Abstract
To improve solution robustness, we introduce the concept of super solutions to constraint programming. An (a,b)-super solution is one in which if a variables lose their values, the solution can be repaired by assigning these variables with a new values and at most b other variables. Super solutions are a generalization of supermodels in propositional satisfiability. We focus in this paper on (1,0)-super solutions, where if one variable loses its value, we can find another solution by re-assigning this variable with a new value. To find super solutions, we explore methods based both on reformulation and on search. Our reformulation methods transform the constraint satisfaction problem so that the only solutions are super solutions. Our search methods are based on a notion of super consistency. Experiments show that super MAC, a novel search-based method shows considerable promise. When super solutions do not exist, we show how to find the most robust solution. Finally, we extend our approach from robust solutions of constraint satisfaction problems to constraint optimization problems.
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References
Dechter, R., Frost, D., Bessière, C., Régin, J.C.: Random uniform CSP generator (1996), url: http://www.ics.uci.edu/~dfrost/csp/generator.html
Dechter, A., Dechter, R.: Belief maintenance in dynamic constraint networks. In: Proceedings AAAI 1988, pp. 37–42 (1988)
Hebrard, E., Hnich, B., Walsh, T.: Super CSPs. Technical Report APES-66-2003, APES Research Group (2003)
Fowler, D.W., Brown, K.N.: Branching constraint satisfaction problems for solutions robust under likely changes. In: Dechter, R. (ed.) CP 2000. D.W. Fowler and K.N. Brown, vol. 1894, pp. 500–504. Springer, Heidelberg (2000)
Freuder, E.C.: A sufficient condition for backtrack-bounded search. Journal of the ACM 32, 755–761 (1985)
Freuder, E.C.: Partial Constraint Satisfaction. In: Proceedings IJCAI 1989, pp. 278–283 (1989)
Freuder, E.C.: Eliminating Interchangeable Values in Constraint Satisfaction Problems. In: Proceedings AAAI 1991, pp. 227–233 (1991)
Gaschnig, J.: A constraint satisfaction method for inference making. In: Proceedings of the 12th Annual Allerton Conference on Circuit and System Theory, University of Illinois, Urbana-Champaign (1974)
Gaschnig, J.: Performance measurement and analysis of certain search algorithms. Technical report CMU-CS-79-124, Carnegie-Mellon University, PhD thesis (1979)
Gent, I., MacIntyre, E., Prosser, P., Walsh, T.: The constrainedness of search. In: Proceedings AAAI 1996, pp. 246–252 (1996)
Jussien, N., Debruyne, R., Boizumault, P.: Maintaining arc-consistency within dynamic backtracking. In: Dechter, R. (ed.) CP 2000. LNCS, vol. 1894, pp. 249–261. Springer, Heidelberg (2000)
Parkes, A., Ginsberg, M., Roy, A.: Supermodels and robustness. In: Proceedings AAAI 1998, pp. 334–339 (1998)
Miguel, I.: Dynamic Flexible Constraint Satisfaction and Its Application to AI Planning. PhD thesis, University of Edinburgh (2001)
Schiex, T., Verfaillie, G.: Nogood recording for static and dynamic constraint satisfaction problem. IJAIT 3(2), 187–207 (1994)
Walsh, T.: SAT v CSP. In: Dechter, R. (ed.) CP 2000. LNCS, vol. 1894, pp. 441–456. Springer, Heidelberg (2000)
Walsh, T.: Stochastic constraint programming. In: Proceedings ECAI 2002 (2002)
Watson, J.P., Barbulescu, L., Howe, A.E., Whitley, L.D.: Algorithms performance and problem structure for flow-shop scheduling. In: Proceedings of the Sixteenth National Conference on Artificial Intelligence (AAAI 1999), pp. 688–695 (1999)
Weigel, R., Bliek, C.: On reformulation of constraint satisfaction problems. In: Proceedings ECAI 1998, pp. 254–258 (1998)
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Hebrard, E., Hnich, B., Walsh, T. (2004). Super Solutions in Constraint Programming. In: Régin, JC., Rueher, M. (eds) Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems. CPAIOR 2004. Lecture Notes in Computer Science, vol 3011. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24664-0_11
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DOI: https://doi.org/10.1007/978-3-540-24664-0_11
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