Genetic algorithms and genetic programming: modern concepts and practical applications
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| Format: | Book |
|---|---|
| Language: | English |
| Published: |
Boca Raton [u. a.]
CRC Press
2009
|
| Series: | Numerical insights
6 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 327 - 358 |
| Physical Description: | XXVII, 365 S. Ill., graph Darst. 24 cm |
| ISBN: | 9781584886297 1584886293 |
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| 245 | 1 | 0 | |a Genetic algorithms and genetic programming |b modern concepts and practical applications |c Michael Affenzeller ... |
| 264 | 1 | |a Boca Raton [u. a.] |b CRC Press |c 2009 | |
| 300 | |a XXVII, 365 S. |b Ill., graph Darst. |c 24 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Numerical insights |v 6 | |
| 490 | 0 | |a A Chapman & Hall book | |
| 500 | |a Literaturverz. S. 327 - 358 | ||
| 650 | 4 | |a Algorithms | |
| 650 | 4 | |a Combinatorial optimization | |
| 650 | 4 | |a Evolutionary computation | |
| 650 | 4 | |a Programming (Mathematics) | |
| 650 | 0 | 7 | |a Genetische Programmierung |0 (DE-588)4500172-8 |2 gnd |9 rswk-swf |
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| adam_text | Contents
List of Tables
xi
List of Figures
xv
List of Algorithms
xxiii
Introduction
xxv
1
Simulating Evolution: Basics about Genetic Algorithms
1
1.1
The Evolution of Evolutionary Computation
......... 1
1.2
The Basics of Genetic Algorithms
............... 2
1.3
Biological Terminology
..................... 3
1.4
Genetic Operators
........................ 6
1.4.1
Models for Parent Selection
...............
б
1.4.2
Recombination (Crossover)
............... 7
1.4.3
Mutation
......................... 9
1.4.4
Replacement Schemes
.................. 9
1.5
Problem Representation
..................... 10
1.5.1
Binary Representation
.................. 11
1.5.2
Adjacency Representation
................ 12
1.5.3
Path Representation
................... 13
1.5.4
Other Representations for Combinatorial Optimization
Problems
......................... 13
1.5.5
Problem Representations for Real-Valued Encoding
. . 14
1.6
GA Theory: Schemata and Building Blocks
.......... 14
1.7
Parallel Genetic Algorithms
................... 17
1.7.1
Global Parallelization
.................. 18
1.7.2
Coarse-Grained Parallel GAs
.............. 19
1.7.3
Fine-Grained Parallel GAs
............... 20
1.7.4
Migration
......................... 21
1.8
The Interplay of Genetic Operators
.............. 22
1.9
Bibliographic Remarks
..................... 23
2
Evolving Programs: Genetic Programming
25
2.1
Introduction: Main Ideas and Historical Background
..... 26
2.2
Chromosome Representation
.................. 28
2.2.1
Hierarchical Labeled Structure Trees
.......... 28
vi
Genetic Algorithms and Genetic Programming
2.2.2
Automatically Defined Functions and Modular Genetic
Programming
....................... 35
2.2.3
Other Representations
.................. 36
2.3
Basic Steps of the GP-Based Problem Solving Process
.... 37
2.3.1
Preparatory Steps
.................... 37
2.3.2
Initialization
....................... 39
2.3.3
Breeding Populations of Programs
........... 39
2.3.4
Process Termination and Results Designation
..... 41
2.4
Typical Applications of Genetic Programming
........ 43
2.4.1
Automated Learning of Multiplexer Functions
..... 43
2.4.2
The Artificial Ant
.................... 44
2.4.3
Symbolic Regression
................... 46
2.4.4
Other GP Applications
................. 49
2.5
GP Schema Theories
...................... 50
2.5.1
Program Component GP Schemata
........... 51
2.5.2
Rooted Tree GP Schema Theories
........... 52
2.5.3
Exact GP Schema Theory
................ 54
2.5.4
Summary
......................... 59
2.0
Current GP Challenges and Research Areas
......... 59
2.7
Conclusion
............................ 62
2.8
Bibliographic Remarks
..................... 62
3
Problems and Success Factors
65
3.1
What Makes GAs and GP Unique among Intelligent
Optimization Methods?
.....................
G5
3.2
Stagnation
aud
Premature Convergence
............ 6(5
4
Preservation of Relevant Building Blocks
69
4.1
What Can Extended Selection Concepts Do to Avoid
Premature
Convergence?
.................... 69
4.2
Offspring Selection (OS)
.................... 70
4.3
The Relevant
Alíeles
Preserving Genetic Algorithm (RAPGA)
73
4.4
Consequences Arising out of Offspring Selection and RAPGA
76
5
SASEGASA
-
More than the Sum of All Parts
79
5.1
The Interplay of Distributed Search and Systematic Recovery
of Essential Genetic
Information
................ 80
5.2
Migration Revisited
....................... 81
5.3
SASEGASA: A Novel and Self-Adapt
ive
Parallel Genetic
Algorithm
............................ 82
5.3.1
The Core Algorithm
................... 83
5.4
Interactions among Genetic Drift. Migration, and
Selí-
Adaptive
Selection Pressure
........................ 86
Table
of Contents
vii
Analysis of Population Dynamics
89
6.1
Parent Analysis
......................... 89
6.2
Genetic Diversity
........................ 90
6.2.1
In Single-Population GAs
................ 90
6.2.2
In Multi-Population GAs
................ 91
6.2.3
Application Examples
.................. 92
Characteristics of Offspring Selection and the RAPGA
97
7.1
Introduction
........................... 97
7.2
Building Block Analysis for Standard GAs
.......... 98
7.3
Building Block Analysis for GAs Using Offspring Selection
. 103
7.4
Building Block Analysis for the Relevant
Alíeles
Preserving GA
(RAPGA)
.... ........................ 113
Combinatorial Optimization: Route Planning
121
8.1
The Traveling Salesman Problem
................ 121
8.1.1
Problem Statement and Solution Methodology
.... 122
8.1.2
Review of Approximation Algorithms and Heuristics
. 125
8.1.3
Multiple Traveling Salesman Problems
......... 130
8.1.4
Genetic Algorithm Approaches
............. 130
8.2
The Capacitated Vehicle Routing Problem
.......... 139
8.2.1
Problem Statement and Solution Methodology
.... 140
8.2.2
Genetic Algorithm Approaches
............. 147
Evolutionary System Identification
157
9.1
Data-Based Modeling and System Identification
....... 157
9.1.1
Basics
........................... 157
9.1.2
An Example
....................... 159
9.1.3
The Basic Steps in System Identification
........ 1(56
9.1.4
Data-Based Modeling Using Genetic Programming
. . 169
9.2
GP-Based System Identification in HeuristicLab
....... 170
9.2.1
Introduction
....................... 170
9.2.2
Problem Representation
................. 171
9.2.3
The Functions and Terminals Basis
........... 173
9.2.4
Solution Representation
................. 178
9.2.5
Solution Evaluation
................... 182
9.3
Local Adaption Embedded in Global Optimization
...... 188
9.3.1
Parameter Optimization
................. 189
9.3.2
Priming
.......................... 192
9.4
Similarity Measures for Solution Candidates
......... 197
9.4.1
Evaluation-Based Similarity Measures
......... 199
9.4.2
Structural Similarity Measures
............. 201
viii Genetic
Algorithms and
Genetic
Programming
10
Applications of Genetic
Algorithms: Combinatorial
Optimization
207
10.1
The Traveling Salesman Problem
................ 208
10.1.1
Performance Increase of Results of Different Crossover
Operators by
Aleaos
of Offspring Selection
....... 208
10.1.2
Scalability of Global Solution Quality by SASEGASA
210
10.1.3
Comparison of the SASEGASA to the Island-Model
Coarse-Grained Parallel GA
............... 214
10.1.4
Genetic Diversity Analysis for the Different GA Types
217
10.2
Capacitated Vehicle Routing
.................. 221
10.2.1
Results Achieved Using Standard Genetic Algorithms
222
10.2.2
Results Achieved Using Genetic Algorithms with
Offspring Selection
....................
22G
11
Data-Based Modeling with Genetic Programming
235
11.1
Time Series Analysis
...................... 235
11.1.1
Time Series Specific Evaluation
............. 236
11.1.2
Application Example: Design of Virtual Sensors for
Emissions of Diesel Engines
............... 237
11.2
Classification
........................... 251
11.2.1
Introduction
....................... 251
11.2.2
Real-Valued Classification with Genetic Programming
251
11.2.3
Analyzing Classifiers
................... 252
11.2.4
Classification Specific Evaluation in GP
........ 258
11.2.5
Application Example: Medical Data Analysis
..... 263
11.3
Genetic Propagation
....................... 285
11.3.1
Test Setup
........................ 285
11.3.2
Test Results
........................ 286
11.3.3
Summary
......................... 288
11.3.4
Additional Tests Using Random Parent Selection
. . . 289
11.4
Single Population Diversity Analysis
.............. 292
11.4.1
GP Test Strategies
.................... 292
11.4.2
Test Results
........................ 293
11.4.3
Conclusion
........................ 297
11.5
Multi-Population Diversity Analysis
.............. 300
ll.ő.l
GP Test Strategies
.................... 300
11.5.2
Test Results
........................ 301
11.5.3
Discussion
......................... 303
11.0
Code Bloat. Pruning, and Population Diversity
........ 306
11.0.1
Introduction
.......................
3()(;
11.6.2
Test Strategies
...................... .407
11.6.3
Test Results
........................ 309
11.6.4
Conclusion
........................ 31^
Conclusion and Outlook
321
Table of Contents
ix
Symbols and Abbreviations
325
References
327
Index
359
List of Tables
7.1
Parameters for test runs using a conventional GA
...... 99
7.2
Parameters for test runs using a GA with offspring selection.
104
7.3
Parameters for test runs using the relevant
alíeles
preserving
genetic algorithm
......................... 113
8.1
Exemplary edge map of the parent tours for an ERX operator.
138
9.1
Data-based modeling example: Training data
......... 160
9.2
Data-based modeling example: Test data
........... 164
10.1
Overview of algorithm parameters
............... 209
10.2
Experimental results achieved using a standard GA
..... 209
10.3
Experimental results achieved using a GA with offspring se¬
lection
............................... 209
10.4
Parameter values used in the test runs of the SASEGASA
algorithms with single crossover operators as well as with a
combination of the operators
.................. 211
10.5
Results showing the scaling properties of SASEGASA with
one crossover operator (OX), with and without mutation.
. 211
10.6
Results showing the scaling properties of SASEGASA with
one crossover operator (ERX), with and without mutation.
212
10.7
Results showing the scaling properties of SASEGASA with
one crossover operator (MPX), with and without mutation.
212
10.8
Results showing the scaling properties of SASEGASA with a
combination of crossover operators (OX. ERX.
ΛΙΡΧ).
with
and without mutation
...................... 213
10.9
Parameter values used in the test runs of a island model GA
with various
operatort;
and various numbers of denies.
. . . 215
10.10
Results showing the scaling properties of an island GA with
one crossover operator (OX) using roulette-wheel selection,
with and without mutation
................... 215
10.11
Results showing the scaling properties of an island GA with
one crossover operator (ERX) using roulette-wheel selection,
with and without mutation
................... 216
10.12
Results showing the scaling properties of an island GA with
one crossover operator (MPX) using roulette-wheel selection,
with and without mutation
................... 216
xi
xii
Genetic
Algorithms and Genetic Programming
10.13
Parameter values used in the CVRP test runs applying a stan¬
dard GA
............................. 223
10.14
Results of a GA using roulette-wheel selection. 3-tournament
selection and various mutation operators
........... 226
10.15
Parameter values used in CVRP test runs applying a GA with
OS
................................. 228
10.16
Results of a GA with offspring selection and population sizes
of
200
and
400
and various mutation operators. The
configu¬
ration
is listed in Table
10.15.................. 232
10.17
Showing results of a GA with offspring and a population size
of
500
and various mutation operators. The configuration is
listed in Table
10.15....................... 234
11.1
Linear correlation of input variables and the target values
(ΜΟ,γ)
in the NOX data set 1
.................. 240
11.2
Mean squared errors on training data for the
ΝΟ_τ
data set I.
241
11.3
Statistic features of the identification relevant variables in the
NOX data set II
......................... 246
11.4
Linear correlation coefficients of the variables relevant in the
ΛΌ.Τ
data set II
......................... 248
11.5
Statistic features of the
:
variables in the NOx data set III.
. 250
ll.fi Linear correlation coefficients of the variables relevant in the
NOX data set III
......................... 250
11.7
Exemplary confusion matrix with three classes
....... 253
11.8
Exemplary confusion matrix with two classes
........ 254
11.9
Set of function and terminal definitions for enhanced GP-
based classification
........................ 264
11.10
Experimental results for the Thyroid data set
......... 270
11.11
Summary of the best GP parameter settings for solving clas¬
sification problems
........................ 271
11.12
Summary of training and test results for the Wisconsin data
set: Correct classification rates (average values and standard
deviation values) for 10-fold
CV
partitions, produced by GP
with offspring selection
..................... 279
11.13
Comparison of machine learning methods: Average test ac¬
curacy of classifiers for the Wisconsin data set
........ 280
11.14
Confusion matrices fur average classification results produced
by GP with OS for the Melanoma data set
.......... 280
11.15
Comparison of machine learning methods: Average, test ac¬
curacy of classifiers for the Me.lunoma data set
........ 281
11.10
Summary of training and test results for the Thyroid data
set: Correct classification rates (average values and standard
deviation values) for 10-fold
CV
partitions, produced by GP
with offspring selection
..................... 282
List of Tables
xiii
11.17
Comparison of machine learning methods: Average test ac¬
curacy of classifiers for the Thyroid data set
......... 283
11.18
GP test strategies
........................ 285
11.19
Test results
............................ 286
11.20
Average overall genetic propagation of population partitions.
287
11.21
Additional test strategies for genetic propagation tests.
. . . 289
11.22
Test results in additional genetic propagation tests (using ran¬
dom parent selection)
...................... 290
11.23
Average overall genetic propagation of population partitions
for random parent selection tests
................ 290
11.24
GP test strategies
........................ 293
11.25
Test results: Solution qualities
................. 294
11.26
Test results: Population diversity (average similarity values:
avg., std.)
............................. 295
11.27
Test results: Population diversity (maximum similarity val¬
ues;
avg., std.)
.......................... 296
11.28
GP test strategies
........................ 302
11.29
Multi-population diversity test results of the GP test runs
using the Thyroid data set
................... 303
11.30
Multi-population diversity test results of the GP test runs
using the JVOj. data set III
................... 304
11.31
GP parameters used for code growth and bloat prevention
tests
................................ 307
11.32
Summary of the code growth prevention strategies applied in
these test series
.......................... 308
11.33
Performance of systematic and ES-based pruning strategies.
310
11.34
Formula size progress in test series (d)
............. 311
11.35
Quality of results produced in test series (d)
......... 311
11.36
Formula size and population diversity progress in test series
(e)
....................*............. 312
11.37
Formula size and population diversity progress in test series
(f)
...................·............. 313
11.38
Quality of results produced in test series (f)
.......... 313
11.39
Formula size and population diversity progress hi test series
(g)
................................. 314
11.40
Quality of results produced in test series (g)
......... 314
11.41
Formula size and population diversity progress in tost series
(h)
.................... . · ·.......... 315
11.42
Quality of results produced in test series (h)
......... 316
11.43
Comparison of best models on training and validation data
(bf and bc, respectively)
..................... 317
11.44
Formula size and population diversity progress in test series
(i)
................................. 320
11.45
Quality of results produced in test series (i)
.......... 320
List of Figures
1.1
The canonical genetic algorithm with binary solution encod¬
ing
................................. 4
1.2
Schematic display of a single point crossover
......... 8
1.3
Global parallelization concepts: A panmictic population struc¬
ture (shown in left picture) and the corresponding master-
slave model (right picture)
................... 18
1.4
Population structure of a coarse-grained parallel GA
..... 19
1.5
Population structure of a fine-grained parallel GA; the special
case of a cellular model is shown here
............. 20
2.1
Exemplary programs given as rooted, labeled structure trees.
30
2.2
Exemplary evaluation of program (a)
............. 31
2.3
Exemplary evaluation of program (b)
............. 32
2.4
Exemplary crossover of programs
(1)
and
(2)
labeled as
par¬
enti
and parent2, respectively. Childl and child,2 are possible
new offspring programs formed out of the genetic material of
their parents
........................... 34
2.5
Exemplary mutation of a program: The programs
mutanti,
mutanti,
and mutants are possible mutants of parent.
. . . 35
2.6
Intron-augmented representation of an exemplary program in
PDGP [Pol99b]
.......................... 38
2.7
Major preparatory steps of the basic GP process
....... 38
2.8
The genetic programming cycle [LP02]
............. 40
2.9
The GP-based problem solving process
............ 41
2.10
GA and GP flowcharts: The conventional genetic algorithm
and genetic programming
.................... 42
2.11
The Boolean multiplexer with three address bits; (a) general
black box model, (b) addressing data bit
(/5.......... 44
2.12
A correct solution to the 3-address Boolean multiplexer prob¬
lem [Koz92b]
........................... 44
2.13
The Santa Fe trail
........................ 45
2.14
A Santa Fe trail solution. The black points represent nodes
referencing to the Prog3 function
................ 46
2.15
A symbolic regression example
................. 48
2.16
Exemplary formulas
....................... 49
2.17
Programs matching Koza s schema H=[(+
χ
3).
y]......
51
xvi
Genetic Algorithms and Genetic Programming
2.18
The rooted tree GP schema
*(=. = (2:.=))
and three exem¬
plary programs of the schema s semantics
........... 53
2.19
The GP schema
H
=
+(*(=,x).=) and exemplary
и
and I
schemata. Cross bars indicate crossover points: shaded re¬
gions show the parts of
H
that are replaced by don t care
symbols
.............................. 56
2.20
The GP hyperschema
*(#, = (.*(%=))
and three exemplary
programs that are a part of the schema s semantics
..... 56
2.21
The GP schema
H
— +(*(=.,
r).
=)
and exemplary
U
and
L
hyperschema building blocks. Cross bars indicate crossover
points: shaded regions show the parts of
Я
that are modified.
57
2.22
Relation-between approximate and exact schema theorems for
different representations and different forms of crossover (in
the absence of mutation)
.................... 58
2.23
Examples for bloat
........................ 60
4.1
Flowchart of the embedding of offspring selection into a ge¬
netic algorithm
.......................... 71
4.2
Graphical representation of the gene pool available at a cer¬
tain generation. Each bar represents a chromosome with its
alíeles
representing the assignment of the genes at the certain
loci
................................ 74
4.
,i The left part of the figure represents the gene pool at gener¬
ation
/
aud
the right part indicates the possible size of gen¬
eration
і
+
I which must not go below a minimum size and
also not exceed an upper limit. These parameters have to be
defined by the user
........................ 74
4.4
Typical development of actual population size between the
two borders (lower and upper limit of population size) dis¬
playing also the identical chromosomes that occur especially
in the last iterations
....................... 76
П.
1.
Flowchart of the reunification of
subpopulations
of a SASEGASA
(light shaded
subpopulations
are still evolving, whereas dark
shaded ones have already converged prematurely)
...... 84
• i.
2
Quality progress of a typical run of the SASEGASA algo¬
rithm
...............................
8П
5.
H
Selection pressure curves for a typical run of the SASEGASA
algorithm
............................. 86
Õ.4
Flowchart showing the main stops of the SASEGASA.
... 87
0.1
Similarity of solutions in the population of a standard GA
after
20
and
200
iterations, shown in the left and the right
charts, respectively.
....................... 93
List of Figures
xvii
6.2
Histograms of the similarities of solutions in the population
of a standard GA after
20
and
200
iterations, shown in the
left and the right charts, respectively.
............. 94
6.3
Average similarities of solutions in the population of a stan¬
dard GA over for the first
2,000
and
10,000
iterations, shown
in the upper and lower charts, respectively.
......... 95
6.4
Multi-population specific similarities of the solutions of a par¬
allel
GAľs
populations after
5.000
generations
......... 96
6.5
Progress of the average multi-population specific similarity
values of a parallel GA s solutions, shown for
10,000
genera¬
tions
................................ 96
7.1
Quality progress for a standard
G A
with OX crossover for
mutation rates of
0%, 5%,
and
10%.............. 99
7.2
Quality progress for a standard GA with ERX crossover for
mutation rates of
0%, 5%,
and
10%.............. 101
7.3
Quality progress for a standard
G
A with MPX crossover for
mutation rates of
0%, 5%,
and
10%.............. 102
7.4
Distribution of the
alíeles
of the global optimal solution over
the run of a standard GA using OX
сгоѕѕол-ег
and a mutation
rate of
5%
(remaining parameters are set according to Table
7.1)................................ 103
7.5
Quality progress for a GA with offspring selection, OX, and
a mutation rate of
5%...................... 105
7.6
Quality progress for a GA with offspring selection, MPX. and
a mutation rate of
5%...................... 106
7.7
Quality progress for a GA with offspring selection, ERX. and
a mutation rate of
5%...................... 107
7.8
Quality progress for a GA with offspring selection. ERX, and
no mutation
........................... 108
7.9
Quality progress for a GA with offspring selection using a
combination of OX. ERX, and MPX. and a mutation rate of
5%................................. 109
7.10
Success progress of the different crossover operators OX. ERX,
and MPX, and a mutation rate of
5%.
The plotted graphs
represent the ratio of successfully produced children to the
population size over the generations
.............. 110
7.11
Distribution of the
alíeles
of the global optimal solution over
the run of an offspring selection GA using ERX crossover
and a mutation rate of 59c (remaining parameters are set
according to Table
7.2).....................
Ill
7.12
Distribution of the
alíeles
of the global optimal solution over
the run of an offspring selection GA using ERX crossover and
no mutation (remaining parameters are set according to Table
7.2)................................ 112
XVIII
Genetic
Algorithms and
Genetic
Programming
7.13
Quality progress for a relevant
alíeles
preserving GA with OX
and a mutation rate of
5%................... 114
7.14
Quality progress for a relevant
alíeles
preserving GA with
MPX and a mutation rate of
5%................ 115
7.15
Quality progress for a relevant
alíeles
preserving GA with
ERX and a mutation rate of
59?................ 115
7.16
Quality progress for a relevant
alíeles
preserving
G
A using a
combination of OX. ERX. and MPX. and a mutation rate of
5%................................. 116
7.17
Quality progress for a relevant
alíeles
preserving GA using a
combination of OX. ERX. and MPX. and mutation switched
off
.................................
Ш
7.18
Distribution of the
alíeles
of the global optimal solution over
the run of a relevant
alíeles
preserving GA using a combi¬
nation of OX. ERX. and MPX. and a mutation rate of 5 X
(remaining parameters are set according to Table
7.3). . . . 118
7.19
Distribution of the
alíeles
of the global optimal solution over
the run of a relevant
alíeles
preserving GA using a combina¬
tion of OX. ERX. and MPX without mutation (remaining are
set parameters according to Table
7.3)............. 119
8.1
Exemplary nearest neighbor solution for a 51-city TSP in¬
stance
([CEGO])
.......................... 126
8.2
Example of a 2-change for a TSP instance with
7
cities.
. . 128
8.3
Example of a
. î-change
for a TSP instance with
11
cities.
. . 129
8.4
Example for a partially matched crossover
........... 134
8.5
Example for an order crossover
................. 135
8.
fi
Example for a cyclic crossover
................. 136
8.7
Exemplary result of the sweep heuristic for a small CVRP.
. 144
8.8
Exemplary sequence-based crossover
.............. 149
8.!)
Exemplary route-based crossover
................ 151
8.10
Exemplary relocate mutation
.................. 152
8.11
Exemplary exchange mutation
................. 152
8.12
Example for a 2-opt mutation for the VRP
.......... 153
8.13
Example for a 2-opt* mutation for the VRP
.......... 153
Н.І4
Example for an or-opt mutation for the VRP
......... 154
9.1
Data-based modeling example: Training data
......... 100
9.2
Data-based modeling example: Evaluation of an optimally fit
linear model
........................... 101
9.3
Data-based modeling example: Evaluation of an optimally fit
cubic model
............................
Ki2
9.4
Data-based modeling example: Evaluation of an optimally fit
polynomial model (n
= 10)................... 102
List of Figures
xix
9.5
Data-based modeling example: Evaluation of an optimally fit
polynomial model (n
= 20)................... 163
9.6
Data-based modeling example: Evaluation of an optimally fit
linear model (evaluated on training and test data)
...... 163
9.7
Data-based modeling example: Evaluation of an optimally fit
cubic model (evaluated on training and test data)
...... 164
9.8
Data-based modeling example: Evaluation of an optimally fit
polynomial model (n
= 10)
(evaluated on training and test
data)
............................... 165
9.9
Data-based modeling example: Summary of training and test
errors for varying numbers of parameters
η
.......... 165
9.10
The basic steps of system identification
............ 167
9.11
The basic steps of GP-based system identification
...... 170
9.12
Structure tree representation of a formula
........... 179
9.13
Structure tree crossover and the functions basis
........ 181
9.14
Simple examples for pruning in GP
............... 195
9.15
Simple formula structure and all included pairs of ancestors
and descendants (genetic information items)
......... 202
10.1
Quality improvement using offspring selection and various
crossover operators
........................ 210
10.2
Degree of similarity/distance for all pairs of solutions in a
SGA s population of
120
solution candidates after
10
genera¬
tions
................................ 218
10.3
Genetic diversity in the population of a conventional GA over
time
................................ 219
10.4
Genetic diversity of the population of a GA with offspring
selection over time
........................ 219
10.5
Genetic diversity of the entire population over time for a
SASEGASA with
5
subpopulations
............... 220
10.6
Quality progress of a standard GA using roulette wheel se¬
lection on the left and 3-toumament selection the right side,
applied to instances of the Taillard CVRP benchmark:
tai75a
(top) and
tai75b
(bottom)
.................... 223
10.7
Genetic diversity in the population of a GA with roulette
wheel selection (shown on the left side) and 3-toumament
selection (shown on the right side)
...............
22Õ
10.8
Box plots of the qualities produced by a GA with roulette
and 3-tournament selection, applied to the problem instances
tai75a (top)
aud
tai7õb
(bottom)
................ 227
10.9
Quality progress of the offspring selection GA for the in¬
stances (from top to bottom)
tai75a
and
tai75b.
The left col¬
umn shows the progress with a population size of
200.
while
in the right column the GA with offspring selection uses a
population size of
400...................... 229
xx
Genetic
Algorithms and Genetic Programming
10.10
Influence of the crossover operators SBX and RBX on each
generation of an offspring selection algorithm. The lighter
line represents the RBX; the darker line represents the SBX.
230
10.11
Genetic diversity in the population of an GA with offspring
selection and a population size of
200
on the left and
400
on
the right for the problem instances
tai75a
and
tai75b
(from
top to bottom)
.......................... 231
10.12
Box plots of the offspring selection GA with a population size
of
200
and
400
for the instances
tai75a
and
tai
75
b......
233
10.13
Box plots of the GA with 3-tournament selection against the
offspring selection GA for the instances
tai75a
(shown in the
upper
part)
and
tai75b
(shown in the lower part)
....... 233
11.1
Dynamic
diesel
engine test bench at the Institute for Design
and Control of Mechatronical Systems, JKU
Linz....... 238
11.2
Evaluation of the best model produced by GP for test strategy
(1)..................... ........... · 241
11.3
Evaluation of the best model produced by GP for test strategy
(2)..................... ...........*. 242
11.4
Evaluation of models for
partie
ulate matter emissions of a
diesel
engine (snapshot showing the evaluation of the model
on validation
/
test samples)
.................. 244
11.5
Errors distribution of models for particulate matter emissions.
244
ll.fi Cumulative errors of models for particulate matter emissions.
245
11.7
Target NO.r
vaines
of NOX data set II. recorded over ap¬
proximately
30
minutes at 20Hz recording frequency yielding
~36.000 samples
......................... 247
11.
(S Target HoribaNOx values of NO.,, data set III
........ 248
11.9
Target HoribaNOx values of NOX data set III. samples
(¡000
7000............................... 249
11.10
Two exemplary ROC curves and their area under the ROC
curve (AUC)
........................... 255
11.11
An exemplary graphical display of a multi-class ROC (MROC)
matrix
............................... 257
11.12
Classification example: Several samples with original class
values C .
Οχ.
and CV, are shown: the class ranges result from
t
lie estimated values for each class and are indicated as cry.
cr·). and rr;>,
............................
2(ii
11.13
An exemplary hybrid structure tree of a combined formula
including arithmetic as well as logical functions
........ 205
11.14
Graphical representation of the best result we obtained for
the Th i/mid data set. CV-partition
9:
Comparison of original
and estimated class values
.................... 272
11.15
ROC curves and their area under the curve (AUC) values for
classification models generated for Thyroid data. CV-set
9. 273
List of Figures
xxi
11.16
MROC charts and their maximum and average area under
the curve (AUC) values for classification models generated
for Thyroid data, CV-set
9................... 274
11.17
Graphical representation of a classification model (formula),
produced for 10-fold cross validation partition
3
of the Thy¬
roid data set
........................... 275
11.18
pctotai values for an exemplary run of series 1
......... 287
11.19
pc total values for an exemplary run of series II
........ 287
11.20
pctotai values for an exemplary run of series III
........ 288
11.21
Selection pressure progress in two exemplary runs of test se¬
ries III and V (extended GP with gender specific parent se¬
lection and strict offspring selection)
.............. 291
11.22
Distribution of similarity values in an exemplary run of NOX
test series A. generation
200.................. 297
11.23
Distribution of similarity values in an exemplary run of NOX
test series A, generation
4000.................. 298
11.24
Distribution of similarity values in an exemplary run of NOX
test series (D). generation
20.................. 298
11.25
Distribution of similarity values in an exemplary run of NOX
test series (D), generation
95.................. 299
11.26
Population diversity progress in exemplary Thyroid test runs
of series (A) and (D) (shown in the upper and lower graph,
respectively)
........................... 299
11.27
Exemplary multi-population diversity of a test run of Thyroid
series
F
at iteration
50.
grayscale representation
....... 305
11.28
Code growth in GP without applying size limits or complexity
punishment strategies (left.: standard GP. right: extended
GP)
................................ 310
11.29
Progress of formula complexity in one of the test runs of series
(lg). shown for the first ~400 iterations
............ 315
11.30
Progress of formula complexity in one of the test runs of series
(lh) (shown left) and one of series (2h) (shown right).
. . . 316
11.31
Model with best fit on training data: Model structure and
full evaluation
.......................... 318
11.32
Model with best fit on validation data: Model structure and
full evaluation
.......................... 318
11.33
Errors distributions of best models: Charts I. II, and III show
the errors distributions of the model with best fit on training
data evaluated on training, validation, and test data, respec¬
tively: charts IV. V. and VI show the errors distributions of
the model with best fit on validation data evaluated on train¬
ing, validation, and test data, respectively.
.......... 319
11.34
A simple workbench in HeuristicLab
2.0............ 323
List of Algorithms
1.1
Basic workflow of a genetic algorithm
.............. 3
4.1
Definition of a genetic algorithm with offspring selection.
... 72
9.1
Exhaustive pruning of a model
m
using the parameters hi, h%,
minimizeModel, cpmax, and detmax
............... 196
9.2
Evolution strategy inspired pruning of a model
m
using the
parameters
λ.
maxUnsuccRounds, hi. h-2- minimizeModel,
CPmax· and detmax
......................... 198
9.3
Calculation of the evaluation-based similarity of two models
m
ι
and rri2 with respect to data base data
............. 200
9.4
Calculation of the structural similarity of two models
гщ
and
m2
................................. 205
ХХШ
|
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| id | DE-604.BV035605084 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T21:41:28Z |
| institution | BVB |
| isbn | 9781584886297 1584886293 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-017660332 |
| oclc_num | 300982916 |
| open_access_boolean | |
| owner | DE-473 DE-BY-UBG DE-824 DE-384 |
| owner_facet | DE-473 DE-BY-UBG DE-824 DE-384 |
| physical | XXVII, 365 S. Ill., graph Darst. 24 cm |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | CRC Press |
| record_format | marc |
| series | Numerical insights |
| series2 | Numerical insights A Chapman & Hall book |
| spelling | Genetic algorithms and genetic programming modern concepts and practical applications Michael Affenzeller ... Boca Raton [u. a.] CRC Press 2009 XXVII, 365 S. Ill., graph Darst. 24 cm txt rdacontent n rdamedia nc rdacarrier Numerical insights 6 A Chapman & Hall book Literaturverz. S. 327 - 358 Algorithms Combinatorial optimization Evolutionary computation Programming (Mathematics) Genetische Programmierung (DE-588)4500172-8 gnd rswk-swf Genetischer Algorithmus (DE-588)4265092-6 gnd rswk-swf Genetischer Algorithmus (DE-588)4265092-6 s Genetische Programmierung (DE-588)4500172-8 s DE-604 Affenzeller, Michael Sonstige oth Numerical insights 6 (DE-604)BV012945885 6 Digitalisierung UB Bamberg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017660332&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Genetic algorithms and genetic programming modern concepts and practical applications Numerical insights Algorithms Combinatorial optimization Evolutionary computation Programming (Mathematics) Genetische Programmierung (DE-588)4500172-8 gnd Genetischer Algorithmus (DE-588)4265092-6 gnd |
| subject_GND | (DE-588)4500172-8 (DE-588)4265092-6 |
| title | Genetic algorithms and genetic programming modern concepts and practical applications |
| title_auth | Genetic algorithms and genetic programming modern concepts and practical applications |
| title_exact_search | Genetic algorithms and genetic programming modern concepts and practical applications |
| title_full | Genetic algorithms and genetic programming modern concepts and practical applications Michael Affenzeller ... |
| title_fullStr | Genetic algorithms and genetic programming modern concepts and practical applications Michael Affenzeller ... |
| title_full_unstemmed | Genetic algorithms and genetic programming modern concepts and practical applications Michael Affenzeller ... |
| title_short | Genetic algorithms and genetic programming |
| title_sort | genetic algorithms and genetic programming modern concepts and practical applications |
| title_sub | modern concepts and practical applications |
| topic | Algorithms Combinatorial optimization Evolutionary computation Programming (Mathematics) Genetische Programmierung (DE-588)4500172-8 gnd Genetischer Algorithmus (DE-588)4265092-6 gnd |
| topic_facet | Algorithms Combinatorial optimization Evolutionary computation Programming (Mathematics) Genetische Programmierung Genetischer Algorithmus |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017660332&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV012945885 |
| work_keys_str_mv | AT affenzellermichael geneticalgorithmsandgeneticprogrammingmodernconceptsandpracticalapplications |