research-article

Improving evolutionary solutions to the game of mastermind using an entropy-based scoring method

Authors:

Juan Julián Merelo-Guervós,

Pedro Castillo,

Antonio M. Mora García,

Anna I. Esparcia-AlcázarAuthors Info & Claims

GECCO '13: Proceedings of the 15th annual conference on Genetic and evolutionary computation

Pages 829 - 836

https://doi.org/10.1145/2463372.2463473

Published: 06 July 2013 Publication History

Abstract

Solving the MasterMind puzzle, that is, finding out a hidden combination by using hints that tell you how close some strings are to that one is a combinatorial optimization problem that becomes increasingly difficult with string size and the number of symbols used in it. Since it does not have an exact solution, heuristic methods have been traditionally used to solve it; these methods scored each combination using a heuristic function that depends on comparing all possible solutions with each other. In this paper we first optimize the implementation of previous evolutionary methods used for the game of mastermind, obtaining up to a 40% speed improvement over them. Then we study the behavior of an entropy-based score, which has previously been used but not checked exhaustively and compared with previous solutions. The combination of these two strategies obtain solutions to the game of Mastermind that are competitive, and in some cases beat, the best solutions obtained so far. All data and programs have also been published under an open source license.

References

[1]

Marc Aldebert and Risto Widenius. Mastermind. Newsgroup comp.ai.games, archived at https://groups.google.com/d/topic/comp.ai.games/FVOEABY4gbQ/discussion, 1995.

[2]

E. Alfaro-Cid, P. A. Castillo, A. Esparcia, K. Sharman, J.J. Merelo, A. Prieto, A.M. Mora, and J.L.J. Laredo. Comparing multiobjective evolutionary ensembles for minimizing type I and II errors for bankruptcy prediction. In WCCI 2008 Proceedings, pages 2907--2913. IEEE Press, 2008.

[3]

Thomas Bāck. Selective pressure in evolutionary algorithms: A characterization of selection mechanisms. In In Proceedings of the First IEEE Conference on Evolutionary Computation, pages 57--62. IEEE Press, 1994.

[4]

L. Berghman, D. Goossens, and R. Leus. Efficient solutions for Mastermind using genetic algorithms. Computers and Operations Research, 36(6):1880--1885, 2009.

Digital Library

[5]

Azer Bestavros and Ahmed Belal. Mastermind, a game of diagnosis strategies. Bulletin of the Faculty of Engineering, Alexandria University, December 1986.

[6]

Y. Chen and D. Evans. Auditing information leakage for distance metrics. In Privacy, security, risk and trust (PASSAT), 2011 ieee third international conference on and 2011 ieee third international conference on social computing (socialcom), pages 1131--1140. IEEE, 2011.

[7]

V. Chvatal. Mastermind. Combinatorica, 3(3--4):325--329, 1983.

[8]

Carlos Cotta, Juan J. Merelo Guervós, Antonio Mora García, and Thomas Runarsson. Entropy-driven evolutionary approaches to the Mastermind problem. In Robert Schaefer, Carlos Cotta, Joanna Kolodziej, and Günter Rudolph, editors, Parallel Problem Solving from Nature PPSN XI, volume 6239 of Lecture Notes in Computer Science, pages 421--431. Springer Berlin / Heidelberg, 2010.

Digital Library

[9]

B. Doerr, R. Spöhel, H. Thomas, and C. Winzen. Playing mastermind with many colors. arXiv preprint arXiv:1207.0773, 2012.

[10]

B. Doerr and C. Winzen. Ranking-based black-box complexity. Algorithmica, pages 1--39, 2012. Article in Press.

[11]

J.A. Durlak and E.P. DuPre. Implementation matters: A review of research on the influence of implementation on program outcomes and the factors affecting implementation. American journal of community psychology, 41(3):327--350, 2008.

[12]

A. E. Eiben and J. E. Smith. Introduction to Evolutionary Computing. Springer, 2003.

Digital Library

[13]

R. Focardi and F.L. Luccio. Guessing bank pins by winning a mastermind game. Theory of Computing Systems, pages 1--20, 2011.

Digital Library

[14]

J. Francis. Strategies for playing MOO, or "Bulls and Cows". http://www.jfwaf.com/Bulls%20and%20Cows.pdf.

[15]

J. Gagneur, M.C. Elze, and A. Tresch. Selective phenotyping, entropy reduction, and the mastermind game. BMC bioinformatics, 12(1):406, 2011. http://www.biomedcentral.com/1471--2105/12/406.

[16]

P. García-Sánchez, J.J. Merelo, J.P. Sevilla, J.L.J. Laredo, A.M. Mora, and P.A. Castillo. Automatic generation of XSLT stylesheets using evolutionary algorithms. In Genetic and Evolutionary Computation Conference, GECCO2008, pages 1701--1702, New York, NY, USA, 2008. ACM Press.

Digital Library

[17]

W. Goddard. A computer/human Mastermind player using grids. South African Computer Journal, 30:3--8, 2003.

[18]

David E. Goldberg. Zen and the art of genetic algorithms. In J. David Schaffer, editor, ICGA, pages 80--85. Morgan Kaufmann, 1989.

Digital Library

[19]

M. T. Goodrich. Learning character strings via mastermind queries, with a case study involving mtdna. IEEE Transactions on Information Theory, 58(11):6726--6736, 2012.

Digital Library

[20]

M.T. Goodrich. The mastermind attack on genomic data. In Security and Privacy, 2009 30th IEEE Symposium on, pages 204--218. IEEE, 2009.

Digital Library

[21]

S. Hubalovsky. Modeling and computer simulation of real process-solution of mastermind board game. International Journal of Mathematics and Computers in Simulation, pages 107--118, 2012.

[22]

R. W. Irving. Towards an optimum Mastermind strategy. Journal of Recreational Mathematics, 11(2):81--87, 1978-79.

[23]

A.B. Khalifa and R.V. Yampolskiy. GA with Wisdom of Artificial Crowds for Solving Mastermind Satisfiability Problem. International Journal of Intelligent Games & Simulation, 6(2):6, 2011.

[24]

Donald E. Knuth. The computer as Master Mind. J. Recreational Mathematics, 9(1):1--6, 1976-77.

[25]

B. Kooi. Yet another Mastermind strategy. ICGA Journal, 28(1):13--20, 2005.

[26]

P.R. Laughlin, R. Lange, and J. Adamopoulos. Selection strategies for "mastermind" problems. Journal of Experimental Psychology: Learning, Memory, and Cognition, 8(5):475, 1982.

[27]

M. Legendre, K. Hollard, O. Buffet, A. Dutech, et al. MineSweeper: Where to probe? Technical Report RR-8041, INRIA, 2012. http://hal.inria.fr/hal-00723550.

[28]

J. J. Merelo, A. M. Mora, and C. Cotta. Finding fast solutions to the game of Mastermind. In Carlos Cotta Antonio Fernández-Leiva and Raúl Lara, editors, GAME-ON 2012, 13th International Conference on Intelligent Games and Simulation, pages 25--28. Eurosis, 2012.

[29]

J.J. Merelo, A.M. Mora, T.P. Runarsson, and C. Cotta. Assessing efficiency of different evolutionary strategies playing mastermind. In Computational Intelligence and Games (CIG), 2010 IEEE Symposium on, pages 38--45, August 2010.

[30]

Juan-Julián Merelo and Thomas P. Runarsson. Finding better solutions to the Mastermind puzzle using evolutionary algorithms. In Cecilia di Chio et al., editor, Applications of Evolutionary Computing, Part I, volume 6024 of Lecture Notes in Computer Science, pages 120--129, Istanbul, Turkey, 7-9 April 2010. Springer-Verlag.

Digital Library

[31]

Juan-J. Merelo-Guervós, Carlos Cotta, and Antonio Mora. Improving and Scaling Evolutionary Approaches to the MasterMind Problem. In Cecilia Di Chio, Stefano Cagnoni, Carlos Cotta, Marc Ebner, Anikó Ekárt, Anna Esparcia-Alcázar, Juan Julián Merelo Guervós, Ferrante Neri, Mike Preuss, Hendrik Richter, Julian Togelius, and Georgios N. Yannakakis, editors, EvoApplications (1), volume 6624 of Lecture Notes in Computer Science, pages 103--112. Springer, 2011.

Digital Library

[32]

Juan-J. Merelo-Guervós, Antonio-Miguel Mora, and Carlos Cotta. Optimizing worst-case scenario in evolutionary solutions to the MasterMind puzzle. In IEEE Congress on Evolutionary Computation, pages 2669--2676. IEEE, 2011.

[33]

Juan-Julián Merelo-Guervós, Antonio-Miguel Mora, Carlos Cotta, and Thomas-Philip Runarsson. An experimental study of exhaustive solutions for the mastermind puzzle. CoRR, abs/1207.1315, 2012.

[34]

Juan-Julián Merelo-Guervós, Gustavo Romero, Maribel García-Arenas, Pedro A. Castillo, Antonio-Miguel Mora, and Juan-Luís Jiménez-Laredo. Implementation matters: Programming best practices for evolutionary algorithms. In Joan Cabestany, Ignacio Rojas, and Gonzalo Joya Caparrós, editors, IWANN (2), volume 6692 of Lecture Notes in Computer Science, pages 333--340. Springer, 2011.

Digital Library

[35]

Zbigniew Michalewicz. Genetic Algorithms Data Structures = Evolution programs. Springer-Verlag, 2nd edition, 1994.

Digital Library

[36]

G. Montgomery. Mastermind: Improving the search. AI Expert, 7(4):40--47, 1992.

[37]

E. Neuwirth. Some strategies for Mastermind. Zeitschrift fur Operations Research. Serie B, 26(8):B257-B278, 1982.

[38]

JH O'Geran, HP Wynn, and AA Zhigljavsky. Mastermind as a test-bed for search algorithms. Chance, 6:31--37, 1993.

[39]

T. P Runarsson and J. J. Merelo. Adapting heuristic Mastermind strategies to evolutionary algorithms. In NICSO'10 Proceedings, Studies in Computational Intelligence, pages 255--267. Springer-Verlag, 2010. Also available from ArXiV: http://arxiv.org/abs/0912.2415v1.

[40]

A. U. Thor-Hidden. Title hidden. In Accepted, to be published in EvoApps proceedings 2013, page 10pp, 2013.

[41]

Giovanni Viglietta. Hardness of Mastermind. CoRR, abs/1111.6922, 2011.

[42]

Wikipedia. Mastermind (board game) -- Wikipedia, The Free Encyclopedia, 2009.

Cited By

Taylor NHofer MNelson J(2020)The Paradox of Help Seeking in the Entropy Mastermind GameFrontiers in Education10.3389/feduc.2020.5339985Online publication date: 23-Sep-2020
https://doi.org/10.3389/feduc.2020.533998
Fiore TLang APerucca A(2018)Tactile Tools for Teaching: Implementing Knuth's Algorithm for Mastering MastermindThe College Mathematics Journal10.1080/07468342.2018.150198949:4(278-286)Online publication date: 6-Sep-2018
https://doi.org/10.1080/07468342.2018.1501989

Index Terms

Improving evolutionary solutions to the game of mastermind using an entropy-based scoring method
1. Mathematics of computing
  1. Mathematical analysis
    1. Mathematical optimization
2. Theory of computation
  1. Design and analysis of algorithms
    1. Mathematical optimization

Recommendations

Finding an Evolutionary Solution to the Game of Mastermind with Good Scaling Behavior
LION 7: Revised Selected Papers of the 7th International Conference on Learning and Intelligent Optimization - Volume 7997

There are two main research issues in the game of Mastermind: one of them is finding solutions that are able to minimize the number of turns needed to find the solution, and another is finding methods that scale well when the size of the search space is ...
Beating exhaustive search at its own game: revisiting evolutionary mastermind
GECCO '10: Proceedings of the 12th annual conference on Genetic and evolutionary computation

The Mastermind puzzle consists in finding out a secret combination by playing others in the same search space and using the hints obtained as a response (which reveal how close the played combination is to the secret one) to produce new combinations and ...
Evolutionary approaches to evolve AI scripts for a RTS game
GECCO Comp '14: Proceedings of the Companion Publication of the 2014 Annual Conference on Genetic and Evolutionary Computation

This paper evaluates three different Evolutionary Algorithms (EAs) for generating non-player characters (NPCs) via Artificial Intelligence scripts for a Real Time Strategy (RTS) game. The first approach executes only a Genetic Algorithm (GA), while the ...

Comments

Information & Contributors

Information

Published In

cover image ACM Conferences

GECCO '13: Proceedings of the 15th annual conference on Genetic and evolutionary computation

July 2013

1672 pages

ISBN:9781450319638

DOI:10.1145/2463372

Editor:
Christian Blum
IKERBASQUE and University of the Basque Country UPV/EHU, Spain
,
General Chair:
Enrique Alba
University of Malaga, Spain

Copyright © 2013 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

Sponsors

SIGEVO: ACM Special Interest Group on Genetic and Evolutionary Computation

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 06 July 2013

Permissions

Request permissions for this article.

Request Permissions

Check for updates

Author Tags

Qualifiers

Research-article

Conference

GECCO '13

Sponsor:

SIGEVO

GECCO '13: Genetic and Evolutionary Computation Conference

July 6 - 10, 2013

Amsterdam, The Netherlands

Acceptance Rates

GECCO '13 Paper Acceptance Rate 204 of 570 submissions, 36%;

Overall Acceptance Rate 1,669 of 4,410 submissions, 38%

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

2
Total Citations
View Citations
163
Total Downloads

Downloads (Last 12 months)6
Downloads (Last 6 weeks)0

Reflects downloads up to 28 Feb 2025

Other Metrics

View Author Metrics

Citations

Cited By

Taylor NHofer MNelson J(2020)The Paradox of Help Seeking in the Entropy Mastermind GameFrontiers in Education10.3389/feduc.2020.5339985Online publication date: 23-Sep-2020
https://doi.org/10.3389/feduc.2020.533998
Fiore TLang APerucca A(2018)Tactile Tools for Teaching: Implementing Knuth's Algorithm for Mastering MastermindThe College Mathematics Journal10.1080/07468342.2018.150198949:4(278-286)Online publication date: 6-Sep-2018
https://doi.org/10.1080/07468342.2018.1501989

View Options

Login options

Check if you have access through your login credentials or your institution to get full access on this article.

Full Access

Get this Publication

View options

PDF

View or Download as a PDF file.

eReader

View online with eReader.

Figures

Tables

Media

View Table of Conten