Applying Adaptive Algorithms to Epistatic Domains

John Holland has shown that when adaptive algorithms are used to search certain kinds of extremely large problem spaces, they will converge on a "good" solution fairly quickly. Such problem spaces are characterized by a low degree of epistasis. A host of classical search problems, however, are epistatic in nature. The present paper describes some new techniques for applying adaptive algorithms to epistatic domains, while retaining some of the strength of Holland's convergence proof. These techniques are described for two-dimensional bin-packing problems, and summarized for graph coloring problems. What makes these problems amenable to an adaptive approach is a two-stage evaluation procedure. Encodings of solutions are mutated and reproduced as they are in non-epistatic domains, but their evaluation is carried out after a decoding process. Using the techniques described, convergence is promoted in two ways: one of the natural mutation operators is a weaker version of Holland's crossover, and domain knowledge may be built into decoding processes so that the size of the search space is radically cut down.