Abstract
Many combinatorial (optimisation) problems have natural models based on, or including, set variables and set constraints. This was already known to the constraint programming community, and solvers based on constructive search for set variables have been around for a long time. In this paper, set variables and set constraints are put into a local-search framework, where concepts such as configurations, penalties, and neighbourhood functions are dealt with generically. This scheme is then used to define the penalty functions for five (global) set constraints, and to model and solve two well-known applications.
This paper significantly extends and revises Technical Report 2004-015 of the Department of Information Technology, Uppsala University, Sweden.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Aarts, E., Lenstra, J.K. (eds.): Local Search in Combinatorial Optimization. John Wiley & Sons Ltd., Chichester (1997)
Azevedo, F., Barahona, P.: Applications of an extended set constraint solver. In: Proc. of the ERCIM / CompulogNet Workshop on Constraints (2000)
Barnier, N., Brisset, P.: Solving the Kirkman’s schoolgirl problem in a few seconds. In: Van Hentenryck, P. (ed.) CP 2002. LNCS, vol. 2470, pp. 477–491. Springer, Heidelberg (2002)
Beldiceanu, N.: Global constraints as graph properties on a structured network of elementary constraints of the same type. In: Dechter, R. (ed.) CP 2000. LNCS, vol. 1894, pp. 52–66. Springer, Heidelberg (2000)
Beldiceanu, N., Petit, T.: Cost evaluation of soft global constraints. In: Régin, J.-C., Rueher, M. (eds.) CPAIOR 2004. LNCS, vol. 3011, pp. 80–95. Springer, Heidelberg (2004)
Bohlin, M.: Design and Implementation of a Graph-Based Constraint Model for Local Search. PhL thesis, Mälardalen University, Västerås, Sweden (April 2004)
Codognet, P., Diaz, D.: Yet another local search method for constraint solving. In: Steinhöfel, K. (ed.) SAGA 2001. LNCS, vol. 2264, pp. 73–90. Springer, Heidelberg (2001)
Corrádi, K.: Problem at Schweitzer competition. Mat. Lapok 20, 159–162 (1969)
Dotú, I., Van Hentenryck, P.: Scheduling social golfers locally. In: Barták, R., Milano, M. (eds.) CPAIOR 2005. LNCS, vol. 3524, pp. 155–167. Springer, Heidelberg (2005)
Galinier, P., Hao, J.-K.: A general approach for constraint solving by local search. In: Proc. of CP-AI-OR 2000 (2000)
Gervet, C.: Interval propagation to reason about sets: Definition and implementation of a practical language. Constraints 1(3), 191–244 (1997)
Michel, L., Van Hentenryck, P.: Localizer: A modeling language for local search. In: Smolka, G. (ed.) CP 1997. LNCS, vol. 1330. Springer, Heidelberg (1997)
Michel, L., Van Hentenryck, P.: A constraint-based architecture for local search. ACM SIGPLAN Notices 37(11), 101–110 (2002); Proc. of OOPSLA 2002
Michel, L., Van Hentenryck, P.: Maintaining longest paths incrementally. In: Rossi, F. (ed.) CP 2003. LNCS, vol. 2833, pp. 540–554. Springer, Heidelberg (2003)
Müller, T., Müller, M.: Finite set constraints in Oz. In: Proc. of 13th Workshop Logische Programmierung, Technische Universität München, pp. 104–115 (1997)
Nareyek, A.: Using global constraints for local search. In: Constraint Programming and Large Scale Discrete Optimization. DIMACS: Series in Discrete Mathematics and Theoretical Computer Science, vol. 57, pp. 9–28. AMS, Providence (2001)
Petit, T., Régin, J.-C., Bessière, C.: Specific filtering algorithms for over constrained problems. In: Walsh, T. (ed.) CP 2001. LNCS, vol. 2239, p. 451. Springer, Heidelberg (2001)
Prestwich, S.: Supersymmetric modeling for local search. In: Proc. of 2nd International Workshop on Symmetry in Constraint Satisfaction Problems, at CP 2002 (2002)
Puget, J.-F.: Finite set intervals. In: Proc. of CP 1996 Workshop on Set Constraints (1996)
Puget, J.-F.: Symmetry breaking revisited. In: Van Hentenryck, P. (ed.) CP 2002. LNCS, vol. 2470, pp. 446–461. Springer, Heidelberg (2002)
Smith, B.M., et al.: The progressive party problem: Integer linear programming and constraint programming compared. Constraints 1, 119–138 (1996)
Van Hentenryck, P., Michel, L.: Localizer. Constraints 5(1–2), 43–84 (2000)
Van Hentenryck, P., Michel, L.: Control abstractions for local search. In: Rossi, F. (ed.) CP 2003. LNCS, vol. 2833, pp. 65–80. Springer, Heidelberg (2003)
Van Hentenryck, P., Michel, L., Liu, L.: Constraint-based combinators for local search. In: Wallace, M. (ed.) CP 2004. LNCS, vol. 3258, pp. 47–61. Springer, Heidelberg (2004)
Walser, J.P.: Integer Optimization by Local Search: A Domain-Independent Approach. LNCS (LNAI), vol. 1637. Springer, Heidelberg (1999)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Ågren, M., Flener, P., Pearson, J. (2005). Set Variables and Local Search. In: Barták, R., Milano, M. (eds) Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems. CPAIOR 2005. Lecture Notes in Computer Science, vol 3524. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11493853_4
Download citation
DOI: https://doi.org/10.1007/11493853_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-26152-0
Online ISBN: 978-3-540-32264-1
eBook Packages: Computer ScienceComputer Science (R0)