Metaheuristics can solve sudoku puzzles

Journal of Heuristics

Volumn 13, Issue 4, 2007, Pages 387-401

  Lewis, Rhyd ^a,b  

^a EDINBURGH NAPIER UNIVERSITY   (United Kingdom)

^b CARDIFF UNIVERSITY   (United Kingdom)

Author keywords

Metaheuristics; Phase transition; Puzzles; Sudoku

Indexed keywords

ALGORITHMS; FORMAL LOGIC; METADATA; PHASE TRANSITIONS; SIMULATED ANNEALING; STOCHASTIC MODELS;

METAHEURISTICS; PUZZLES; SUDOKU;

HEURISTIC METHODS;

EID: 34547201691     PISSN: 13811231     EISSN: 15729397     Source Type: Journal    
DOI: 10.1007/s10732-007-9012-8     Document Type: Article

References (19)

1. Abramson, D., Krishnamoorthy, H., Dang, H.: Simulated annealing cooling schedules for the school timetabling problem. Asia-Pac. J. Oper. Res. 16, 1-22 (1996)
2. Armstrong, S.: X-wing and Swordfish. Online resource. http://www.simes.clara.co.uk/programs/sudokutechnique6.htm (accessed July 2005)
3. Cheeseman, P., Kanefsky, B., Taylor, W.: Where the really hard problems are. In: Mylopoulos, J., Reiter, R. (eds.) Proceedings of IJCAI-91, pp. 331-337. Morgan Kaufmann, San Mateo (1991)
4. Colbourn, C.J., Colbourn, M.J., Stinson, D.R.: The computational complexity of recognising critical sets. In: Graph Theory. Lecture Notes in Mathematics, vol. 1073, pp. 248-253. Springer, New York (1984)
5. Eiben, A.E., van der Hauw, J., van Hemert, J.: Graph coloring with adaptive evolutionary algorithms. J. Heuristics 4(1), 25-46 (1998)
6. Garey, M.R., Johnson, D.S.: Computers and Intractability. Freeman, San Francisco (1979)
7. Glover, F., Laguna, M.: Tabu search. In: Pardalos, P.M., Resende, M.G.C. (eds.) Handbook of Applied Optimization, pp. 194-208. Oxford University Press, Oxford (2002)
8. Huckvale, M.: Mark huckvale-sudoku puzzles. Online resource. http://www.phon.ucl.ac.uk/home/mark/sudoku/ (accessed July 2005)
9. Kirkpatrick, S., Gelatt, C., Vecchi, M.: Optimization by simulated annealing. Science 4598, 671-680 (1983)
10. Lourenco, H.R., Martin, O., Stützle, T.: Iterated local search. In: Glover, F., Kochenberger, G. (eds.) Handbook of Metaheuristics, pp. 321-353. Kluwer Academic, Norwel (2002)
11. Lynce, I., Ouaknine, J.: Sudoku as a SAT problem. In: Proceedings of the 9th Symposium on Artificial Intelligence and Mathematics (2006)
12. Pendlebury, P.: Can you sudoku. In: The Mail on Sunday, London, 8th May 2005. An online version is also available at http://www.mailonsunday.co.uk/ pages/live/articles/news/news.html?in_article_=348348&in-page_id= 1770&in_a_source= (accessed July 2005)
13. Ross, P., Corne, D., Fang, H.-L.: Improving evolutionary timetabling with delta evaluation and directed mutation. In: Davidor, Y., Schwefel, H., Reinhard, M. (eds.) Parallel Problem Solving from Nature III (PPSN). Lecture Notes in Computer Science, vol. 866, pp. 556-565. Springer, Berlin (1994)
14. Ross, P., Corne, D., Terashima-Marin, H.: The phase-transition niche for evolutionary algorithms in timetabling. In: Burke, E., Ross, P. (eds.) The Practice and Theory of Automated Timetabling (PATAT). Lecture Notes in Computer Science, vol. 1153, pp. 309-325. Springer, Berlin (1996)
15. Simonis, H.: Sudoku as a constraint problem. In: Hnich, B., Prosser, P., Smith, B. (eds.) Proceedings of the 4th International Workshop on Modelling and Reformulating Constraint Satisfaction Problems. pp. 13-27 (2005)
16. Smith, B.: Phase transitions and the mushy region in constraint satisfaction problems. In: Cohn, A. (ed.) Proceedings of the 11th European Conference on Artificial Intelligence, pp. 100-104. Wiley, New York (1994)
17. Turner, J.S.: Almost all k-colorable graphs are easy to color. J. Algorithms 9, 63-82 (1988)
18. van Laarhoven, P., Aarts, E.: Simulated Annealing: Theory and Applications. Reidel, Dordrecht (1987)
19. Yato, T., Seta, T.: Complexity and completeness of finding another solution and its application to puzzles. IEICE Trans. Fundam. E 86-A(5), 1052-1060 (2003)