Abstract
Research on constraints started in the early 1970s. We are approaching 40 years since the beginning of this successful field, and it is an opportunity to revise what has been reached. This paper is a personal view of the accomplishments in this field. We summarize the main achievements along three dimensions: constraint solving, modelling and programming. We devote special attention to constraint solving, covering popular topics such as search, inference (especially arc consistency), combination of search and inference, symmetry exploitation, global constraints and extensions to the classical model. For space reasons, several topics have been deliberately omitted.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Apt, K.R.: Principles of Constraint Programming. Cambridge University Press (2003)
Bacchus, F., van Beek, P.: On the conversion between non-binary and binary constraint satisfaction problems. In: Proceedings of 15th AAAI, pp. 311–318 (1998)
Bacchus, F., van Run, P.: Dynamic variable ordering in csps. In: Proceedings of 1st CP, pp. 258–275 (1995)
Baker, A.B.: The hazards of fancy backtracking. In: Proceedings of 12th AAAI, pp. 288–293 (1994)
Beacham, A., Chen, X., Sillito, J., van Beek, P.: Constraint programming lessons learned from crossword puzzles. In: Proceedings of 14th Canadian Conference on AI, pp. 78–87 (2001)
Beldiceanu, N., Carlsson, M., Rampon, J.-X.: Global Constraint Catalog. Working version of SICS technical report T2010L07 (2011)
Benhamou, F., Goualart, F., Granvilliers, L., Puget, J.-F.: Revising hull and box consistency. In: Proceedings of 16th ICLP, pp. 124–138 (1999)
Benhamou, F., Granvilliers, L.: Continuous and interval Constraints. In: Handbook of Constraint Programming. Elsevier (2006)
Bessiere, C.: Constraint propagation. In: Handbook of Constraint Programming. Elsevier (2006)
Bessiere, C., Van Hentenryck, P.: To be or not to be . . . a global constraint. In: Proceedings of 9th CP, pp. 789–794 (2003)
Bessiere, C., Katsirelos, G., Narodyska, N., Quimper, C.G., Walsh, T.: Decompositions of alldifferent, global cardinality and related constrains. In: Proceedings of 21th IJCAI, pp. 419–424 (2009)
Bessiere C., Meseguer P., Freuder E., Larrosa J.: On forward checking for non-binary constraint satisfaction. Artif. Intell. 141, 205–224 (2002)
Bessiere, C., Regin, J.C.: Refining the basic arc consistency algorithm. In: Proceedings of 17th IJCAI, pp. 309–315 (2001)
Bistareli, S., Montanari, U., Rossi, F.: Constraint solving over semirings. In: Proceedings of 14th IJCAI, pp. 624–630 (1995)
Bitner J.R., Reingold E.M.: Backtrack programming techniques. Commun. ACM 18, 651–656 (1975)
Blum C., Roli A.: Metaheuristics in combinatorial optimization: Overview and conceptual comparison. ACM Comput. Surveys 35, 268–308 (2003)
Bruynooghe M.: Solving combinatorial optimization problems by intelligent backtracking. Inf. Process. Lett. 11, 36–39 (1981)
Carchae, T., Beck, J.: Principles for the design of large neighborhood search. J. Math. Model. Algorithms 8, 245–270 (2009)
Carlsson, M., et al.: SICStus Prolog User’s Manual (release 4.2.0). Swedish Institute of Computer Science (2011)
Cheng B.M.W., Choi K.M.F., Lee J.H.M., Wu J.C.K.: Increasing constraint propagation by redundant modelling: an experience report. Constraints 4, 167–192 (1999)
Cohen, D.A., Jeavons, P., Jefferson, C., Petrie, K.E., Smith, B.: Symmetry definitions for constraint satisfaction problems. In: Proceedings of 11th CP, pp. 17–31 (2005)
Cooper M.C.: An optimal k-consistency algorithm. Artif. Intell. 41, 89–95 (1990)
Crawford, J., Ginsberg, M.L., Luks, E., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of 5th KR, pp. 148–159 (1996)
Davenport, A., Tsang, E., Wang, C., Zhu, K.: Genet: A connectionist architecture for solving constraint satisfaction problems by iterative improvement. In: Proceedings of 12th AAAI, pp. 325–330 (1994)
Dechter R.: Enhancement schems for constraint processing: backjumping, learning and cutset decomposition. Artif. Intell. 41, 273–312 (1990)
Dechter, R.: Mini-bucket: a general scheme of generating approximations in automated reasoning. In: Proceedings of 15th IJCAI, pp. 1297–1302 (1997)
Dechter R.: Bucket elimination: a unifying framework for reasoning. Artif. Intell. 113, 41–85 (1999)
Dechter, R.: Constraint Processing. Morgan Kaufmann. (2003)
Dechter R., Pearl J.: Network-based heuristics for constraint satisfaction problems. Artif. Intell. 34, 1–38 (1987)
Dincbas, M., Simonis, H., van Hentenryck, P.: Solving the car-sequencing problem in constraint logic programming. In: Proceedings of 8th ECAI, pp. 290–295 (1988)
Dotu, I., del Val, A., Cebrian, M.: Redundant modeling for the quasigroup completion problem. In: Proceedings of 9th CP, pp. 288–302 (2003)
Dynadec.: Comet Tutorial (version 2.1). Dynamic Decision Technologies Inc. (2010)
Fahle, T., Schamberger, S., Sellmann, M.: Symmetry breaking. In: Proceedings of 7th CP, pp. 93–107 (2001)
Faltings B.: Arc consistency for continuous variables. Artif. Intell. 65, 363–376 (1994)
Fikes R.E.: Ref-arf: a system for solving problems stated as procedures. Artif. Intell. 1, 27–120 (1970)
Freuder E.C.: Synthesizing constraint expressions. Commun. ACM 21, 958–965 (1978)
Freuder E.C.: A sufficient condition for backtrack-free search. J. ACM 29, 24–32 (1982)
Freuder E.C.: In pursuit of the holy grail. Constraints 2, 57–61 (1997)
Freuder, E.C.: Modeling: the final frontier. In: Proceedings of PACLP, pp. 15–21 (1999)
Frisch, A., Jefferson, C., Martinez, B., Miguel, I.: The rules of constraint modelling. In: Proceedings of 19th IJCAI, pp. 311–318 (2005)
Frisch, A., Jefferson, C., Miguel, I.: Symmetry-breaking as a prelude for implied constraints: a constraint modelling pattern. In: Proceedings of 16th ECAI, pp. 171–175 (2004)
Gaschnig, J.: A general backtracking algorithm that eliminates most redundant tests. In: Proceedings of 5th IJCAI, p. 457 (1977)
Gent, I., Petrie, K.E., Puget, J.F.: Symmetry in constraint programming. In: Handbook of Constraint Programming. Elsevier (2006)
Gent, I., Smith, B.: Symmetry breaking in constraint programming. In: Proceedings of 14th ECAI, pp. 599–603 (2000)
Ginsberg M.L.: Dynamic backtracking. J. AI Res. 1, 25–46 (1993)
Glover, F., Laguna, M.: Tabu Search. Kluwer, Dordrecht (1997)
Goldberg, D.E.: Genetic Algorithms in Search, Optimization and Machine Learning. Addison-Wesley (1989)
Golomb S., Baumert L.: Backtrack programming. J. ACM 12, 516–524 (1965)
Haralick R.M., Elliot G.L.: Increasing tree search efficiency for constraint satisfaction problems. Artif. Intell. 14, 263–313 (1980)
Van Hentenryck, P.: Constraint Satisfaction in Logic Programming. The MIT Press (1989)
Van Hentenryck, P., Michell, L.: Constraint-Based Local Search. MIT Press (2005)
Hoos, H., Stutzle, T.: Stochastic Local Search: Foundations and Applications. Elsevier/Morgan Kauffman (2004)
IBM. IBM ILOG CPLEX Optimization Studio documentation. IBM (2010)
Kask K., Dechter R.: A general scheme for automatic search heuristics from specification dependencies. Artif. Intell. 129, 91–131 (2001)
Kirpatrick S., Gelatt C.D., Vecchi M.P.: Optimization by simulated annealing. Science 220, 671–680 (1983)
Kiziltan, Z.: Symmetry breaking ordering constraints. PhD thesis, Uppsala University, Department of Information Science (2004)
Kondrak G., van Beek P.: A theoretical evaluation of selected backtracking algorithms. Artif. Intell. 89, 365–387 (1997)
Laburthe, F., Jussien, N.: Choco Solver Documentation. Ecole de Mines de Nantes (2011)
Larrosa J., Dechter R.: Boosting search with variable elimination in constraint optimization and constraint satisfaction problems. Constraints 8, 303–326 (2003)
Larrosa J., Schiex T.: Solving weighted csp by maintaining arc consistency. Artif. Intell. 159, 1–26 (2004)
Law, Y.C., Lee, J.H.M.: Model induction: a new source of csp model redundancy. In: Proceedings of 15th AAAI, pp. 54–60 (2002)
Mackworth A.: Consistency in networks of relations. Artif. Intell. 8, 99–118 (1977)
Marriot, K., Stuckey, P.J.: Programming with Constraints. The MIT Press (1998)
Marriot, K., Stuckey, P.J., De Koninck, L., Samulowitz, H.: An introduction to MiniZinc (version 1.4). University of Melbourne and NICTA (2011)
McAllister, D., Selman, B., Kautz, H.: Evidence for invariants in local search. In: Proceedings of 14th AAAI, pp. 321–326 (1997)
Meisels A., Zivan R.: Asynchronous forward-checking for discsps. Constraints 12, 131–150 (2007)
Meseguer, P., Rossi, F., Schiex T.: Soft constraints. In: Handbook of Constraint Programming. Elsevier (2006)
Minton S., Johnston M., Philips A., Laird P.: Minimizing conflicts: a heuristic repair method for constraint satisfaction and scheduling problems. Artif. Intell. 58, 161–205 (1992)
Modi P.J., Shen W.M., Tambe M., Yokoo M.: Adopt: asynchronous distributed constraint optimization with quality guarantees. Artif. Intell. 161, 149–180 (2005)
Mohr R., Henderson T.C.: Arc and path consistency revisited. Artif. Intell. 28, 225–233 (1986)
Montanari U.: Networks of constraints: fundamental properties and applications to picture processing. Inf. Sci. 7, 95–132 (1974)
Morris, P.: The breakout method for escaping from local minima. In: Proceedings of 11th AAAI, pp. 40–45 (1993)
Petcu, A., Faltings, B.: A scalable method for multiagent constraint optimization. In: Proceedings of 19th IJCAI, pp. 266–271 (2005)
Prosser, P.: Domain filtering can degrade intelligent backtracking search. In: Proceedings of 13th IJCAI, pp. 262–267 (1993)
Puget, J.-F.: Constraint programming: a great AI success. In: Proceedings of 13th ECAI, pp. 698–675 (1998)
Puget, J.-F.: Constraint programming next challenge: simplicity of use. In: Proceedings of 10th CP, pp. 5–8 (2004)
Regin, J.C.: A filtering algorithm for constraints of difference in csps. In: Proceedings of 12th AAAI, pp. 362–367 (1994)
Rossi, F., Van Beek, P., Walsh, T.: Handbook of Constraint Programming. Elsevier (2006)
Sabin, D., Freuder, E.: Contradicting conventional wisdom in constraint satisfaction. In: Proceedings of 11th ECAI, pp. 125–129 (1994)
Schiex, T., Fargier, H., Verfaillie, G.: Values constraint satisfaction problems: hard and easy problems. In: Proceedings of 14th IJCAI, pp. 631–637 (1995)
Schulte, C., Carlsson, M.: Finite constraint programming systems. In: Handbook of Constraint Programming. Elsevier (2006)
Schulte, C., Tack, G., Lagerkvist, M.: Modelling and Programming with Gecode (version 3.7.1) (2011)
Selman, B., Johnston, M., Philips, A., Laird, P.: A new method for solving hard satisfiability problems. In: Proceedings of 10th AAAI, pp. 440–446 (1992)
Selman, B., Kautz, H., Cohen, B.: Noise strategies for improving local search. In: Proceedings of 12th AAAI, pp. 337–343 (1994)
Silaghi M.C., Sam-Haroud D., Faltings B.: Asynchronous consistency and maintenance in distributed constraint satisfaction. Artif. Intell. 161, 25–53 (2005)
Smith, B.: Modelling. In: Handbook of Constraint Programming. Elsevier (2006)
Smith, B., Grant, S.: Trying harder to fail first. In: Proceedings of 13th ECAI, pp. 249–253 (1998)
Stallman R.M., Sussman G.J.: Forward reasoning and dependency-directed backtracking in a system for computer-aided circuit analysis. Artif. Intell. 9, 135–196 (1977)
Tsang, E.P.K.: Foundations of Constraint Satisfaction. Academic Press (1993)
van Hoewe, W.J., Katriel, I.: Global constraints. In: Handbook of Constraint Programming. Elsevier (2006)
van Hoewe W.J., Pesant G., Rousseau L.-M.: On global warming: flow-based soft global constraints. J. Heuristics 12, 347–373 (2006)
Voudouris, C., Tsang, E.: Guided local search. In: Handbook of Metaheuristics. Kluwer (2003)
Walsh, T.: Sat \({\vee}\) csp. In: Proceedings of 6th CP, pp. 441–456 (2000)
Walsh, T.: Constraint patterns. In: Proceedings of 9th CP, pp. 53–64 (2003)
Waltz, D.: Understanding line drawings of scenes with shadows. In: The Psychology of Computer Vision, pp. 19–91. McGraw-Hill (1975)
Yeoh W., Felner A., Koenig S.: BnB-ADOPT: asynchronous branch-and-bound dcop algorithm. J. AI Res. 38, 85–133 (2010)
Yokoo, M., Durfee, E., Ishida, T., Kuwabara, K.: The distributed constraint satisfaction problem: formalization and algorithms. IEEE Trans. Knowl. Data Eng. 10, 673–685 (1998)
Zivan R., Meisels A.: Dynamic ordering for asynchronous backtracking on discsps. Constraints 11, 179–197 (2006)
Author information
Authors and Affiliations
Corresponding author
Additional information
Partially supported by the Spanish project TIN2009-13591-C02-02 and Generalitat de Catalunya grant 2009-SGR-1434.
Rights and permissions
About this article
Cite this article
Meseguer, P. Towards 40 years of constraint reasoning. Prog Artif Intell 1, 25–43 (2012). https://doi.org/10.1007/s13748-011-0006-2
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s13748-011-0006-2