Evolution of Developmental Timing for Solving Hierarchically Dependent Deceptive Problems

Conventional evolutionary algorithms EAs cannot solve given optimization problems efficiently when their evolutionary operators do not accommodate to the structures of the problems. We previously proposed a mutation-based EA that does not use a recombination operator and does not have this problem of the conventional EAs. The mutation-based EA evolves timings at which probabilities for generating phenotypic values developmental timings change, and brings different evolution speed to each phenotypic variable, so that it can solve a given problem hierarchically. In this paper we first propose the evolutionary algorithm evolving developmental timing EDT by adding a crossover operator to the mutation-based EA and then devise a new test problem that conventional EAs are likely to fail in solving and for which the features of the proposed EA are well utilized. The test problem consists of multiple deceptive problems among which there is hierarchical dependency, and has the feature that the hierarchical dependency is represented by a graph structure. We apply the EDT and the conventional EAs, the PBIL and cGA, for comparison to the new test problem and show the usefulness of the evolution of developmental timing.