Abstract
Many real world discrete optimization problems are expressible as nested problems where we solve one optimization or satisfaction problem as a subproblem of a larger meta problem. Nested problems include many important problem classes such as: stochastic constraint satisfaction/ optimization, quantified constraint satisfaction/optimization and minimax problems. In this paper we define a new class of problems called nested constraint programs (NCP) which include the previously mentioned problem classes as special cases, and describe a search-based CP solver for solving NCP’s.We briefly discuss how nogood learning can be used to significantly speedup such an NCP solver. We show that the new solver can be significantly faster than existing solvers for the special cases of stochastic/ quantified CSP/COP’s, and that it can solve new types of problems which cannot be solved with existing solvers.
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References
Tarim, A., Manandhar, S., Walsh, T.: Stochastic Constraint Programming: A Scenario-Based Approach. Constraints 11, 53–80 (2006)
Walsh, T.: Stochastic Constraint Programming.. In: van Harmelen, F. (ed.) ECAI, pp. 111–115. IOS Press (2002)
Benedetti, M., Lallouet, A., Vautard, J.: Quantified constraint optimization. In: Stuckey, P.J. (ed.) CP 2008. LNCS, vol. 5202, pp. 463–477. Springer, Heidelberg (2008)
Giunchiglia, E., Narizzano, M., Tacchella, A.: Clause/term resolution and learning in the evaluation of quantified Boolean formulas. J. Artif. Intell. Res. (JAIR) 26, 371–416 (2006)
Zhang, L., Malik, S.: Conflict driven learning in a quantified Boolean satisfiability solver. In: Proceedings of the 2002 IEEE/ACM International Conference on Computer-aided Design, pp. 442–449. ACM (2002)
Ohrimenko, O., Stuckey, P., Codish, M.: Propagation via lazy clause generation. Constraints 14, 357–391 (2009)
Feydy, T., Stuckey, P.J.: Lazy Clause Generation Reengineered. In: Gent, I.P. (ed.) CP 2009. LNCS, vol. 5732, pp. 352–366. Springer, Heidelberg (2009)
Marriott, K., Nethercote, N., Rafeh, R., Stuckey, P., Garcia de la Banda, M., Wallace, M.: The design of the Zinc modelling language. Constraints 13, 229–267 (2008)
Schwenk, A.J.: Take-away games. Fibonacci Quarterly 8, 225–234 (1970)
Chen, H.: The Computational Complexity of Quantified Constraint Satisfaction. PhD thesis, Cornell University (2004)
Samulowitz, H.: Solving Quantified Boolean Formulas. PhD thesis, University of Toronto (2007)
Benedetti, M., Lallouet, A., Vautard, J.: Reusing CSP propagators for qCSPs. In: Azevedo, F., Barahona, P., Fages, F., Rossi, F. (eds.) CSCLP. LNCS (LNAI), vol. 4651, pp. 63–77. Springer, Heidelberg (2007)
Schulte, C., Stuckey, P.J.: Effcient constraint propagation engines. ACM Transactions on Programming Languages and Systems (TOPLAS) 31, 2 (2008)
Chu, G., Stuckey, P.J.: Inter-instance nogood learning in constraint programming. In: Milano, M. (ed.) CP 2012. LNCS, vol. 7514, pp. 238–247. Springer, Heidelberg (2012)
Pralet, C., Verfailles, G., Schiex, T.: An algebraic graphical model for decision with uncertainties, feasibilities, and utilities. Journal of Artificial Intelligence Research 29, 421–489 (2007)
de Moura, L., Bjørner, N.S.: Z3: An efficient SMT solver. In: Ramakrishnan, C.R., Rehof, J. (eds.) TACAS 2008. LNCS, vol. 4963, pp. 337–340. Springer, Heidelberg (2008)
Ge, Y., Barrett, C., Tinelli, C.: Solving quantified verification conditions using satisfiability modulo theories. In: Pfenning, F. (ed.) CADE 2007. LNCS (LNAI), vol. 4603, pp. 167–182. Springer, Heidelberg (2007)
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Chu, G., Stuckey, P.J. (2014). Nested Constraint Programs. In: O’Sullivan, B. (eds) Principles and Practice of Constraint Programming. CP 2014. Lecture Notes in Computer Science, vol 8656. Springer, Cham. https://doi.org/10.1007/978-3-319-10428-7_19
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DOI: https://doi.org/10.1007/978-3-319-10428-7_19
Publisher Name: Springer, Cham
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