Scalability of Selectorecombinative Genetic Algorithms for Problems with Tight Linkage

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 population 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 problems, 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.