Foundations of Genetic Algorithms

Lecture Notes in Computer Science Commenced Publication in 1973 Founding and Former Series Editors: Gerhard Goos, Juris Hartmanis, and Jan van Leeuwen Editorial Board David Hutchison Lancaster University, UK Takeo Kanade Carnegie Mellon University, Pittsburgh, PA, USA Josef Kittler University of Surrey, Guildford, UK Jon M. Kleinberg Cornell University, Ithaca, NY, USA Friedemann Mattern ETH Zurich, Switzerland John C. Mitchell Stanford University, CA, USA Moni Naor Weizmann Institute of Science, Rehovot, Israel Oscar Nierstrasz University of Bern, Switzerland C. Pandu Rangan Indian Institute of Technology, Madras, India Bernhard Steffen University of Dortmund, Germany Madhu Sudan Massachusetts Institute of Technology, MA, USA Demetri Terzopoulos University of California, Los Angeles, CA, USA Doug Tygar University of California, Berkeley, CA, USA Moshe Y. Vardi Rice University, Houston, TX, USA Gerhard Weikum Max-Planck Institute of Computer Science, Saarbruecken, Germany 4436 Christopher R. Stephens Marc Toussaint Darrell Whitley Peter F. Stadler (Eds.) Foundations of Genetic Algorithms 9th International Workshop, FOGA 2007 Mexico City, Mexico, January 8-11, 2007 Revised Selected Papers 13 Volume Editors Christopher R. Stephens Universidad Nacional Autonoma de Mexico, Instituto de Ciencias Nucleares Circuito Exterior, A. Postal 70-543, Mexico D.F. 04510, Mexico E-mail: [email protected] Marc Toussaint TU Berlin Franklinstr. 28/29, 10587 Berlin, Germany E-mail: [email protected] Darrell Whitley Colorado State University, Department of Computer Science Fort Collins, CO 80523, USA E-mail: [email protected] Peter F. Stadler Universität Leipzig, Institut für Informatik Härtelstr. 16-18, 04107 Leipzig, Germany E-mail: [email protected] Library of Congress Control Number: 2007929644 CR Subject Classification (1998): F.1-2, I.2, I.2.6, I.2.8, D.2.2 LNCS Sublibrary: SL 1 – Theoretical Computer Science and General Issues ISSN ISBN-10 ISBN-13 0302-9743 3-540-73479-1 Springer Berlin Heidelberg New York 978-3-540-73479-6 Springer Berlin Heidelberg New York This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, re-use of illustrations, recitation, broadcasting, reproduction on microfilms or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law. Springer is a part of Springer Science+Business Media springer.com © Springer-Verlag Berlin Heidelberg 2007 Printed in Germany Typesetting: Camera-ready by author, data conversion by Scientific Publishing Services, Chennai, India Printed on acid-free paper SPIN: 12087204 06/3180 543210 Editorial Introduction Since their inception in 1990, the FOGA (Foundations of Genetic Algorithms) workshops have been one of the principal reference sources for theoretical developments in evolutionary computation (EC) and, in particular, genetic algorithms (GAs). The ninth such workshop, FOGA IX, was held at the Instituto de Ciencias Nucleares of the Universidad Nacional Autónoma de México, Mexico City during January 8–11, 2007. One of the main reasons the FOGA series of conferences has had a large impact in EC has been its distinct profile as the only conference dedicated to theoretical issues of a “foundational” nature – both conceptual and technical. In this FOGA conference, and in keeping with this tradition, special attention was paid to the biological foundations of EC. The essential mathematical structure behind many evolutionary algorithms is the one familiar from population genetics, whose basic elements have been around now for at least 70 years. The last 20 years or so, however, have witnessed huge changes in our understanding of how genomes and other genetic structures work due to a plethora of new experimental techniques and results. How does this new phenomenology change our understanding of what genetic systems do and how they do it? And how can we design “better” ones? In this spirit, the first 2 days of the conference consisted of organized discussions built around sets of lectures given by two world authorities on the “old” biology and the “new” biology – Reinhard Burger (University of Vienna) and Jim Shapiro (University of Chicago). The motivation behind this was that by a careful presentation of the main ideas, a useful transfer of knowledge of the latest developments and understanding of genetic dynamics in biology would be fruitful for the EC community in better understanding and designing artificial genetic systems. In particular the following questions were addressed: – How do real genetic systems work? – Why do they work that way? – From this, what can we learn in order to design “better” artificial genetic systems? One of the most important conclusions from this confrontation between the old and the new, was that the genotype – phenotype map and the huge variety of complex ways by which genomes can interchange and mix genetic material are not represented adequately in the standard “selection on a fixed fitness landscape, mutation and homologous recombination” picture so dominant in EC and, particularly, GAs. Secondly, it became clear that the canonical picture of population genetics was not an appropriate framework for considering “macroevolution” over long time scales, where the restructuring of genomes can be enormous. Both these facts potentially pose great challenges for EC. For instance, under what circumstances are all the diverse exchange and restructuring VI Preface mechanisms for genomes useful in an EC setting? It is hard to imagine that optimizing the 3,456-city Travelling Salesman problem needs such sophisticated apparatus. Such a limited combinatorial optimization context is probably much more akin to the evolution of specific phenotypic characteristics, as treated in standard population genetics. No doubt that is one of the main reasons for the success of GAs in combinatorial optimization. However, it is not clear if such a paradigm is adequate for producing a more intelligent robot. To understand then why biology uses certain representations and operators, it is necessary to understand what a biological system has to “do” when compared with EC systems. Surviving in an uncertain, time-dependent environment is surely an infinitely more complex task than finding a set of allele values that represent an optimal solution to a combinatorial optimization problem. In this sense, one may wonder if there are any biological systems that are at least similar to typical problems faced in EC. Peter Stadler presented probably one of the closest analogies – evolution of macromolecules in the context of an RNA world – where the fitness function for a particular RNA configuration is its replication rate. However, such simple chemical evolution seems far removed from the macroevolution of entire organisms. Hopefully, some of the fruits of this more intense examination of the relationship between biological evolution and EC will appear in the next FOGA. The second two days of the conference were of a more standard FOGA format with contributed talks and ample time for discussion between them. For this workshop there were 22 submissions which were each sent in a double-blind review to three referees. Twelve high quality submissions that cover a wide range of theoretical topics were eventually accepted after two more rounds of revisions and are presented in this volume. We would like to thank our co-organizers, Peter Stadler and Darrell Whitley, for their efforts and input. Katya Rodrı́guez formed part of the Local Organizing Committee and played an important role in making the conference run smoothly, as did Trinidad Ramı́rez and various student helpers. Thanks go to the Instituto de Ciencias Nucleares for providing its facilities and to the Macroproyecto Tecnologias para la Universidad de la Información y de la Computación for financial and technical support. April 2007 Christopher R. Stephens Marc Toussaint Organization FOGA 2007 was organized in cooperation with ACM/SIGEVO at the Instituto de Ciencias Nucleares, Universidad Nacional Autonoma de Mexico (UNAM), Mexico City, January 8–11, 2007. Executive Committees Organizing Committee: Chris Stephens (UNAM) Darrell Whitley (Colorado State University) Peter Stadler (University of Leipzig) Marc Toussaint (University of Edinburgh) Local Organizing Committee: Chris Stephens (UNAM) Katya Rodriguez (UNAM) Program Committee: Chris Stephens (UNAM) Darrell Whitley (Colorado State University) Peter Stadler (University of Leipzig) Marc Toussaint (University of Edinburgh) Referees J.E. Rowe W.B. Langdon A. Prügel-Bennett C. Witt R. Drechsler J. Branke W.E. Hart C. Igel L.M. Schmitt B. Mitavskiy I. Wegener A. Eremeev R. Heckendorn A.H. Wright H.-G. Beyer M. Pelikan Y. Gao M. Gallagher J. Shapiro J. He S. Droste A. Bucci M. Schoenauer J. Smith T. Jansen R. Poli W. Gutjahr A. Auger P. Stadler D. Whitley M. Vose O. Teytaud Sponsoring Institutions ACM Special Interest Group on Genetic and Evolutionary Computation, SIGEVO. Instituto de Ciencias Nucleares, UNAM. Macroproyecto Universitario “Tecnologias para la Universidad de la Informacion y la Computacion,” UNAM. Posgrado en Ciencia y Ingenieria de la Computacion, UNAM. Table of Contents Inbreeding Properties of Geometric Crossover and Non-geometric Recombinations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Alberto Moraglio and Riccardo Poli 1 Just What Are Building Blocks? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Christopher R. Stephens and Jorge Cervantes 15 Sufficient Conditions for Coarse-Graining Evolutionary Dynamics . . . . . . Keki Burjorjee 35 On the Brittleness of Evolutionary Algorithms . . . . . . . . . . . . . . . . . . . . . . . Thomas Jansen 54 Mutative Self-adaptation on the Sharp and Parabolic Ridge . . . . . . . . . . . Silja Meyer-Nieberg and Hans-Georg Beyer 70 Genericity of the Fixed Point Set for the Infinite Population Genetic Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Tomáš Gedeon, Christina Hayes, and Richard Swanson 97 Neighborhood Graphs and Symmetric Genetic Operators . . . . . . . . . . . . . Jonathan E. Rowe, Michael D. Vose, and Alden H. Wright 110 Decomposition of Fitness Functions in Random Heuristic Search . . . . . . . Yossi Borenstein and Riccardo Poli 123 On the Effects of Bit-Wise Neutrality on Fitness Distance Correlation, Phenotypic Mutation Rates and Problem Hardness . . . . . . . . . . . . . . . . . . . Riccardo Poli and Edgar Galván-López 138 Continuous Optimisation Theory Made Easy? Finite-Element Models of Evolutionary Strategies, Genetic Algorithms and Particle Swarm Optimizers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Riccardo Poli, William B. Langdon, Maurice Clerc, and Christopher R. Stephens 165 Saddles and Barrier in Landscapes of Generalized Search Operators . . . . Christoph Flamm, Ivo L. Hofacker, Bärbel M.R. Stadler, and Peter F. Stadler 194 Author Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213