Abstract
Cumulative resource constraints can model scarce resources in scheduling problems or a dimension in packing and cutting problems.In order to efficiently solve such problems with a constraint programming solver, it is important to have strong and fast propagators for cumulative resource constraints. Time-table-edge-finding propagators are a recent development in cumulative propagators, that combine the current resource profile (time-table) during the edge-finding propagation. The current state of the art for solving scheduling and cutting problems involving cumulative constraints are lazy clause generation solvers, i.e., constraint programming solvers incorporating nogood learning, have proved to be excellent at solving scheduling and cutting problems. For such solvers, concise and accurate explanations of the reasons for propagation are essential for strong nogood learning. In this paper, we develop a time-table-edge-finding propagator for cumulative that explains its propagations. We give results using this propagator in a lazy clause generation system on resource-constrained project scheduling problems from various standard benchmark suites. On the standard benchmark suite PSPLib, we are able to improve the lower bound of about 60% of the remaining open instances, and close 6 open instances.
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References
Achterberg, T.: SCIP: solving constraint integer programs. Mathematical Programming Computation 1, 1–41 (2009)
Aggoun, A., Beldiceanu, N.: Extending CHIP in order to solve complex scheduling and placement problems. Mathematical and Computer Modelling 17(7), 57–73 (1993)
Alvarez-Valdés, R., Tamarit, J.M.: Heuristic algorithms for resource-constrained project scheduling: A review and an empirical analysis. In: Advances in Project Scheduling, pp. 113–134. Elsevier (1989)
Baptiste, P., Le Pape, C.: Constraint propagation and decomposition techniques for highly disjunctive and highly cumulative project scheduling problems. Constraints 5(1-2), 119–139 (2000)
Baptiste, P., Le Pape, C., Nuijten, W.: Satisfiability tests and time-bound adjustments for cumulative scheduling problems. Annals of Operations Research 92, 305–333 (1999)
Baptiste, P., Le Pape, C., Nuijten, W.: Constraint-Based Scheduling. Kluwer Academic Publishers, Norwell (2001)
Berthold, T., Heinz, S., Lübbecke, M., Möhring, R., Schulz, J.: A constraint integer programming approach for resource-constrained project scheduling. In: Lodi, A., Milano, M., Toth, P. (eds.) CPAIOR 2010. LNCS, vol. 6140, pp. 313–317. Springer, Heidelberg (2010)
Carlier, J., Néron, E.: On linear lower bounds for the resource constrained project scheduling problem. European Journal of Operational Research 149(2), 314–324 (2003)
Feydy, T., Somogyi, Z., Stuckey, P.J.: Half reification and flattening. In: Lee, J. (ed.) CP 2011. LNCS, vol. 6876, pp. 286–301. Springer, Heidelberg (2011)
Feydy, T., Stuckey, P.J.: Lazy clause generation reengineered. In: Gent (ed.) [11], pp. 352–366
Gent, I.P. (ed.): CP 2009. LNCS, vol. 5732. Springer, Heidelberg (2009)
Heinz, S., Schulz, J.: Explanations for the cumulative constraint: An experimental study. In: Pardalos, P.M., Rebennack, S. (eds.) SEA 2011. LNCS, vol. 6630, pp. 400–409. Springer, Heidelberg (2011)
Jussien, N.: The versatility of using explanations within constraint programming. Research Report 03-04-INFO, École des Mines de Nantes, Nantes, France (2003)
Jussien, N., Barichard, V.: The PaLM system: explanation-based constraint programming. In: Proceedings of TRICS: Techniques foR Implementing Constraint Programming Systems, a Post-conference Workshop of CP 2000, Singapore, pp. 118–133 (2000)
Katsirelos, G., Bacchus, F.: Generalized nogoods in CSPs. In: Veloso, M.M., Kambhampati, S. (eds.) Proceedings on Artificial Intelligence – AAAI 2005, pp. 390–396. AAAI Press/The MIT Press (2005)
Kolisch, R., Sprecher, A.: PSPLIB – A project scheduling problem library. European Journal of Operational Research 96(1), 205–216 (1997)
Kolisch, R., Sprecher, A., Drexl, A.: Characterization and generation of a general class of resource-constrained project scheduling problems. Management Science 41(10), 1693–1703 (1995)
Koné, O., Artigues, C., Lopez, P., Mongeau, M.: Event-based MILP models for resource-constrained project scheduling problems. Computers & Operations Research 38(1), 3–13 (2011)
Liess, O., Michelon, P.: A constraint programming approach for the resource-constrained project scheduling problem. Annals of Operations Research 157(1), 25–36 (2008)
Moskewicz, M.W., Madigan, C.F., Zhao, Y., Zhang, L., Malik, S.: Chaff: Engineering an efficient SAT solver. In: Proceedings of Design Automation Conference – DAC 2001, pp. 530–535. ACM, New York (2001)
Nuijten, W.P.M.: Time and Resource Constrained Scheduling. Ph.D. thesis. Eindhoven University of Technology (1994)
Ohrimenko, O., Stuckey, P.J., Codish, M.: Propagation via lazy clause generation. Constraints 14(3), 357–391 (2009)
Schulte, C., Stuckey, P.J.: Efficient constraint propagation engines. ACM Transactions on Programming Languages and Systems 31(1), Article No. 2 (2008)
Schutt, A.: Improving Scheduling by Learning. Ph.D. thesis, The University of Melbourne (2011), http://repository.unimelb.edu.au/10187/11060
Schutt, A., Feydy, T., Stuckey, P.J., Wallace, M.G.: Why cumulative decomposition is not as bad as it sounds. In: Gent (ed.) [11], pp. 746–761
Schutt, A., Feydy, T., Stuckey, P.J., Wallace, M.G.: Explaining the cumulative propagator. Constraints 16(3), 250–282 (2011)
Schutt, A., Feydy, T., Stuckey, P.J., Wallace, M.G.: Solving RCPSP/max by lazy clause generation. Journal of Scheduling, 1–17 (2012), online first
Schutt, A., Stuckey, P., Verden, A.: Optimal carpet cutting. In: Lee, J. (ed.) CP 2011. LNCS, vol. 6876, pp. 69–84. Springer, Heidelberg (2011)
Schutt, A., Wolf, A.: A new \({\mathcal O}(n^2\log n)\) not-first/not-last pruning algorithm for cumulative resource constraints. In: Cohen, D. (ed.) CP 2010. LNCS, vol. 6308, pp. 445–459. Springer, Heidelberg (2010)
Somogyi, Z., Henderson, F., Conway, T.: The execution algorithm of Mercury, an efficient purely declarative logic programming language. The Journal of Logic Programming 29(1-3), 17–64 (1996)
Stuckey, P.J., de la Banda, M.G., Maher, M.J., Marriott, K., Slaney, J.K., Somogyi, Z., Wallace, M., Walsh, T.: The G12 project: Mapping solver independent models to efficient solutions. In: Gabbrielli, M., Gupta, G. (eds.) ICLP 2005. LNCS, vol. 3668, pp. 9–13. Springer, Heidelberg (2005)
Vilím, P.: Computing explanations for the unary resource constraint. In: Barták, R., Milano, M. (eds.) CPAIOR 2005. LNCS, vol. 3524, pp. 396–409. Springer, Heidelberg (2005)
Vilím, P.: Edge finding filtering algorithm for discrete cumulative resources in \({\mathcal O}(kn\log n)\). In: Gent (ed.) [11], pp. 802–816
Vilím, P.: Timetable edge finding filtering algorithm for discrete cumulative resources. In: Achterberg, T., Beck, J.C. (eds.) CPAIOR 2011. LNCS, vol. 6697, pp. 230–245. Springer, Heidelberg (2011)
Walsh, T.: Search in a small world. In: Proceedings of Artificial intelligence – IJCAI 1999, pp. 1172–1177. Morgan Kaufmann (1999)
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Schutt, A., Feydy, T., Stuckey, P.J. (2013). Explaining Time-Table-Edge-Finding Propagation for the Cumulative Resource Constraint. 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_16
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