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The Computer Journal Advance Access published online on March 6, 2007
The Computer Journal, doi:10.1093/comjnl/bxm006
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© The Author 2007. Published by Oxford University Press on behalf of The British Computer Society. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

A Two-Phase Optimization Algorithm For Mastermind

Shan-Tai Chen1, Shun-Shii Lin2,* and Li-Te Huang2

1 Department of Computer Science, Chung Cheng Institute of Technology, National Defense University, Tao-Yuan, Taiwan, R.O.C.
2 Graduate Institute of Computer Science and Information Engineering, National Taiwan Normal University, No. 88, Sec. 4, Ting-Chow Rd., Taipei, Taiwan, R.O.C.

* Corresponding author: linss{at}csie.ntnu.edu.tw

Received 6 January 2006; revised 30 November 2006

This paper presents a systematic model, two-phase optimization algorithms (TPOA), for Mastermind. TPOA is not only able to efficiently obtain approximate results but also effectively discover results that are getting closer to the optima. This systematic approach could be regarded as a general improver for heuristics. That is, given a constructive heuristic, TPOA has a higher chance to obtain results better than those obtained by the heuristic. Moreover, it sometimes can achieve optimal results that are difficult to find by the given heuristic. Experimental results show that (i) TPOA with parameter setting (k, d) = (1, 1) is able to obtain the optimal result for the game in the worst case, where k is the branching factor and d is the exploration depth of the search space. (ii) Using a simple heuristic, TPOA achieves the optimal result for the game in the expected case with (k, d) = (180, 2). This is the first approximate approach to achieve the optimal result in the expected case.

Key Words: algorithm • Mastermind • search strategies • deductive game


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