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Global Optimization Algorithms
– Theory and Application –
2ndEd
Evolutionary Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
Genetic Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
Genetic Programming . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
Learning Classifier Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . 233
Hill Climbing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253
Simulated Annealing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .263
Example Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 315
Sigoa – Implementation in Java . . . . . . . . . . . . . . . . . . . . . . . 439
Background (Mathematics, Computer Science, . . . ) . . . 455
Thomas Weise
Version: 2009-06-26
Newest Version:
http://www.it-weise.de/


Preface
This e-book is devoted to global optimization algorithms, which are methods to find opti-
mal solutions for given problems. It especially focuses on Evolutionary Computation by dis-
cussing evolutionary algorithms, genetic algorithms, Genetic Programming, Learning Classi-
fier Systems, Evolution Strategy, Differential Evolution, Particle Swarm Optimization, and
Ant Colony Optimization. It also elaborates on other metaheuristics like Simulated An-
nealing, Extremal Optimization, Tabu Search, and Random Optimization. The book is no
book in the conventional sense: Because of frequent updates and changes, it is not really
intended for sequential reading but more as some sort of material collection, encyclopedia,
or reference work where you can look up stuff, find the correct context, and are provided
with fundamentals.
With this book, two major audience groups are addressed:
1. It can help students since we try to describe the algorithms in an understandable, consis-
tent way and, maybe even more important, includes much of the background knowledge
needed to understand them. Thus, you can find summaries on stochastic theory and the-
oretical computer science in Part IV on page 455. Additionally, application examples are
provided which give an idea how problems can be tackled with the different techniques
and what results can be expected.
2. Fellow researchers and PhD students may find the application examples helpful too. For
them, in-depth discussions on the single methodologies are included that are supported
with a large set of useful literature references.
If this book contains something you want to cite or reference in your work, please use the
citation suggestion provided in
Chapter D on page 591.
In order to maximize the utility of this electronic book, it contains automatic, clickable links.
They are shaded with dark gray so the book is still b/w printable. You can click on
1. entries in the table of contents,
2. citation references like [916],
3. page references like “
95”,
4. references such as “see
Figure 2.1 on page 96” to sections, figures, tables, and listings,
and
5. URLs and links like “
http://www.lania.mx/
~
ccoello/EMOO/ [accessed 2007-10-25]”.
1
The following scenario is now for example possible: A student reads the text and finds a
passage that she wants to investigate in-depth. She clicks on a citation in that seems inter-
esting and the corresponding reference is shown. To some of the references which are online
1
URLs are usually annotated with the date we have accessed them, like
http://www.lania.
mx/
~
ccoello/EMOO/
[accessed 2007-10-25]. We can neither guarantee that their content remains u n-
changed, nor that these sites stay available. We also assume no responsibility for anything we
linked to.

4
available, links are provided in the reference text. By clicking on such a link, the Adobe
Reader
R
2
will open another window and load the regarding document (or a browser window
of a site that links to the document). After reading it, the student may use the “backwards”
button in the navigation utility to go back to the text initially read in the e-book.
The contents of this book are divided into four parts. In the first part, different optimization
technologies will be introduced and their features are described. Often, small examples will
be given in order to ease understanding. In the second part starting at page
315, we elab-
orate on different application examples in detail. With the Sigoa framework, one possible
implementation of optimization algorithms in Java, is discussed and we show how some of
solutions of the previous problem instances can be realized in
Part III on page 439. Finally,
in the last part following at page 455, the background knowledge is provided for the rest of
the book. Optimization is closely related to stochastic, and hence, an introduction into this
subject can be found here. Other important background information concerns theoretical
computer science and clustering algorithms.
However, this book is currently worked on. It is still in a very preliminary phase where
major parts are still missing or under construction. Other sections or texts are incomplete
(tagged with
TODO). There may as well be errors in the contents or issues may be stated
ambiguously (I do not have proof-readers). Additionally, the sequence of the content is not
very good. Because of frequent updates, small sections may grow and become chapters, be
moved to another place, merged with other sections, and so on. Thus, this book will change
often. I choose to update, correct, and improve this book continuously instead of providing
a new version each half year or so because I think this way it has a higher utility because
it provides more information earlier. By doing so, I also risk confusing you with strange
grammar and structure, so if you find something fishy, please let me know so I can correct
and improve it right away.
The updates and improvements will result in new versions of the book, which will regularly
appear on the website
http://www.it-weise.de/. The direct download link to the newest
version of this book is http://www.it-weise.de/projects/book.pdf. The L
A
T
E
X source
code of this book including all graphics and the bibliography is available at
http://www.
it-weise.de/projects/bookSource.zip. The source may not always be the one of the
most current version of the book. Compiling it requires multiple runs of BibT
E
X because of
the nifty way the references are incorporated.
I would be very happy if you provide feedback, report errors or missing things that you have
found, criticize something, or have any additional ideas or suggestions. Do not hesitate to
contact me via my email address tweise@gmx.de.
Matter of fact, a large number of people helped me to improve this book over time. I
have enumerated the most important contributors in
Chapter C – Thank you guys, I really
appreciate your help!
Copyright
c
2006-2009 Thomas Weise.
Permission is granted to copy, distribute and/or modify this document under the terms
of the GNU Free Documentation License, Version 1.2 or any later version published by
the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no
Back-Cover Texts. A copy of the license is included in the section entitled GNU F
ree
D
ocumentation License (FDL). You can find a copy of the GNU Free Documentation Li-
cense in appendix Chapter A on page 575.
2
The Adobe Reader
R
is available for download at
http://www.adobe.com/products/reader/
[accessed 2007-08-13].

5
At many places in this book we refer to Wikipedia [2219] which is a great source of knowl-
edge. Wikipedia [2219] contains articles and definitions for many of the aspects discussed in
this book. Like this book, it is updated and improved frequently. Therefore, including the
links adds greatly to the book’s utility, in my opinion.
Important Notice
Be aware that this version of this book marks a point of transition from the first edition to
the second one. Major fractions of the text of the first edition have not yet been revised and
are, thus, not included in this document. However, I believe that this version corrects many
shortcomings as well as inconsistencies from the first edition plus is better structured.
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