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

Zusammenfassung
Contains a refresher on the linear algebra used in the text as well as an elementary introductory chapter on genetic algorithms. This monograph is suitable for graduate and advanced undergraduate students in mathematics and computer science, as well as researchers working in the domains of optimization, artificial intelligence, and others.

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