A Simple Two-Module Problem to Exemplify Building-Block Assembly Under Crossover

Theoretically and empirically it is clear that a genetic algorithm with crossover will outperform a genetic algorithm without crossover in some fitness landscapes, and vice versa in other landscapes. Despite an extensive literature on the subject, and recent proofs of a principled distinction in the abilities of crossover and non-crossover algorithms for a particular theoretical landscape, building general intuitions about when and why crossover performs well when it does is a different matter. In particular, the proposal that crossover might enable the assembly of good building-blocks has been difficult to verify despite many attempts at idealized building-block landscapes. Here we show the first example of a two-module problem that shows a principled advantage for crossover. This allows us to understand building-block assembly under crossover quite straightforwardly and build intuition about more general landscape classes favoring crossover or disfavoring it.

[1]  S. Wright.  Evolution in mendelian populations , 1931 .

[2]  Gilbert Syswerda,et al.  Uniform Crossover in Genetic Algorithms , 1989, ICGA.

[3]  D. E. Goldberg,et al.  Genetic Algorithms in Search , 1989 .

[4]  Richard A. Watson,et al.  Analysis of recombinative algorithms on a non-separable building-block problem , 2000, FOGA.

[5]  Melanie Mitchell,et al.  The royal road for genetic algorithms: Fitness landscapes and GA performance , 1991 .

[6]  John H. Holland,et al.  Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence , 1992 .

[7]  Ingo Wegener,et al.  Real royal road functions--where crossover provably is essential , 2001, Discret. Appl. Math..

[8]  Kalyanmoy Deb,et al.  Analyzing Deception in Trap Functions , 1992, FOGA.

[9]  John H. Holland,et al.  Building Blocks, Cohort Genetic Algorithms, and Hyperplane-Defined Functions , 2000, Evolutionary Computation.

[10]  G. Wagner,et al.  Recombination induced hypergraphs: a new approach to mutation-recombination isomorphism , 1996 .

[11]  J. Pollack,et al.  Compositional evolution: interdisciplinary investigations in evolvability, modularity, and symbiosis , 2002 .

[12]  Peter F. Stadler,et al.  Algebraic Theory of Recombination Spaces , 1997, Evolutionary Computation.

[13]  R. A. Fisher,et al.  The Genetical Theory of Natural Selection , 1931 .

[14]  Michael D. Vose,et al.  The simple genetic algorithm - foundations and theory , 1999, Complex adaptive systems.

[15]  Samir W. Mahfoud.  Niching methods for genetic algorithms , 1996 .

[16]  S. Wright,et al.  Evolution in Mendelian Populations. , 1931, Genetics.

[17]  Heinz Mühlenbein,et al.  How Genetic Algorithms Really Work: Mutation and Hillclimbing , 1992, PPSN.

[18]  William M. Spears,et al.  Crossover or Mutation? , 1992, FOGA.

[19]  John H. Holland,et al.  When will a Genetic Algorithm Outperform Hill Climbing , 1993, NIPS.

[20]  Jordan B. Pollack,et al.  Modeling Building-Block Interdependency , 1998, PPSN.

[21]  R. A. Fisher,et al.  The Genetical Theory of Natural Selection , 1931 .

[22]  Joseph C. Culberson,et al.  Mutation-Crossover Isomorphisms and the Construction of Discriminating Functions , 1994, Evolutionary Computation.

[23]  Melanie Mitchell,et al.  Relative Building-Block Fitness and the Building Block Hypothesis , 1992, FOGA.

[24]  Schloss Birlinghoven,et al.  How Genetic Algorithms Really Work I.mutation and Hillclimbing , 2022 .

[25]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .

[26]  Tim Jones.  Evolutionary Algorithms, Fitness Landscapes and Search , 1995 .

[27]  David H. Wolpert,et al.  No free lunch theorems for optimization , 1997, IEEE Trans. Evol. Comput..

[28]  A. Rogers,et al.  A solvable model of a hard optimisation problem , 2001 .