Biologically inspired optimization methods: an introduction
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| Language: | English |
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Southampton [u.a.]
WIT Press
2008
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| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 218 S. Ill., graph. Darst. |
| ISBN: | 9781845641481 |
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| 100 | 1 | |a Wahde, Mattias |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Biologically inspired optimization methods |b an introduction |c M. Wahde |
| 264 | 1 | |a Southampton [u.a.] |b WIT Press |c 2008 | |
| 300 | |a 218 S. |b Ill., graph. Darst. | ||
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-016731956 | ||
Record in the Search Index
| _version_ | 1804138008760287232 |
|---|---|
| adam_text | Contents
Abbreviations
xi
Preface iffl
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
..................................................
Ill
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
б
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.I.I Neurons and synapses
..................................151
A.1.2 Biological neural networks
..............................152
A.1.3 Learning
..............................................153
A.l.3.1 Hebbian learning
..............................154
A.l.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
В
Analysis of optimization algorithms
B.I Classical optimization
.........................................173
B.I.I Global minima of convex functions
......................173
B.1.2 Properties of the gradient
...............................174
B.2
Genetic
algorithms
............................................174
В.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
imitation
.....................................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
АСО
algorithm
.............184
B.4 Particle swarm optimization
....................................188
B.4.1 Particle trajectories in PSO
.............................188
С
Data analysis
C.I Hypothesis evaluation
.........................................193
C.2 Experiment design
............................................200
D
Benchmark functions
D.I 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
|
| adam_txt |
Contents
Abbreviations
xi
Preface iffl
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
.
Ill
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
б
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.I.I Neurons and synapses
.151
A.1.2 Biological neural networks
.152
A.1.3 Learning
.153
A.l.3.1 Hebbian learning
.154
A.l.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
В
Analysis of optimization algorithms
B.I Classical optimization
.173
B.I.I Global minima of convex functions
.173
B.1.2 Properties of the gradient
.174
B.2
Genetic
algorithms
.174
В.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
imitation
.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
АСО
algorithm
.184
B.4 Particle swarm optimization
.188
B.4.1 Particle trajectories in PSO
.188
С
Data analysis
C.I Hypothesis evaluation
.193
C.2 Experiment design
.200
D
Benchmark functions
D.I 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 |
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| spelling | Wahde, Mattias Verfasser aut Biologically inspired optimization methods an introduction M. Wahde Southampton [u.a.] WIT Press 2008 218 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Ant algorithms Textbooks Combinatorial optimization Textbooks Evolutionary programming (Computer science) Textbooks Evolutionärer Algorithmus (DE-588)4366912-8 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content Evolutionärer Algorithmus (DE-588)4366912-8 s DE-604 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016731956&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Wahde, Mattias Biologically inspired optimization methods an introduction Ant algorithms Textbooks Combinatorial optimization Textbooks Evolutionary programming (Computer science) Textbooks Evolutionärer Algorithmus (DE-588)4366912-8 gnd |
| subject_GND | (DE-588)4366912-8 (DE-588)4151278-9 |
| title | Biologically inspired optimization methods an introduction |
| title_auth | Biologically inspired optimization methods an introduction |
| title_exact_search | Biologically inspired optimization methods an introduction |
| title_exact_search_txtP | Biologically inspired optimization methods an introduction |
| title_full | Biologically inspired optimization methods an introduction M. Wahde |
| title_fullStr | Biologically inspired optimization methods an introduction M. Wahde |
| title_full_unstemmed | Biologically inspired optimization methods an introduction M. Wahde |
| title_short | Biologically inspired optimization methods |
| title_sort | biologically inspired optimization methods an introduction |
| title_sub | an introduction |
| topic | Ant algorithms Textbooks Combinatorial optimization Textbooks Evolutionary programming (Computer science) Textbooks Evolutionärer Algorithmus (DE-588)4366912-8 gnd |
| topic_facet | Ant algorithms Textbooks Combinatorial optimization Textbooks Evolutionary programming (Computer science) Textbooks Evolutionärer Algorithmus Einführung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016731956&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT wahdemattias biologicallyinspiredoptimizationmethodsanintroduction |