Solving Mastermind Using Genetic Algorithms

Abstract

The MasterMind game involves decoding a secret code. The classic game is a code of six possible colors in four slots. The game has been analyzed and optimal strategies have been posed by computer scientists and mathematicians. In this paper we will survey previous work done on solving MasterMind, including several approaches using Genetic Algorithms. We will also analyze the solution sets and compare our results using a novel scoring system inside a GA against previous work using Genetic and Heuristic algorithms. Our GA is performing closer to optimal then previously published work. The GA we present is a Steady State GA using Fitness Proportional Reproduction (FPR), where the fitness function incorporates a simple heuristic algorithm. We also present a scoring method that is simpler then those used by other researchers. In larger games such as 10 colors and 8 slots our GA clearly outperform the heuristic algorithm. In fact if one wishes to tradeoff a higher average number of guesses to a faster running time, extremely large games such as 12 × 10 can be solved in a reasonable time (i.e. minutes) of run time.