1 research outputs found
An experimental study of exhaustive solutions for the Mastermind puzzle
Mastermind is in essence a search problem in which a string of symbols that
is kept secret must be found by sequentially playing strings that use the same
alphabet, and using the responses that indicate how close are those other
strings to the secret one as hints. Although it is commercialized as a game, it
is a combinatorial problem of high complexity, with applications on fields that
range from computer security to genomics. As such a kind of problem, there are
no exact solutions; even exhaustive search methods rely on heuristics to
choose, at every step, strings to get the best possible hint. These methods
mostly try to play the move that offers the best reduction in search space size
in the next step; this move is chosen according to an empirical score. However,
in this paper we will examine several state of the art exhaustive search
methods and show that another factor, the presence of the actual solution among
the candidate moves, or, in other words, the fact that the actual solution has
the highest score, plays also a very important role. Using that, we will
propose new exhaustive search approaches that obtain results which are
comparable to the classic ones, and besides, are better suited as a basis for
non-exhaustive search strategies such as evolutionary algorithms, since their
behavior in a series of key indicators is better than the classical algorithms.Comment: 41 pages, to be submitted to Computers and Operations Researc