1. Entropy-Driven Evolutionary Approaches to the Mastermind
Problem C. Cotta J.J. Merelo A. Mora T.P. Runarsson University of
Mlaga University of Granada University of Iceland M ASTERMIND Find
the secret combination of colors using the information provided by
the codemaker, e.g., h (,) =hidden combination played combination 1
correct peg 2 pegs of the right colot butout of place Mastermind is
a dynamic constraint satisfaction problem.Consistencyis the key.
Assume these are the available colors:and let the hidden
combination be... 1 stguess 64 combinations are initially possible
12 combinations remain feasible after 1 stmove 2 ndguess Only 2
possible combinations remained after 2 ndmove 3 rdguess
Acombinationcis feasibleiff h( c , g i ) = h( g i ,c h ) for alli ,
whereg iare previous guesses andc his the secret combination. Let={
c 1 ,... c k }be a collection of feasible combinations, given the
information gathered in previous moves. We compute the partition
matrix ibw= |{c | h( c , c i ) = < b , w > }| We pickc isuch
that theentropy of i[]is maximal , i.e., we maximize the
information obtained when playing a combination. An EA tries to
findfeasible solutions(1st-level goal)maximizing entropy(2nd-level
goal). Experiments The algorithms have been tested on instances
with4 pegsand6 or 8 colors . A comparison is done withEvoRank , a
state-of-the-art EA for this problem. E GAs perform comparably to
EvoRank with amuch lower computational effort . E GAC Mis the bestE
GA,statistically indistinguishableof EvoRank in number of guesses.
Seeded initializationis essential for good performance.
