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How well does a single-point crossover mix building blocks with tight linkage.pdf

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How well does a single-point crossover mix building blocks with tight linkage

How Well Does A Single-Point Crossover Mix Building Blocks with Tight Linkage? Kumara Sastry David E. Goldberg IlliGAL Report No. 2002013 May, 2002 Illinois Genetic Algorithms Laboratory (IlliGAL) Department of General Engineering University of Illinois at Urbana-Champaign 117 Transportation Building 104 S. Mathews Avenue, Urbana, IL 61801 How Well Does A Single-Point Crossover Mix Building Blocks with Tight Linkage? Kumara Sastry and David E. Goldberg Illinois Genetic Algorithms Laboratory (IlliGAL) Department of General Engineering University of Illinois at Urbana-Champaign 104 S. Mathews Ave, Urbana, IL 61801 {ksastry,deg}@ Abstract Ensuring building-block (BB) mixing is critical to the success of genetic and evolutionary algorithms. This study develops facetwise models to predict the BB mixing time and the pop- ulation sizing dictated by BB mixing for single-point crossover. Empirical results are used to validate these models. The population-sizing model suggests that for moderate-to-large prob- lems, BB mixing—instead of BB decision making and BB supply—bounds the population size required to obtain a solution of constant quality. Furthermore, the population sizing for single- point crossover scales as O ( 2km1.5 ) , where k is the BB size and m is the number of BBs. 1 Introduction Since the inception of genetic algorithms (GAs), the importance of building blocks have been recognized (Holland, 1975; Goldberg, 1989b). Based on Holland’s notion of BBs, Goldberg proposed a design decomposition method for a successful design of GAs (Goldberg, 1991; Goldberg Liepens, 1991; Goldberg, Deb, Clark, 1992). This design decomposition currently consists of sevens steps (Goldberg, in press) and can be stated as follows: (1) Know what GAs process—building blocks (BBs), (2) solve problems that are of bounded BB difficulty, (3) ensure an adequate supply of raw BBs, (4) ensure increased market share for superior BBs, (5) know BB takeover and convergence times, (6) ensure that B