Self-Adaptive Crossover

Abstract

Just as a child creates magnificent fortresses through the arrangement of simple blocks, so does a genetic algorithm seek near optimal performance through the juxtaposition of short, low-order, high-performance schemata, or building blocks. Goldberg about the building block hypothesis [47], p. 41.

Crossover plays a controversially discussed role within EAs. The building block hypothesis (BBH) assumes that crossover combines different useful blocks of parents. The genetic repair effect (GR) hypothesis assumes that common properties of parental solutions are mixed. Most of today’s crossover operators do not exhibit adaptive properties, but are either completely random or fixed. In this chapter self-adaptive crossover operators for string and combinatorial representations are introduced. For GAs in string representation self-adaptive crossover means the automatic adaptation of crossover points. With self-adaptive crossover we take a step towards exploiting the structure of the problem automatically, i.e. finding the building blocks or common features self-adaptively. The features we prose to control self-adaptively are crossover points for string representations and recombination factors for ES. A success of self-adaptive crossover would be a hint for the existence of building blocks. A failure would not prove that building blocks do not exist, but could either be a hint for their absence or for the fact that they cannot be identified with self-adaptive crossover points.