Foundations of Generic Optimization

This book deals with combinatorial aspects of epistasis, a notion that existed for years in genetics and appeared in the ?eld of evolutionary algorithms in the early 1990s. Even thoughthe?rst chapterputsepistasisintheperspective ofevolutionary algorithms and arti?cial intelligence, and applications occasionally pop up in other chapters, thisbookisessentiallyaboutmathematics, aboutcombinatorialtechniques to compute in an e?cient and mathematically elegant way what will be de?ned as normalized epistasis. Some of the material in this book ?nds its origin in the PhD theses of Hugo Van Hove [97] and Dominique Suys [95]. The sixth chapter also contains material that appeared in the dissertation of Luk Schoofs [84]. Together with that of M. Teresa Iglesias [36], these dissertations form the backbone of a decade of mathematical ventures in the world of epistasis. The authors wish to acknowledge support from the Flemish Fund of Scienti?c - search (FWO-Vlaanderen) and of the Xunta de Galicia. They also wish to explicitly mentiontheintellectualandmoralsupporttheyreceivedthroughoutthepreparation of this work from their family and their colleagues Emilio Villanueva, Jose Mar a Barja and Arnold Beckelheimer, as well as our local T T Xpert Jan Adriaenssens.

Only book dealing exclusively with the notion of epistasis in the framework of evelotionary algorithms and genetic algorithms in particular Completely self-contained (even includes a mathematical refresher intended for users with more computer science than math background) Chapter 0 is intended for neophytes in the field of genetic algorithms and optimization theory; it provides in a very readable way the basics of genetic algorithms Provides new questions (and answers) in the field between combinatorics and optimization theory, between discrete and mathematics and theoretical computer science, between linear algebra and complexity theory

Klappentext

The success of a genetic algorithm when applied to an optimization problem depends upon several features present or absent in the problem to be solved, including the quality of the encoding of data, the geometric structure of the search space, deception or epistasis. This book deals essentially with the latter notion, presenting for the first time a complete state-of-the-art research on this notion, in a structured completely self-contained and methodical way.In particular, it contains a refresher on the linear algebra used in the text as well as an elementary introductory chapter on genetic algorithms aimed at readers unacquainted with this notion.In this way, the monograph aims to serve a broad audience consisting of graduate and advanced undergraduate students in mathematics and computer science, as well as researchers working in the domains of optimization, artificial intelligence, theoretical computer science, combinatorics and evolutionary algorithms.

Zusammenfassung

From the reviews:

"This book deals with combinatorial aspects of epistasis, especially normalized epistasis, a concept that exists in genetics and evolutionary algorithms. It starts with the theory of evolutionary algorithms. This illustrative introduction makes the book readable independent on other textbooks. ... The book is very well written and presents many important and useful results. ... It shows also that difficult practical problems can only be efficiently solved by a combination of Modelling, Mathematics and Computing." (Christian Posthoff, Zentralblatt MATH, Vol. 1108 (10), 2007)

Inhalt
Genetic algorithms: a guide for absolute beginners.- Evolutionary algorithms and their theory.- Epistasis.- Examples.- Walsh transforms.- Multary epistasis.- Generalized Walsh transforms.