Abstract
Fast and powerful propagators are the main key to the success of constraint programming on scheduling problems. It is, for example, the case with the cumulative constraint, which is used to model tasks sharing a resource of discrete capacity. In this paper, we propose a new not-first/not-last rule, which we call the horizontally elastic not-first/not-last, based on strong relaxation of the earliest completion time of a set of tasks. This computation is obtained when scheduling the tasks in a horizontally elastic way. We prove that the new rule is sound and is able to perform additional adjustments missed by the classic not-first/not-last rule. We use the new data structure called Profile to propose a \(\mathcal {O}(n^3)\) filtering algorithm for a relaxed variant of the new rule where n is the number of tasks sharing the resource. We prove that the proposed algorithm still dominates the classic not-first/not-last algorithm. Experimental results on highly cumulative instances of resource constrained project scheduling problems (RCPSP) show that using this new algorithm can substantially improve the solving process of instances with an occasional and marginal increase of running time.
This work was partially supported by a grant from the Niels Henrik Abel board and the University Laval.
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References
Aggoun, A., Beldiceanu, N.: Extending CHIP in order to solve complex scheduling and placement problems. Math. Comput. Model. 17(7), 57–73 (1993)
Garey, M.R., Johnson, D.S.: Computers and Intractability, vol. 29. W. H. Freeman, New York (2002)
Baptiste, P., Le Pape, C., Nuijten, W.: Constraint-Based Scheduling: Applying Constraint Programming to Scheduling Problems. Kluwer, Boston (2001)
Kameugne, R., Fotso, L.P., Scott, J., Ngo-Kateu, Y.: A quadratic edge-finding filtering algorithm for cumulative resource constraints. Constraints 19(3), 243–269 (2014)
Gay, S., Hartert, R., Schaus, P.: Simple and scalable time-table filtering for the cumulative constraint. In: Pesant, G. (ed.) CP 2015. LNCS, vol. 9255, pp. 149–157. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-23219-5_11
Kameugne, R., Fotso, L.P.: A cumulative not-first/not-last filtering algorithm in \(\cal{O}(n^2 \rm {log}(\rm n))\). Indian J. Pure Appl. Math. 44(1), 95–115 (2013)
Vilím, P.: Edge finding filtering algorithm for discrete cumulative resources in \({\cal{O}}(kn\,{\rm log}\,n)\). In: Gent, I.P. (ed.) CP 2009. LNCS, vol. 5732, pp. 802–816. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-04244-7_62
Gingras, V., Quimper, C.-G.: Generalizing the edge-finder rule for the cumulative constraint. In: Proceedings of the 25th International Joint Conference on Artificial Intelligence (IJCAI 2016), pp. 3103–3109 (2016)
Fahimi, H., Ouellet, Y., Quimper, C.-G.: Linear-time filtering algorithms for the disjunctive constraint and a quadratic filtering algorithm for the cumulative not-first not-last. Constraints (2018). https://urldefense.proofpoint.com/v2/url?u=https-3A__doi.org_10.1007_s10601-2D018-2D9282-2D9&d=DwIGaQ&c=vh6FgFnduejNhPPD0fl_yRaSfZy8CWbWnIf4XJhSqx8&r=UyK1_569d50MjVlUSODJYRW2epEY0RveVNq0YCmePcDz4DQHW-CkWcttrwneZ0md&m=aL081BMc0-Mz9R68wFZEUyFJk8ey6WR_yrftmQnZo5M&s=hgOsaJRlHR1tDxzWdCLdLc6yr4SUt5P6x9Nz5aecTfQ&e
Schutt, A., Wolf, A.: A new \({\cal{O}}(n^2\log n)\) 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). https://doi.org/10.1007/978-3-642-15396-9_36
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)
Derrien, A., Petit, T.: A new characterization of relevant intervals for energetic reasoning. In: O’Sullivan, B. (ed.) CP 2014. LNCS, vol. 8656, pp. 289–297. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-10428-7_22
Carlier, J., Néron, E.: On linear lower bounds for the resource constrained project scheduling problem. Eur. J. Oper. Res. 149(2), 314–324 (2003)
Koné, O., Artigues, C., Lopez, P., Mongeau, M.: Event-based milp models for resource-constrained project scheduling problems. Comput. Oper. Res. 38(1), 3–13 (2011)
Letort, A., Beldiceanu, N., Carlsson, M.: A scalable sweep algorithm for the cumulative constraint. In: Milano, M. (ed.) CP 2012. LNCS, pp. 439–454. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-33558-7_33
Gay, S., Hartert, R., Lecoutre, C., Schaus, P.: Conflict ordering search for scheduling problems. In: Pesant, G. (ed.) CP 2015. LNCS, vol. 9255, pp. 140–148. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-23219-5_10
Prud’homme, C., Fages, J.-G., Lorca, X.: Choco Solver Documentation, TASC, INRIA Rennes, LINA CNRS UMR 6241, COSLING S.A.S. (2016). http://www.choco-solver.org
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Kameugne, R., Betmbe Fetgo, S., Gingras, V., Ouellet, Y., Quimper, CG. (2018). Horizontally Elastic Not-First/Not-Last Filtering Algorithm for Cumulative Resource Constraint. In: van Hoeve, WJ. (eds) Integration of Constraint Programming, Artificial Intelligence, and Operations Research. CPAIOR 2018. Lecture Notes in Computer Science(), vol 10848. Springer, Cham. https://doi.org/10.1007/978-3-319-93031-2_23
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