Adapting heuristic mastermind strategies to evolutionary algorithms

Abstract

The art of solving the Mastermind puzzle was initiated by Donald Knuth and is already more than thirty years old; despite that, it still receives much attention in operational research and computer games journals, not to mention the natureinspired stochastic algorithm literature. In this paper we try to suggest a strategy that will allow nature-inspired algorithms to obtain results as good as those based on exhaustive search strategies; in order to do that, we first review, compare and improve current approaches to solving the puzzle; then we test one of these strategies with an estimation of distribution algorithm. Finally, we try to find a strategy that falls short of being exhaustive, and is then amenable for inclusion in nature inspired algorithms (such as evolutionary of particle swarm algorithms). This paper proves that by the incorporation of what we call local entropy into the fitness function of the evolutionary algorithm it becomes a better player than a random one, and gives a rule of thumb on how to incorporate the best heuristic strategies to evolutionary algorithms without incurring in an excessive computational cost. © 2010 Springer-Verlag Berlin Heidelberg.