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Negative Effects of Modeling Techniques on Search Performance

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Abstract

Symmetries occur in many combinatorial problems, and a great deal of research has been done on symmetry breaking techniques for backtrack search. However, few results have been reported on the use of symmetry breaking with local search. On four classes of problem we find that adding symmetry breaking constraints to a model impairs local search performance, in terms of both execution time and search steps. We also find that implied constraints can impair backtrack search performance. These results show that modeling techniques and search heuristics should be combined with caution. They also motivate a novel modeling technique for local search: removing constraints to add new symmetries.

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References

  1. W.C. Babcock, Intermodulation interference in radio systems, Bell Systems Technical Journal (January 1953) 63–73.

  2. R. Backofen and S. Will, Excluding symmetries in constraint-based search, in: Proceedings of the Fifth International Conference on Principles and Practice of Constraint Programming, Lecture Notes in Computer Science, Vol. 1713 (Springer, Berlin, 1999) pp. 73–87.

    Google Scholar 

  3. I.M. Bomze, M. Budinich, P.M. Pardalos and M. Pelillo, The maximum clique problem, in: Handbook of Combinatorial Optimization, Vol. 4, eds. D.-Z. Du and P.M. Pardalos (Kluwer Academic, Boston, MA, 1999).

    Google Scholar 

  4. C.A. Brown, L. Finkelstein and P.W. Purdom, Jr., Backtrack searching in the presence of symmetry, in: Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, Lecture Notes in Computer Science, Vol. 357, ed. T. Mora (Springer, Berlin, 1988) pp. 99–110.

    Google Scholar 

  5. B. Cha and K. Iwama, Adding new clauses for faster local search, in: Proceedings of the Fourteenth National Conference on Artificial Intelligence (American Association for Artificial Intelligence, 1996) pp. 332–337.

  6. D. Clark, J. Frank, I. Gent, E. MacIntyre, N. Tomov and T. Walsh, Local search and the number of solutions, in: Proceedings of the Second International Conference on Principles and Practices of Constraint Programming, Lecture Notes in Computer Science, Vol. 1118 (Springer, Berlin, 1996) pp. 119–133.

    Google Scholar 

  7. C.J. Colbourn and J.H. Dinitz (eds.), in: CRC Handbook of Combinatorial Designs (CRC Press, 1996).

  8. S. Colton, L. Drake, A.M. Frisch, I. Miguel and T. Walsh, Automatic generation of implied constraints: initial progress, in: Proceedings of the Eighth Workshop on Automated Reasoning, York (2001) pp. 17–18.

  9. M. Crawford, M. Ginsberg, E. Luks and A. Roy, Symmetry breaking predicates for search problems, in: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning (1996) pp. 148–159.

  10. T. Fahle, S. Schamberger and M. Sellman, Symmetry breaking, in: Proceedings of the Seventh International Conference on Principles and Practices of Constraint Programming, Lecture Notes in Computer Science, Vol. 2239 (Springer, Berlin, 2001) pp. 93–107.

  11. P. Flener, A. Frisch, B. Hnich, Z. Kiziltan, I. Miguel, J. Pearson and T. Walsh, Symmetry in matrix models, Technical Report APES–30–2001, APES Group (2001).

  12. F. Focacci and M. Milano, Global cut framework for removing symmetries, in: Proceedings of the Seventh International Conference on Principles and Practices of Constraint Programming, Lecture Notes in Computer Science, Vol. 2239 (Springer, Berlin, 2001) pp. 77–92.

  13. J.W. Freeman, Improvements to propositional satisfiability search algorithms, Doctoral Dissertation, University of Pennsylvania, PA (1994).

    Google Scholar 

  14. E.C. Freuder, Modeling: the final frontier, in: Proceedings of the First International Conference and Exhibition on The Practical Application of Constraint Technologies and Logic Programming (Practical Application Company Ltd., 1999).

  15. E.C. Freuder, P.D. Hubbe and D. Sabin, Inconsistency and redundancy do not imply irrelevance, in: Proceedings of the AAAI Fall Symposium on Relevance, New Orleans, LA, USA (1994).

  16. I.P. Gent and B. Smith, Symmetry breaking during search in constraint programming, in: Proceedings of the Fourteenth European Conference on Artificial Intelligence (2000) pp. 599–603.

  17. I. Gent and T.Walsh, The SAT phase transition, in: Proceedings of the Eleventh European Conference on Artificial Intelligence (Wiley, New York, 1994) pp. 105–109.

    Google Scholar 

  18. C. Gomes, B. Selman and H. Kautz, Boosting combinatorial search through randomization, in: Proceedings of the Fifteenth National Conference on Artificial Intelligence and Tenth Innovative Applications of Artificial Intelligence Conference (AAAI Press/MIT Press, 1998) pp. 431–437.

  19. M. Henz, Constraint programming – an Oz perspective, in: Proceedings of the Fifth Pacific Rim International Conference on Artificial Intelligence, NUS, Singapore (November 1998) tutorial.

  20. D. Joslin and A. Roy, Exploiting symmetry in lifted CSPs, in: Proceedings of the Fourteenth National Conference on Artificial Intelligence, American Association for Artificial Intelligence (1997) pp. 197–203.

  21. K. Kask and R. Dechter, GSAT and local consistency, in: Proceedings of the Fourteenth International Joint Conference on Artificial Intelligence (Morgan Kaufmann, San Mateo, CA, 1995) pp. 616–622.

    Google Scholar 

  22. C.M. Li and Anbulagan, Look-ahead versus look-back for satisfiability problems, in: Proceedings of the Third International Conference on Principles and Practice of Constraint Programming, Lecture Notes in Computer Science, Vol. 1330 (Springer, Berlin, 1997) pp. 341–355.

    Google Scholar 

  23. P. Meseguer and C. Torras, Exploiting symmetries within constraint satisfaction search, Artificial Intelligence 129(1–2) (2001) 133–163.

    Google Scholar 

  24. S. Minton, M.D. Johnston, A.B. Philips and P. Laird, Minimizing conflicts: a heuristic repair method for constraint satisfaction and scheduling problems, Artificial Intelligence 58(1–3) (1992) 160–205.

    Google Scholar 

  25. M.W. Moskewicz, C.F. Madigan, Y. Zhao, L. Zhang and S. Malik, Chaff: engineering an efficient SAT solver, in: Proceedings of the Thirty-Ninth Design Automation Conference, Las Vegas (June 2001).

  26. S.D. Prestwich, A hybrid search architecture applied to hard random 3-SAT and low-autocorrelation binary sequences, in: Proceedings of the Sixth International Conference on Principles and Practice of Constraint Programming, Lecture Notes in Computer Science, Vol. 1894 (Springer, Berlin, 2000) pp. 337–352.

    Google Scholar 

  27. S.D. Prestwich, First-solution search with symmetry breaking and implied constraints, in: CP '01 Workshop on Modeling and Formulation (2001).

  28. S.D. Prestwich, Combining the scalability of local search with the pruning techniques of systematic search, Annals of Operations Research, to appear.

  29. S.D. Prestwich, Randomised backtracking for linear pseudo-Boolean constraint problems, in: Fourth International Workshop on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimisation Problems, Le Croisic, France (2002) pp. 7–20.

  30. S.D. Prestwich and S. Bressan, A SAT approach to query optimization in mediator systems, in: Fifth International Symposium on the Theory and Applications of Satisfiability Testing, University of Cincinatti (2002) pp. 252–259.

  31. P. Prosser, Domain filtering can degrade intelligent backjumping search, in: Proceedings of the Thirteenth International Joint Conference on Artificial Intelligence, Chambery, France (Morgan Kaufmann, San Mateo, CA, 1993) pp. 262–267.

    Google Scholar 

  32. P. Prosser and E. Selensky, On the encoding of constraint satisfaction problems with 0/ 1 variables, in: CP '01 Workshop on Modeling and Problem Formulation (2001).

  33. J.-F. Puget, On the satisfiability of symmetrical constrained satisfaction problems, in: Methodologies for Intelligent Systems, Proceedings of the International Symposium on Methodologies for IntelligentSystems, Lecture Notes in Computer Science, Vol. 689, eds. J. Komorowski and Z.W. Ras (Springer, Berlin, 1993) pp. 350–361.

    Google Scholar 

  34. W.T. Rankin, Optimal Golomb rulers: an exhaustive parallel search implementation, Master's thesis, Duke University (1993).

  35. J.-C. Régin, Minimization of the number of breaks in sports league scheduling problems using constraint programming, in: DIMACS Series in Discrete Mathematics and Theoretical Computer Science, Vol. 57 (Amer. Math. Soc., Providence, RI, 2001).

    Google Scholar 

  36. D. Sabin and E.C. Freuder, Contradicting conventional wisdom in constraint satisfaction, in: Proceedings of the Second International Workshop on Principles and Practice of Constraint Programming, Lecture Notes in Computer Science, Vol. 874 (Springer, Berlin, 1994) pp. 125–129.

    Google Scholar 

  37. B. Selman, H. Kautz and B. Cohen, Noise strategies for improving local search, in: Proceedings of the Twelfth National Conference on Artificial Intelligence (AAAI Press, 1994) pp. 337–343.

  38. B. Smith, K. Stergiou and T. Walsh, Using auxiliary variables and implied constraints to model nonbinary problems, in: Proceedings of the Seventeenth National Conference on Artificial Intelligence and Twelfth Innovative Applications of AI Conference (2000) pp. 182–187.

  39. T. Walsh, SAT v CSP, in: Proceedings of the Sixth International Conference on Principles and Practice of Constraint Programming, Lecture Notes in Computer Science, Vol. 1894 (Springer, Berlin, 2000) pp. 441–456.

    Google Scholar 

  40. M. Yokoo, Why adding more constraints makes a problem easier for hill-climbing algorithms: analyzing landscapes of CSPs, in: Proceedings of the Third International Conference on Principles and Practice of Constraint Programming, Lecture Notes in Computer Science, Vol. 1330 (Springer, Berlin, 1997) pp. 356–370.

    Google Scholar 

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Authors and Affiliations

  1. Cork Constraint Computation Centre, Department of Computer Science, University College, Cork, Ireland

    S. Prestwich

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Prestwich, S. Negative Effects of Modeling Techniques on Search Performance. Annals of Operations Research 118, 137–150 (2003). https://doi.org/10.1023/A:1021809724362

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