Abstract
Constraint Violation Minimization Problems arise when dealing with over-constrained CSPs. Unfortunately, experiments and practice show that they quickly become too large and too difficult to be optimally solved. In this context, multiple methods (limited tree search, heuristic or stochastic local search) are available to produce non-optimal, but good quality solutions, and thus to provide the user with anytime upper bounds of the problem optimum. On the other hand, few methods are available to produce anytime lower bounds of this optimum. In this paper, we explore some ways of producing such bounds. All of them are algorithmic variants of a Branch and Bound search. More specifically, we show that a new algorithm, resulting from a combination of the Russian Doll Search and Iterative Deepening algorithms, clearly outperforms five known algorithms and allows high lower bounds to be rapidly produced
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References
S. Bistarelli, H. Fargier, U. Montanari, F. Rossi, T. Schiex, and G. Verfaillie. Semiring-based CSPs and Valued CSPs: Basic Properties and Comparison. In M. Jampel, E. Freuder, and M. Maher, editors, Over-Constrained Systems (LNCS 1106, Selected papers from the Workshop on Over-Constrained Systems at CP-95, reprints and background papers), pages 111–150. Springer, 1996.
S. Bistarelli, U. Montanari, and F. Rossi. Constraint Solving over Semirings. In Proc. of the 14th International Joint Conference on Artificial Intelligence (IJCAI-95), pages 624–630, Montréal, Canada, 1995.
S. de Givry, G. Verfaillie, and T. Schiex. Bounding the Optimum of Constraint Optimization Problems. In Proc. of the 3rd International Conference on Principles and Practice of Constraint Programming (CP-97), Schloss Hagenberg, Austria, 1997.
H. Fargier, D. Dubois, and H. Prade. Problèmes de satisfaction de contraintes flexibles: une approche égalitariste. Revue d’Intelligence Artificielle, 9(3):311–354, 1995.
H. Fargier and J. Lang. Uncertainty in Constraint Satisfaction Problems: a Probabilistic Approach. In Proc. of the European Conference on Symbolic and Quantitavive Approaches of Reasoning under Uncertainty (ECSQARU-93), pages 97–104, Grenade, Spain, 1993.
E. Freuder and R. Wallace. Partial Constraint Satisfaction. Artificial Intelligence, 58:21–70, 1992.
S. Kirkpatrick, C. Gelatt, and M. Vecchi. Optimization by Simulated Annealing. Science, 220, 1983.
R. Korf. Depth-First Iterative Deepening: An Optimal Admissible Tree Search. Artificial Intelligence, 27:97–109, 1985.
R. Korf. Linear-space Best-first Search. Artificial Intelligence, 62:41–78, 1993.
J. Larrosa and P. Meseguer. Expoiting the Use of DAC in MAX-CSP. In Proc. of the 2nd International Conference on Principles and Practice of Constraint Programming (CP-96, LNCS 1118), pages 308–322, Cambridge, MA, USA, 1996.
J. Larrosa and P. Meseguer. Phase Transition in MAX-CSP. In Proc. of the 12th European Conference on Artificial Intelligence (ECAI-96), pages 190–194, Budapest, Hungary, 1996.
C. Papadimitriou. Computational Complexity. Addison-Wesley Publishing Company, 1994.
J. Pearl. HEURISTICS, Intelligent Search Strategies for Computer Problem Solving. Addison-Wesley Publishing Company, 1984.
A. Rosenfeld, R. Hummel, and S. Zucker. Scene Labeling by Relaxation Operations. IEEE Transactions on Systems, Man, and Cybernetics, 6(6):173–184, 1976.
T. Schiex. Possibilistic Constraint Satisfaction Problems or “How to handle soft constraints?”. In Proc. of the 8th International Conference on Uncertainty in Artificial Intelligence (UAI-92), Stanford, CA, USA, 1992.
T. Schiex, H. Fargier, and G. Verfaillie. Problèmes de satisfaction de contraintes valués. Revue d’Intelligence Artificielle, 11(3):339–373, 1997.
B. Smith. Phase Transition and the Mushy Region in Constraint Satisfaction Problems. In Proc. of the 11th European Conference on Artificial Intelligence (ECAI-94), pages 100–104, Amsterdam, The Netherlands, 1994.
G. Verfaillie and S. de Givry. Algorithmic problems and solutions in the Valued Constraint Satisfaction Problem framework. In Proc. of the EUFIT-97 session on “Valued Constraint Satisfaction”, Aachen, Germany, 1997.
G. Verfaillie, M. LemaÎtre, and T. Schiex. Russian Doll Search for Solving Constraint Optimization Problems. In Proc. of the 13th National Conference on Artificial Intelligence (AAAI-96), pages 181–187, Portland, OR, USA, 1996.
R. Wallace. Directed Arc Consistency Preprocessing. In Proc. of the ECAI-94 Workshop on Constraint Processing (LNCS 923), pages 121–137. Springer, 1994.
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Cabon, B., de Givry, S., Verfaillie, G. (1998). Anytime Lower Bounds for Constraint Violation Minimization Problems. In: Maher, M., Puget, JF. (eds) Principles and Practice of Constraint Programming — CP98. CP 1998. Lecture Notes in Computer Science, vol 1520. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-49481-2_10
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DOI: https://doi.org/10.1007/3-540-49481-2_10
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