Abstract
A recent paper by Heinz and Beck (CPAIOR 2012) found that mixed integer software has become competitive with or superior to logic-based Benders decomposition for the solution of facility assignment and scheduling problems. Their implementation of Benders differs, however, from that described in the literature they cite and therefore results in much slower performance than previously reported. We find that when correctly implemented, the Benders method remains 2 to 3 orders of magnitude faster than the latest commercial mixed integer software on larger instances, thus reversing the conclusion of the earlier paper.
Partial support from NSF grant CMMI-1130012 and AFOSR grant FA-95501110180.
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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)
Beck, J.C., Ku, W.-Y.: Personal communication (September 14, 2012)
Benders, J.F.: Partitioning procedures for solving mixed-variables programming problems. Numerische Mathematik 4, 238–252 (1962)
Benini, L., Bertozzi, D., Guerri, A., Milano, M.: Allocation and scheduling for MPSoCs via decomposition and no-good generation. In: van Beek, P. (ed.) CP 2005. LNCS, vol. 3709, pp. 107–121. Springer, Heidelberg (2005)
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)
Chu, Y., Xia, Q.: Generating Benders cuts for a class of integer programming problems. In: Régin, J.-C., Rueher, M. (eds.) CPAIOR 2004. LNCS, vol. 3011, pp. 127–141. Springer, Heidelberg (2004)
Coban, E., Hooker, J.N.: Single-facility scheduling over long time horizons by logic-based benders decomposition. In: Lodi, A., Milano, M., Toth, P. (eds.) CPAIOR 2010. LNCS, vol. 6140, pp. 87–91. Springer, Heidelberg (2010)
Corréa, A.I., Langevin, A., Rousseau, L.M.: Dispatching and conflict-free routing of automated guided vehicles: A hybrid approach combining constraint programming and mixed integer programming. In: Régin, J.-C., Rueher, M. (eds.) CPAIOR 2004. LNCS, vol. 3011, pp. 370–378. Springer, Heidelberg (2004)
Harjunkoski, I., Grossmann, I.E.: A decomposition approach for the scheduling of a steel plant production. Computers and Chemical Engineering 25, 1647–1660 (2001)
Harjunkoski, I., Grossmann, I.E.: Decomposition techniques for multistage scheduling problems using mixed-integer and constraint programming methods. Computers and Chemical Engineering 26, 1533–1552 (2002)
Heinz, S., Beck, J.C.: Reconsidering mixed integer programming and MIP-based hybrids for scheduling. In: Beldiceanu, N., Jussien, N., Pinson, É. (eds.) CPAIOR 2012. LNCS, vol. 7298, pp. 211–227. Springer, Heidelberg (2012)
Hooker, J.N.: Logic-Based Methods for Optimization: Combining Optimization and Constraint Satisfaction. Wiley, New York (2000)
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.: Planning and scheduling problem instances (with documentation), website (2004), web.tepper.cmu.edu/jnh/instances.htm
Hooker, J.N.: A hybrid method for planning and scheduling. Constraints 10, 385–401 (2005)
Hooker, J.N.: Planning and scheduling to minimize tardiness. In: van Beek, P. (ed.) CP 2005. LNCS, vol. 3709, pp. 314–327. Springer, Heidelberg (2005)
Hooker, J.N.: An integrated method for planning and scheduling to minimize tardiness. Constraints 11, 139–157 (2006)
Hooker, J.N.: Integrated Methods for Optimization. Springer (2007)
Hooker, J.N.: Planning and scheduling by logic-based Benders decomposition. Operations Research 55, 588–602 (2007)
Hooker, J.N.: Integrated Methods for Optimization, 2nd edn. Springer (2012)
Hooker, J.N., Ottosson, G.: Logic-based Benders decomposition. Mathematical Programming 96, 33–60 (2003)
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, 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)
Maravelias, C.T., Grossmann, I.E.: Using MILP and CP for the scheduling of batch chemical processes. In: Régin, J.-C., Rueher, M. (eds.) CPAIOR 2004. LNCS, vol. 3011, pp. 1–20. Springer, Heidelberg (2004)
Terekhov, D., Beck, J.C., Brown, K.N.: Solving a stochastic queueing design and control problem with constraint programming. In: Proceedings of the 22nd National Conference on Artificial Intelligence (AAAI 2005), pp. 261–266 (2005)
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)
Timpe, C.: Solving planning and scheduling problems with combined integer and constraint programming. OR Spectrum 24, 431–448 (2002)
Yunes, T.H., Aron, I., Hooker, J.N.: An integrated solver for optimization problems. Operations Research 58, 342–356 (2010)
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Ciré, A., Coban, E., Hooker, J.N. (2013). Mixed Integer Programming vs. Logic-Based Benders Decomposition for Planning and Scheduling. In: Gomes, C., Sellmann, M. (eds) Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems. CPAIOR 2013. Lecture Notes in Computer Science, vol 7874. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38171-3_22
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