Deception, dominance and implicit parallelism in genetic search

This paper presents several theorems concerning the nature of deception, its relationship to hyperplane dominance, and the central role that deception plays in function optimization using genetic algorithms. The theoretical results relate to four general themes. First, the concept of a “deceptive attractor” is introduced; it is shown that a deceptive attractor must be the complement of the global solution for a problem to be fully deceptive. It is also shown that the deceptive attractor must either be a local optimum in Hamming space, or adjacent to a local optimum in Hamming space if the problem is fully deceptive. Second, it can be shown that the global solution to nondeceptive problems can be inferred (theoretically and often in practice) by determining the “winners” of the order-1 hyperplanes. The third theme relates the concept of deception and dominance. If a dominance relationship exists between two hyperplanes then deception is impossible between those two partitions of hyperspace; analogously, deception between two hyperplanes precludes a dominance relationship. The fourth theme relates to deception and implicit parallelism. It can be shown that if a genetic algorithm reliably allocates exponentially more trials to the observed best, then implicit parallelism (and the 2-arm bandit analogy) breaks down when deception is present.