Productive Recombination and Propagating and Preserving Schemata

Stochastic sampling algorithms, the class to which genetic algorithms (GAs) belong, may be characterized by their sampling biases. A stronger bias will generally yield more efficient search, and thus better function optimization, but on a smaller class of problems than a weaker bias. We identify two biases for studying crossover operators—recombinative bias and schema bias—and demonstrate how they affect GA performance on specific problem classes. We show how a combination of high recombinative bias and low schema bias can combat premature convergence due to hitchhiking. However, high recombinative bias can be a liability for problems with competing conventions or traps. Competing conventions are a crossover-frustrating form of multimodality introduced by the representation. Traps lead to a phenomenon analogous to Gresham's Law in Economics where bad schemata drive out good schemata. We argue that it is susceptibility to this phenomenon that predicts whether a GA will be mislead and not the property of being fully deceptive. Finally, we present a method for automatically adapting the recombinative bias to the function being optimized.