Finding a needle in a haystack using hints and evolutionary computation: the case of evolutionary MasterMind

In this paper we present a new version of an evolutionary algorithm that finds the hidden combination in the game of MasterMind by using hints on how close is a combination played to it. The evolutionary algorithm finds the hidden combination in an optimal number of guesses, is efficient in terms of memory and CPU, and examines only a minimal part of the search space. The algorithm is fast, and indeed previous versions can be played in real time on the world wide web. This new version of the algorithm is presented and compared with theoretical bounds and other algorithms. We also examine how the algorithm scales with search space size, and its performance for different values of the EA parameters. # 2005 Published by Elsevier B.V.

[1]  Eli Biham,et al.  Differential Cryptanalysis of Snefru, Khafre, REDOC-II, LOKI and Lucifer , 1991, CRYPTO.

[2]  Mehrdad Salami,et al.  A fast evaluation strategy for evolutionary algorithms , 2003, Appl. Soft Comput..

[3]  A. Bestavros,et al.  MasterMind A game of Diagnosis Strategies , 1986 .

[4]  Nicolai Petkov,et al.  From Natural to Artificial Neural Computation , 1995, Lecture Notes in Computer Science.

[5]  Joerg joke Heitkoetter,et al.  The hitch-hiker''s guide to evolutionary computation , 2001 .

[6]  Ker-I Ko,et al.  On the Number of Queries Necessary to Identify a Permutation , 1986, J. Algorithms.

[7]  J. R. Roche.  The value of adaptive questions in generalized Mastermind , 1997, Proceedings of IEEE International Symposium on Information Theory.

[8]  Melanie Mitchell,et al.  The royal road for genetic algorithms: Fitness landscapes and GA performance , 1991 .

[9]  Erich Neuwirth,et al.  Some strategies for mastermind , 1982, Z. Oper. Research.

[10]  Dan Boneh,et al.  On genetic algorithms , 1995, COLT '95.

[11]  Tom Kalisker,et al.  Solving Mastermind Using Genetic Algorithms , 2003, GECCO.

[12]  Maarten Keijzer,et al.  Evolving Objects: A General Purpose Evolutionary Computation Library , 2001, Artificial Evolution.

[13]  D. Knuth.  The Computer as Master Mind , 1977 .

[14]  Dan Boneh,et al.  Where Genetic Algorithms Excel , 2001, Evolutionary Computation.

[15]  Agostinho C. Rosa,et al.  Mastermind by evolutionary algorithms , 1999, SAC '99.

[16]  Ivan Tanev,et al.  Hybrid evolutionary algorithm-based real-world flexible job shop scheduling problem: application service provider approach , 2004, Appl. Soft Comput..

[17]  Zhixiang Chen,et al.  Finding a Hidden Code by Asking Questions , 1996, COCOON.

[18]  Pei-Chann Chang,et al.  Genetic algorithms applied in BOPP film scheduling problems: minimizing total absolute deviation and setup times , 2003, Appl. Soft Comput..

[19]  Vasek Chvátal,et al.  Mastermind , 1983, Comb..

[20]  K. Koyama,et al.  An Optimal Mastermind Strategy , 1993 .

[21]  K. Dejong,et al.  An analysis of the behavior of a class of genetic adaptive systems , 1975 .

[22]  Juan Julián Merelo Guervós,et al.  Solving Master Mind Using GAs and Simulated Annealing: A Case of Dynamic Constraint Optimization , 1996, PPSN.

[23]  Elizabeth M. Rudnick,et al.  Sequential Circuit Test Generation in a Genetic Algorithm Framework , 1994, 31st Design Automation Conference.