Recombination Without Respect: Schema Combination and Disruption in Genetic Algorithm Crossover

One-point (or n-point) crossover has the property that schemata exhibited by both parents are ‘respected’transferred to the offspring without disruption. In addition, new schemata may, potentially, be created by combination of the genes on which the parents differ. Some argue that the preservation of similarity is the important aspect of crossover, and that the combination of differences (key to the building-block hypothesis) is unlikely to be valuable. In this paper, we discuss the operation of recombination on a hierarchical buildingblock problem. Uniform crossover, which preserves similarity, fails on this problem. Whereas, one-point crossover, that both preserves similarity and combines differences, succeeds. In fact, a somewhat perverse recombination operator, that combines differences but destroys schemata that are common to both parents, also succeeds. Thus, in this problem, combination of schemata from dissimilar parents is required, and preserving similarity is not required. The test problem represents an extreme case, but it serves to illustrate the different aspects of recombination that are available in regular operators such as one-point crossover.