Abstract
One of the most appealing features of constraint programming is its rich constraint language for expressing combinatorial optimization problems. This paper demonstrates that traditional combinators from constraint programming have natural counterparts for local search, although their underlying computational model is radically different. In particular, the paper shows that constraint combinators, such as logical and cardinality operators, reification, and first-class expressions can all be viewed as differentiable objects. These combinators naturally support elegant and efficient modelings, generic search procedures, and partial constraint satisfaction techniques for local search. Experimental results on a variety of applications demonstrate the expressiveness and the practicability of the combinators.
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Reference
Codognet, C., & Diaz, D. (2001). Yet another local search method for constraint solving. In Proceedings of the International Symposium on Stochastic Algorithms: Foundations and Applications (SAGA 2001), pages 73–90. Berlin, Germany (December).
Dell'Amico, M., & Trubian, M. (1993). Applying tabu search to the job-shop scheduling problem. Ann. Oper. Res. 41: 231–252.
Di Gaspero, L., & Schaerf, A. (2002). Writing local search algorithms using EASYLOCAL ++. In VOß, S. & Woodrubb, D.L., eds., Optimization Software Class Libraries, Kluwer, Boston, MA.
Dotú, I., Van Hentenryck, P., & Michel, L. (2005). Scheduling social golfers locally. In Proceedings of the Second International Conference on the Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems (CP-AI-OR'05). Prague.
Freuder, E. (1992). Partial constraint satisfaction. Artif. Intell. 58: 21–70.
Galinier, P., & Hao, J.-K. (2000). A general approach for constraint solving by local search. In Proceedings of the Second International Workshop on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems (CP-AI-OR'00), pages 57–69. Paderborn, Germany (March).
Harvey, W., & Stuckey, P. (2003). Improving linear constraint propagation by changing constraint representation. Constraints, 8(2): 173–207.
Ilog Solver 4.4. (1998). Reference Manual. Ilog SA, Gentilly, France.
Johnson, D., Aragon, C., McGeoch, L., & Schevon, C. (1989). Optimization by simulated annealing: An experimental evaluation; part I, graph partitioning. Oper. Res. 37(6): 865–893.
Laburthe, F., & Caseau, Y. (1998). SALSA: A language for search algorithms. In Fourth International Conference on the Principles and Practice of Constraint Programming (CP'98). Pisa (October).
Michel, L., & Van Hentenryck, P. (2000). Localizer. Constraints. 5: 41–82.
Michel, L., & Van Hentenryck, P. (2002). A constraint-based architecture for local search. In Conference on Object-Oriented Programming Systems, Languages, and Applications, pages 101–110. Seattle (November).
Michel, L., & Van Hentenryck, P. (2004). A simple Tabu search for warehouse location. Eur. J. Oper. Res. 157(3): 576–591.
Minton, S., Johnston, M. D., & Philips, A. B. (1990). Solving large-scale constraint satisfaction and scheduling problems using a heuristic repair method. In Proceedings of the Eighth National Conference on Artificial Intelligence (AAAI-90), pages 17–24. Boston (August).
Nareyek, A. (1998). Constraint-Based Agents. Springer Verlag, Berlin.
Nareyek, A. (2004). Dragonbreath. www.ai-center.com/projects/dragonbreath/..
Petit, T., Regin, J.-C., & Bessiere, C. (2001). Specific filtering Algorithms for over–constrained problems. In Proceedings of 7th International Conference on the Principles and Practice of Constraint Programming (CP'01), pages 451–463. Paphos, Cyprus (November).
Prestwich, S. D. (2002). Super symmetric modeling for local search. In Second International Workshop on Symmetry in Constraint Satisfaction Problems.
Prestwich, S. D. (2003). Negative effects of modeling techniques on search performance. Ann. Oper. Res. 118: 137–150.
Ramalingam, G. (1993). Bounded Incremental Computation. Ph.D. thesis. University of Wisconsin-Madison.
Selman, B., Kautz, H., & Cohen, B. (1994). Noise strategies for improving local search. In Proceedings of the Eleventh National Conference on Artificial Intelligence (AAAI-94), pages 337–343. Seattle (July).
Shaw, P., De Backer, B., & Furnon, V. (2002). Improved local Search for CP toolkits. Ann. Oper. Res. 115: 31–50.
Van Hentenryck, P. (2002). Constraint and integer programming in OPL. INFORMS J. Comput. 14(4): 345–372.
Van Hentenryck, P., & Deville, Y. (1991). The cardinality operator: A new logical connective and its application to constraint logic programming. In The 8th International Conference on Logic Programming (ICLP-91), pages 745–759. Paris, France (June).
Van Hentenryck, P., & Michel, L. (2003). Control abstractions for local search. In Proceedings of the Ninth International Conference on Principles and Practice of Constraint Programming, pages 65–80. Cork, Ireland.
Van Hoeve, W. J., Pesant, G., & Rousseau, L.-M. (2004). On global warming (Softening global constraints). In Proceedings of 6th International Workshop on Preferences and Soft Constraints, Toronto, Canada (September).
Voss, S., & Woodruff, D. (2002). Optimization Software Class Libraries. Kluwer Academic Publishers.
Voudouris, C., & Tsang, E. (1996). Partial constraint satisfaction problems and guided local search. In Proceedings of the International Conference on Practical Applications of Constraint Technology (PACT-96), pages 337–356. London (April).
Walser, J. (1998). Integer Optimization by Local Search. Springer Verlag.
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Van Hentenryck, P., Michel, L. & Liu, L. Contraint-Based Combinators for Local Search. Constraints 10, 363–384 (2005). https://doi.org/10.1007/s10601-005-2811-3
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DOI: https://doi.org/10.1007/s10601-005-2811-3