitute a rapidly expanding field of research, with new applications appearing on an almost daily basis, as optimization problems of ever-increasing complexity appear in science and technology. This book provides a general introduction to such optimization methods, along with descriptions of the biological systems upon which the methods are based. The book also covers classical optimization methods, making it possible for the reader to determine whether a classical optimization method or a biologically inspired one is most suitable for a given problem.

The book is primarily intended as a course book for students with a background covering basic engineering mathematics and elementary computer programming. Each method is illustrated with several basic examples, as well as more complex examples taken from the research literature. In addition, several exercises are provided, ranging from basic theoretical questions to programming examples. While theoretical results are presented, the book is mainly centered on practical applications of the optimization methods considered.



Biologically inspired optimization methods constitute a rapidly expanding field of research, with new applications appearing on an almost daily basis, as optimization problems of ever-increasing complexity appear in science and technology. This book provides a general introduction to such optimization methods, along with descriptions of the biological systems upon which the methods are based. The book also covers classical optimization methods, making it possible for the reader to determine whether a classical optimization method or a biologically inspired one is most suitable for a given problem.

Biologically inspired optimization methods constitute a rapidly expanding field of research, with new applications appearing on an almost daily basis, as optimization problems of ever-increasing complexity appear in science and technology. This book provides a general introduction to such optimization methods, along with descriptions of the biological systems upon which the methods are based. The book also covers classical optimization methods, making it possible for the reader to determine whether a classical optimization method or a biologically inspired one is most suitable for a given problem.The book is primarily intended as a course book for students with a background covering basic engineering mathematics and elementary computer programming. Researchers and industry representatives who want an introduction to the field of biologically inspired optimization methods would also find the book useful. Each method is illustrated with several basic examples, as well as more complex examples taken from the research literature. In addition, several exercises are provided, ranging from basic theoretical questions to programming examples. While theoretical results are presented, the book is mainly centered on practical applications of the optimization methods considered.
Abbreviations xi
Preface xiii
Notation xvii
Acknowledgements xix
1 Introduction
1.1 The importance of optimization
1
1.2 Inspiration from biological phenomena
2
1.3 Optimization of a simple behaviour for an autonomous robot
5
2 Classical optimization
2.1 Introduction
9
2.1.1 Local and global optima
9
2.1.2 Objective functions
10
2.1.3 Constraints
11
2.2 Taxonomy of optimization problems
11
2.3 Continuous optimization
12
2.3.1 Properties of local optima
12
2.3.2 Global optima of convex functions
14
2.3.2.1 Convex sets and functions
14
2.3.2.2 Optima of convex functions
16
2.4 Algorithms for continuous optimization
16
2.4.1 Unconstrained optimization
17
2.4.1.1 Line search
17
2.4.1.2 Gradient descent
19
2.4.1.3 Newton's method
21
2.4.2 Constrained optimization
24
2.4.2.1 The method of Lagrange multipliers
25
2.4.2.2 An analytical method for optimization under inequality constraints
29
2.4.2.3 Penalty methods
30
2.5 Limitations of classical optimization
33
Exercises
34
3 Evolutionary algorithms
3.1 Biological background
35
3.2 Genetic algorithms
40
3.2.1 Components of genetic algorithms
46
3.2.1.1 Encoding schemes
46
3.2.1.2 Selection
48
3.2.1.3 Crossover
52
3.2.1.4 Mutation
53
3.2.1.5 Replacement
55
3.2.1.6 Elitism
55
3.2.1.7 A standard genetic algorithm
55
3.2.1.8 Parameter selection
56
3.2.2 Properties of genetic algorithms
59
3.2.2.1 The schema theorem
59
3.2.2.2 Exact models
60
3.2.2.3 Premature convergence
67
3.3 Linear genetic programming
72
3.3.1 Registers and instructions
73
3.3.2 LGP chromosomes
74
3.3.3 Evolutionary operators in LGP
75
3.4 Interactive evolutionary computation
78
3.5 Biological vs. artificial evolution
82
3.6 Applications
83
3.6.1 Optimization of truck braking systems
83
3.6.2 Determination of orbits of interacting galaxies
86
3.6.3 Prediction of cancer survival
92
Exercises
96
4 Ant colony optimization
4.1 Biological background
100
4.2 Ant algorithms
104
4.2.1 Ant system
105
4.2.2 Max–min ant system
109
4.3 Applications
111
4.3.1 Single-machine scheduling
112
4.3.2 Co-operative transport using autonomous robots
114
Exercises
116
5 Particle swarm optimization
5.1 Biological background
117
5.1.1 A model of swarming
118
5.2 Algorithm
120
5.3 Properties of PSO
124
5.3.1 Best-in-current-swarm vs. best-ever
125
5.3.2 Neighbourhood topologies
125
5.3.3 Maintaining coherence
126
5.3.4 Inertia weight
127
5.3.5 Craziness operator
128
5.4 Discrete versions
129
5.4.1 Variable truncation
129
5.4.2 Binary PSO
130
5.5 Applications
130
5.5.1 Optimization of neural networks
131
5.5.1.1 Prediction of pollutant levels
133
5.5.1.2 Prediction of elephant migration patterns
134
5.5.2 Optimization of cancer chemotherapy
136
Exercises
137
6 Performance comparison
6.1 Unconstrained function optimization
140
6.2 Constrained function optimization
143
6.3 Optimization of feedforward neural networks
145
6.4 The travelling salesman problem
146
A Neural networks
A.1 Biological background
151
A.1.1 Neurons and synapses
151
A.1.2 Biological neural networks
152
A.1.3 Learning
153
A.1.3.1 Hebbian learning
154
A.1.3.2 Habituation and sensitization
154
A.2 Artificial neural networks
156
A.2.1 Artificial neurons
158
A.2.2 Feedforward neural networks and backpropagation
159
A.2.2.1 The Delta rule
159
A.2.2.2 Limitations of single-layer networks
161
A.2.2.3 Backpropagation
161
A.2.3 Recurrent neural networks
169
A.2.4 Other networks
171
A.3 Applications
172
B Analysis of optimization algorithms
B.1 Classical optimization
173
B.1.1 Global minima of convex functions
173
B.1.2 Properties of the gradient
174
B.2 Genetic algorithms
174
B.2.1 The schema theorem
174
B.2.2 The genetic algorithm as a Markov process
176
B.2.2.1 Number of populations of a given size
176
B.2.3 Infinite population models
177
B.2.3.1 Representing the crossover operator
177
B.2.3.2 Initial distribution of chromosomes
178
B.2.3.3 Elementary properties of binomial coefficients
178
B.2.3.4 The mutation operator for functions of unitation
179
B.2.3.5 Selection and mutations for the Onemax problem
180
B.2.4 Expected runtime of a simple GA
181
B.2.5 Estimating optimal mutation rates
182
B.3 Ant colony optimization
183
B.3.1 Pheromone limits in MMAS
183
B.3.2 Convergence proof
184
B.3.3 Runtime analysis for a simple ACO algorithm
184
B.4 Particle swarm optimization
188
B.4.1 Particle trajectories in PSO
188
C Data analysis
C.1 Hypothesis evaluation
193
C.2 Experiment design
200
D Benchmark functions
D.1 The Goldstein—Price function
206
D.2 The Rosenbrock function
206
D.3 The Sine square function
207
D.4 The Colville function
208
D.5 A multidimensional benchmark function
208
Answers to selected exercises 209
Bibliography 211
Index 215
Mattias Wahde is a researcher and teacher Adaptive Systems research group Vehicle Safety Division of the Applied Mechanics Department at the Chalmers University of Technology in Goteborg, Sweden, where research focuses on the development of control systems for autonomous robots capable of carrying out a variety of tasks, often tedious or dangerous, that are currently carried out by people. The research is based on biologically inspired computation methods, especially evolutionary algorithms.
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