Abstract
We present an algorithmic framework for integrating solution methods that is based on search, inference, and relaxation and their interactions. We show that the following are special cases: branch and cut, CP domain splitting with propagation, popular global optimization methods, DPL methods for SAT with conflict clauses, Benders decomposition and other nogood-based methods, partial-order dynamic backtracking, various local search metaheuristics, and GRASPs (greedy randomized adaptive search procedures). The framework allows elements of different solution methods to be combined at will, resulting in a variety of integrated methods. These include continuous relaxations for global constraints, the linking of integer and constraint programming via Benders decomposition, constraint propagation in global optimization, relaxation bounds in local search and GRASPs, and many others.
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References
Aron, I., Hooker, J.N., Yunes, T.H.: SIMPL: A system for integrating optimization techniques. In: Régin, J.-C., Rueher, M. (eds.) CPAIOR 2004. LNCS, vol. 3011, pp. 21–36. Springer, Heidelberg (2004)
Benders, J.F.: Partitioning procedures for solving mixed-variables programming problems. Numerische Mathematik 4, 238–252 (1962)
Bliek, C.T.: Generalizing partial order and dynamic backtracking. In: Proceedings of AAAI, pp. 319–325. AAAI Press, Menlo Park (1998)
Bockmayr, A., Kasper, T.: Branch and infer: A unifying framework for integer and finite domain constraint programming. INFORMS Journal on Computing 10, 287–300 (1998)
Cambazard, H., Hladik, P.-E., Déplanche, A.-M., Jussien, N., Trinquet, Y.: Decomposition and Learning for a Hard Real Time Task Allocation Problem. In: Wallace, M. (ed.) CP 2004. LNCS, vol. 3258, pp. 153–167. Springer, Heidelberg (2004)
Eremin, A., Wallace, M.: Hybrid Benders decomposition algorithms in constraint logic programming. In: Walsh, T. (ed.) CP 2001. LNCS, vol. 2239, p. 1. Springer, Heidelberg (2001)
Geoffrion, A.M.: Generalized Benders decomposition. Journal of Optimization Theory and Applications 10, 237–260 (1972)
Ginsberg, M.L.: Dynamic backtracking. Journal of Artificial Intelligence Research 1, 25–46 (1993)
Ginsberg, M.L., McAllester, D.A.: GSAT and dynamic backtracking. In: Second Workshop on Principles and Practice of Constraint Programming (CP 1994), pp. 216–225 (1994)
Hooker, J.N.: Logic-based methods for optimization. In: Borning, A. (ed.) PPCP 1994. LNCS, vol. 874, pp. 336–349. Springer, Heidelberg (1994)
Hooker, J.N.: Constraint satisfaction methods for generating valid cuts. In: Woodruff, D.L. (ed.) Advances in Computational and Stochasic Optimization, Logic Programming and Heuristic Search, pp. 1–30. Kluwer, Dordrecht (1997)
Hooker, J.N.: Logic-Based Methods for Optimization: Combining Optimization and Constraint Satisfaction. John Wiley & Sons, New York (2000)
Hooker, J.N.: A framework for integrating solution methods. In: Bhargava, H.K., Ye, M. (eds.) Proceedings of ICS 2003 Computational Modeling and Problem Solving in the Networked World, pp. 3–30. Kluwer, Dordrecht (2003)
Hooker, J.N.: A hybrid method for planning and scheduling. In: Wallace, M. (ed.) CP 2004. LNCS, vol. 3258, pp. 305–316. Springer, Heidelberg (2004)
Hooker, J.N., Osorio, M.A.: Mixed logical/linear programming. Discrete Applied Mathematics 96-97, 395–442 (1999)
Hooker, J.N., Ottosson, G.: Logic-based Benders decomposition. Mathematical Programming 96, 33–60 (2003)
Hooker, J.N., Ottosson, G., Thorsteinsson, E., Kim, H.-J.: A scheme for unifying optimization and constraint satisfaction methods. Knowledge Engineering Review 15, 11–30 (2000)
Hooker, J.N., Yan, H.: Logic circuit verification by Benders decomposition. In: Saraswat, V., Van Hentenryck, P. (eds.) Principles and Practice of Constraint Programming: The Newport Papers (CP 1995), pp. 267–288. MIT Press, Cambridge (1995)
Jain, V., Grossmann, I.E.: Algorithms for hybrid MILP/CP models for a class of optimization problems. INFORMS Journal on Computing 13, 258–276 (2001)
Moskewicz, M.W., Madigan, C.F., Zhao, Y., Zhang, L., Malik, S.: Chaff: Engineering an efficient SAT solver. In: Proceedings of the 38th Design Automation Conference (DAC 2001), pp. 530–535 (2001)
Neumaier, A.: Complete search in continuous global optimization and constraint satisfaction. In: Iserles, A. (ed.) Acta Numerica 2004, vol. 13. Cambridge University Press, Cambridge (2004)
Pinter, J.D.: Applied Global Optimization: Using Integrated Modeling and Solver Environments. CRC Press, Boca Raton (forthcoming)
Prestwich, S.: Exploiting relaxation in local search. In: First International Workshop on Local Search Techniques in Constraint Satisfaction (2004)
Sahinidis, N.V., Tawarmalani, M.: Convexification and Global Optimization in Continuous and Mixed-Integer Nonlinear Programming. Kluwer Academic Publishers, Dordrecht (2003)
Silva, J.P.M., Sakallah, K.A.: GRASP–A search algorithm for propositional satisfiability. IEEE Transactions on Computers 48, 506–521 (1999)
Thorsteinsson, E.S.: Branch-and-Check: A hybrid framework integrating mixed integer programming and constraint logic programming. In: Walsh, T. (ed.) CP 2001. LNCS, vol. 2239, pp. 16–30. Springer, Heidelberg (2001)
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Hooker, J.N. (2005). A Search-Infer-and-Relax Framework for Integrating Solution Methods. In: Barták, R., Milano, M. (eds) Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems. CPAIOR 2005. Lecture Notes in Computer Science, vol 3524. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11493853_19
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DOI: https://doi.org/10.1007/11493853_19
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