Abstract
Typically local search methods for solving constraint satisfaction problems such as GSAT, WalkSAT, DLM, and ESG treat the problem as an optimisation problem. Each constraint contributes part of a penalty function in assessing trial valuations. Local search examines the neighbours of the current valuation, using the penalty function to determine a “better” neighbour valuation to move to, until finally a solution which satisfies all the constraints is found. In this paper we investigate using some of the constraints as “hard” constraints, that are always satisfied by every trial valuation visited, rather than as part of a penalty function. In this way these constraints reduce the possible neighbours in each move and also the overall search space. The treating of some constraints as hard requires that the space of valuations that are satisfied is “connected” in order to guarantee that a solution can be found from any starting position within the region; thus the concept of islands and the name “island confinement method” arises. Treating some constraints as hard provides new difficulties for the search mechanism since the search space becomes more jagged, and there are more deep local minima. A new escape strategy is needed. To demonstrate the feasibility and generality of our approach, we show how the island confinement method can be incorporated in, and significantly improve, the search performance of two successful local search procedures, DLM and ESG, on SAT problems arising from binary CSPs.
Similar content being viewed by others
References
Brafman, R.: A simplifier for propositional formulas with many binary clauses. In: Proceedings of IJCAI’01, pp. 515–522 (2001)
Choi, K., Lee, J., Stuckey, P.: A Lagrangian reconstruction of GENET. Artif. Intell. 123(1–2), 1–39 (2000)
Davenport, A., Tsang, E., Wang, C., Zhu, K.: GENET: a connectionist architecture for solving constraint satisfaction problems by iterative improvement. In: Proceedings of AAAI’94, pp. 325–330 (1994)
Fang, H., Kilani, Y., Lee, J., Stuckey, P.: Reducing search space in local search for constraint satisfaction. In: Dechter, R., Sutton, R., Kearns, M. (eds.) Proceedings of the 18th National Conference on Artificial Intelligence, pp. 28–33 (2002)
Fang, H., Kilani, Y., Lee, J., Stuckey, P.: Islands for SAT. Technical report, Computing Research Repository (CORR) (2006). http://arxiv.org/abs/cs.AI/0607071
Hoos, H.: On the run-time behavior of stochastic local search algorithms for SAT. In: Proceedings of AAAI’99, pp. 661–666 (1999)
Hutter, F., Tompkins, D., Hoos, H.: Scaling and probabilistic smoothing: efficient dynamic local search for SAT. In: Proceedings of CP’02, pp. 233–248 (2002)
Mackworth, A.: Consistency in networks of relations. Artif. Intell. 8(1), 99–118 (1977)
Minton, S., Johnston, M., Philips, A., Laird, P.: Minimizing conflicts: a heuristic repair method for constraint satisfaction and scheduling. Artif. Intell. 58, 161–205 (1992)
Morris, P.: The breakout method for escaping from local minima. In: Proceeding of AAAI’93, pp. 40–45 (1993)
Schuurmans, D., Southey, F.: Local search characteristics of incomplete SAT procedures. In: Proceedings of AAAI’00, pp. 297–302 (2000)
Schuurmans, D., Southey, F., Holte, R.: The exponentiated subgradient algorithm for heuristic boolean programming. In: Proceedings of IJCAI’01, pp. 334–341 (2001)
Selman, B., Kautz, H.: Domain-independent extensions to GSAT: solving large structured satisfiability problems. In: Proceedings of IJCAI’93, pp. 290–295 (1993)
Selman, B., Levesque, H., Mitchell, D.: A new method for solving hard satisfiability problems. In: Proceedings of AAAI’92, pp. 440–446 (1992)
Selman, B., Kautz, H., Cohen, B.: Noise strategies for improving local search. In: Proceedings of AAAI’94, pp. 337–343 (1994)
Stuckey, P.J., Tam, V.: Extending GENET with lazy arc consistency. IEEE Trans. Syst. Man Cybern. 28(5), 698–703 (1998)
Thornton, J., Pham, D., Bain, S., Ferreira, V. Jr.: Additive versus multiplicative clause weight for SAT. In: Proceedings of AAAI’04, pp. 191–196 (2004)
Wu, Z., Wah, B.: Trap escaping strategies in discrete Lagrangian methods for solving hard satisfiability and maximum satisfiability problems. In: Proceedings of AAAI’99, pp. 673–678 (1999)
Wu, Z., Wah, B.: An efficient global-search strategy in discrete Lagrangian methods for solving hard satisfiability problems. In: Proceedings of AAAI’00, pp. 310–315 (2000)
Author information
Authors and Affiliations
Corresponding author
Additional information
A preliminary version of this paper appeared in AAAI’2002.
Rights and permissions
About this article
Cite this article
Fang, H., Kilani, Y., Lee, J.H.M. et al. The island confinement method for reducing search space in local search methods. J Heuristics 13, 557–585 (2007). https://doi.org/10.1007/s10732-007-9020-8
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10732-007-9020-8