Abstract
Many combinatorial problems can be modeled as 0/1 integer linear programs. Problems expressed in this form are usually solved by Operations Research algorithms, but good results have also been obtained using generalised SAT algorithms based on backtracking or local search, after transformation to pseudo-Boolean form. A third class of SAT algorithm uses non-systematic backtracking to combine constraint propagation with local search-like scalability, at the cost of completeness. This paper describes such an algorithm for pseudo-Boolean models. Experimental results on a variety of problems are encouraging, in some cases yielding improved solutions or performance compared to previous algorithms.
Similar content being viewed by others
References
Aloul, F.A., A. Ramani, I. Markov, and K. Sakallah. (2002). “PBS: A Backtrack-Search Pseudo-Boolean Solver and Optimizer.” In Fifth International Symposium on Theory and Applications of Satisfiability Testing, Cincinnati, OH, pp. 346–353.
Barth, P. (1995). “A Davis–Putnam Based Enumeration Algorithm for Linear Pseudo-Boolean Optimization.” Research Report mpi-i-95-2-003, Max-Plank Institut für Informatik, Saarbrucken.
Baumgartner, P. and F. Massacci. (2000). “The Taming of the (X)OR.” In First International Conference on Computational Logic, Stream on Automated Deduction: Putting Theory into Practice, Lecture Notes in Artificial Intelligence, Vol. 1861, pp. 508–522. Berlin: Springer.
Béjar, R., A. Cabiscol, C. Fernandez, F. Manyà, and C. Gomes. (2001). “Capturing Structure with Satisfiability.” In Seventh International Conference on Principles and Practice of Constraint Programming, Lecture Notes in Computer Science, Vol. 2239, pp. 137–152. New York: Springer.
Béjar, R. and F. Manyà. (2000). “Solving the Round Robin Problem Using Propositional Logic.” In Seventeenth National Conference on Artificial Intelligence, Austin, TX, pp. 262–266.
Bofill, P. and C. Torras. (2001). “Neural Cost Functions and Search Strategies for the Generation of Block Designs: An Experimental Evaluation.” International Journal of Neural Systems 11(2), 187–202.
Bosch, R. (1999). “Integer Programming and Conway's Game of Life.” SIAM Review 41(3), 594–604.
Bosch, R. and M. Trick. (2001). “Constraint Programming and Hybrid Formulations for Life.” In Workshop on Modelling and Problem Formulation, Cyprus.
Colbourn, C.J. and J.H. Dinitz (eds.). (1996). The CRC Handbook of Combinatorial Designs. Boca Raton, FL: CRC Press.
Davis, M., G. Logemann, and D. Loveland. (1962). “A Machine Program for Theorem Proving.” Communications of the ACM 5, 394–397.
Debruyne, R. (1996). “Arc-Consistency in Dynamic CSPs Is No More Prohibitive.” In Eighth Conference on Tools with Artificial Intelligence, Toulouse, France, pp. 299–306.
Dixon, H.E. and M.L. Ginsberg. (2002). “Combining Satisfiability Techniques from AI and OR.” The Knowledge Engineering Review 15(1), 31–45.
Flener, P., A.M. Frisch, B. Hnich, Z. Kiziltan, I. Miguel, and T. Walsh. (2001). “Matrix Modelling.” In Workshop on Modelling and Problem Formulation, Cyprus.
Ginsberg, M.L. (1993). “Dynamic Backtracking.” Journal of Artificial Intelligence Research 1, 25–46.
Hirsch, E.A. and A. Kojevnikov. (2001). “Solving Boolean Satisfiability Using Local Search Guided by Unit Clause Elimination.” In Seventh International Conference on Principles and Practice of Constraint Programming, Cyprus.
Jussien, N. and O. Lhomme. (2002). “Local Search with Constraint Propagation and Conflict-Based Heuristics.” Artificial Intelligence 139(1), 21–45.
Li, C.-M. (2000). “Integrating Equivalency Reasoning into Davis–Putnam Procedure.” In Seventeenth National Conference on Artificial Intelligence, Austin, TX, pp. 291–296.
McAloon, K., C. Tretkoff, and G. Wetzel. (1997). “Sports League Scheduling.” In ILOG Optimization Suite International Users' Conference, Paris.
Meseguer, P. and C. Torras. (2001). “Exploiting Symmetries within Constraint Satisfaction Search.” Special Issue on Heuristic Search Artificial Intelligence 129(1/2), 133–163.
Moskewicz, M.W., C.F. Madigan, Y. Zhao, L. Zhang, and S. Malik. (2001). “Chaff: Engineering an Efficient SAT Solver.” In Thirty-Ninth Design Automation Conference,LasVegas,NV.
Prestwich, S.D. (2000). “A Hybrid Search Architecture Applied to Hard Random 3-SAT and Low-Autocorrelation Binary Sequences.” In Sixth International Conference on Principles and Practice of Constraint Programming, Lecture Notes in Computer Science, Vol. 1894, pp. 337–352. New York: Springer.
Prestwich, S.D. (2001). “Balanced Incomplete Block Design as Satisfiability.” In Twelfth Irish Conference on Artificial Intelligence and Cognitive Science, Maynooth, Ireland, pp. 189–198.
Prestwich, S.D. (2002a). “Coloration Neighbourhood Search with Forward Checking.” Annals of Mathematics and Artificial Intelligence 34(4), 327–340.
Prestwich, S.D. (2002b). “SAT Problems with Chains of Dependent Variables.” Discrete Applied Mathematics 3037, 1–22.
Prestwich, S.D. (2002c). “Combining the Scalability of Local Search with the Pruning Techniques of Systematic Search.” Annals of Operations Research 115, 51–72.
Prestwich, S.D. (2002d). “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, pp. 7–20.
Prestwich, S.D. and S. Bressan. (2002). “A SAT Approach to Query Optimization in Mediator Systems.” In Fifth International Symposium on the Theory and Applications of Satisfiability Testing, University of Cincinnati, pp. 252–259.
Prestwich, S.D. (2003). “Negative Effects of Modeling Techniques on Search Performance.” Annals of Operations Research 18, 137–150.
Prosser, P. (1993). “Hybrid Algorithms for the Constraint Satisfaction Problem.” Computational Intelligence 9(3), 268–299.
Prosser, P. and E. Selensky. (2001). “On the Encoding of Constraint Satisfaction Problems with 0/1 Variables.” In Workshop on Modelling and Problem Formulation, Cyprus.
Selman, B., H. Kautz, and B. Cohen. (1994). “Noise Strategies for Improving Local Search.” In Twelfth National Conference on Artificial Intelligence, pp. 337–343. AAAI Press.
Selman, B., H. Levesque and D. Mitchell. (1992). “A New Method for Solving Hard Satisfiability Problems.” In Tenth National Conference on Artificial Intelligence, pp. 440–446. AAAI Press.
Smith, B. (2001). “Reducing Symmetry in a Combinatorial Design Problem.” In Third International Workshop on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems, Ashford, Kent, England, pp. 351–359.
Velev, M.N. and R.E. Bryant. (2001). “Effective Use of Boolean Satisfiability Procedures in the Formal Verification of Superscalar and VLIW Microprocessors.” In Thirty-Eighth Design Automation Conference, pp. 226–231.
Walser, J.P. (1997). “Solving Linear Pseudo-Boolean Constraints with Local Search.” In Eleventh Conference on Artificial Intelligence, pp. 269–274. AAAI Press.
Whittemore, J., J. Kim, and K. Sakallah. (2001). “SATIRE: A New Incremental Satisfiability Engine.” In Thirty-Eighth Design Automation Conference, pp. 542–545.
Yokoo, M. (1994). “Weak-Commitment Search for Solving Constraint Satisfaction Problems.” In Twelfth National Conference on Artificial Intelligence, pp. 313–318. AAAI Press.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Prestwich, S. Incomplete Dynamic Backtracking for Linear Pseudo-Boolean Problems. Annals of Operations Research 130, 57–73 (2004). https://doi.org/10.1023/B:ANOR.0000032570.90510.8f
Issue Date:
DOI: https://doi.org/10.1023/B:ANOR.0000032570.90510.8f