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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.

Keywords

Constraint Programming Constraint Satisfaction Problem Robust Solution Constraint Optimization Problem Super Solution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Dechter, R., Frost, D., Bessière, C., Régin, J.C.: Random uniform CSP generator (1996), url: http://www.ics.uci.edu/~dfrost/csp/generator.html
  2. 2.
    Dechter, A., Dechter, R.: Belief maintenance in dynamic constraint networks. In: Proceedings AAAI 1988, pp. 37–42 (1988)Google Scholar
  3. 3.
    Hebrard, E., Hnich, B., Walsh, T.: Super CSPs. Technical Report APES-66-2003, APES Research Group (2003)Google Scholar
  4. 4.
    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)CrossRefGoogle Scholar
  5. 5.
    Freuder, E.C.: A sufficient condition for backtrack-bounded search. Journal of the ACM 32, 755–761 (1985)CrossRefMathSciNetzbMATHGoogle Scholar
  6. 6.
    Freuder, E.C.: Partial Constraint Satisfaction. In: Proceedings IJCAI 1989, pp. 278–283 (1989)Google Scholar
  7. 7.
    Freuder, E.C.: Eliminating Interchangeable Values in Constraint Satisfaction Problems. In: Proceedings AAAI 1991, pp. 227–233 (1991)Google Scholar
  8. 8.
    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)Google Scholar
  9. 9.
    Gaschnig, J.: Performance measurement and analysis of certain search algorithms. Technical report CMU-CS-79-124, Carnegie-Mellon University, PhD thesis (1979)Google Scholar
  10. 10.
    Gent, I., MacIntyre, E., Prosser, P., Walsh, T.: The constrainedness of search. In: Proceedings AAAI 1996, pp. 246–252 (1996)Google Scholar
  11. 11.
    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)CrossRefGoogle Scholar
  12. 12.
    Parkes, A., Ginsberg, M., Roy, A.: Supermodels and robustness. In: Proceedings AAAI 1998, pp. 334–339 (1998)Google Scholar
  13. 13.
    Miguel, I.: Dynamic Flexible Constraint Satisfaction and Its Application to AI Planning. PhD thesis, University of Edinburgh (2001)Google Scholar
  14. 14.
    Schiex, T., Verfaillie, G.: Nogood recording for static and dynamic constraint satisfaction problem. IJAIT 3(2), 187–207 (1994)Google Scholar
  15. 15.
    Walsh, T.: SAT v CSP. In: Dechter, R. (ed.) CP 2000. LNCS, vol. 1894, pp. 441–456. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  16. 16.
    Walsh, T.: Stochastic constraint programming. In: Proceedings ECAI 2002 (2002)Google Scholar
  17. 17.
    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)Google Scholar
  18. 18.
    Weigel, R., Bliek, C.: On reformulation of constraint satisfaction problems. In: Proceedings ECAI 1998, pp. 254–258 (1998)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Emmanuel Hebrard
    • 1
  • Brahim Hnich
    • 1
  • Toby Walsh
    • 1
  1. 1.Cork Constraint Computation CentreUniversity College Cork 

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