Influence of selective pressure on quality of solutions and speed of evolutionary mastermind

Mastermind is a puzzle in which a hidden code of length ℓ and made with κ colors has to be discovered via making guesses of the code and receiving hints that express the distance from the guess to the code, in terms of number of symbols in the right position and with the right color. Solutions to these problem are mainly heuristic and thus finding the correct parameters for these solutions has to be done via systematic experimentation. Since diversity in the population is one of the main factors affecting performance, in this paper we will experiment with selective pressure via two different parameters: population size and size of tournament in tournament selection. We will study the influence of them in three different measures: algorithm performance (measured in average number of guesses needed), number of evaluations and time needed to find the solution. We will prove that while, in general, increasing population size improves performance, there is an optimal size over which no further improvement is achieved. On the other hand, tournament size does not have a clear influence on performance, although it influences time needed to find the solution. We will also show that the number of evaluations is correlated positively with time, and it increases with population size so that a trade-off has to be found among solution quality and population size. After evaluating the result of the experiments, we will try to advance a rule of thumb for sizing population for the general MasterMind problem.