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. In this paper, we develop a time-table edge-finding energy propagator for cumulative constraint which can reason more strongly based on energy. We give results using this propagator in a lazy clause generation system on rectangle packing and evacuation scheduling problems. We are able to prune the search space and reduce solve time compared with a time-table or time-table edge-finding propagator.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Aggoun, A., Beldiceanu, N.: Extending CHIP in order to solve complex scheduling and placement problems. Math. Comput. Modell. 17(7), 57–73 (1993)
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)
Beldiceanu, N.: Global constraints as graph properties on structured network of elementary constraints of the same type. SICS Technical report T2000/01, SICS, Uppsala, Sweden (2000)
COSYTEC SA: CHIP v5.12.2.0 finite domain constraints reference manual. Technical report, COSYTEC SA (2017)
Even, C., Schutt, A., Van Hentenryck, P.: A constraint programming approach for non-preemptive evacuation scheduling. In: Pesant, G. (ed.) CP 2015. LNCS, vol. 9255, pp. 574–591. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-23219-5_40
Garey, M.R., Johnson, D.R.: Computers and Intractability. W.H Freeman and Co, San Francisco (1979)
Gingras, V., Quimper, C.G.: Generalizing the edge-finder rule for the cumulative constraint. In: IJCAI, pp. 3103–3109 (2016)
Kameugne, R., Fotso, L.P.: A cumulative not-first/not-last filtering algorithm in \(O(n^2 \log (n))\). Indian J. Pure Appl. Math. 44(1), 95–115 (2013)
Kameugne, R., Fotso, L.P., Scott, J.: A quadratic extended edge-finding filtering algorithm for cumulative resource constraints. Int. J. Plan. Sched. 1(4), 264–284 (2013)
Korf, R.: Optimal rectangle packing: initial results. In: Giunchiglia, E., Muscettola, N., Nau, D. (eds.) Proceedings of the Thirteenth International Conference on Automated Planning and Scheduling (ICAPS 2003), pp. 287–295. AAAI PRess (2003)
Ohrimenko, O., Stuckey, P.J., Codish, M.: Propagation via lazy clause generation. Constraints 14(3), 357–391 (2009)
Ouellet, P., Quimper, C.-G.: Time-table extended-edge-finding for the cumulative constraint. In: Schulte, C. (ed.) CP 2013. LNCS, vol. 8124, pp. 562–577. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-40627-0_42
Ouellet, Y., Quimper, C.-G.: A \(O(n \log ^2 n)\) checker and \(O(n^2 \log n)\) filtering algorithm for the energetic reasoning. In: van Hoeve, W.-J. (ed.) CPAIOR 2018. LNCS, vol. 10848, pp. 477–494. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-93031-2_34
Schutt, A., Feydy, T., Stuckey, P.J.: Explaining time-table-edge-finding propagation for the cumulative resource constraint. In: Gomes, C., Sellmann, M. (eds.) CPAIOR 2013. LNCS, vol. 7874, pp. 234–250. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-38171-3_16
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
Tesch, A.: Improving energetic propagations for cumulative scheduling. In: Hooker, J. (ed.) CP 2018. LNCS, vol. 11008, pp. 629–645. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-98334-9_41
VilÃm, P.: Max energy filtering algorithm for discrete cumulative resources. In: van Hoeve, W.-J., Hooker, J.N. (eds.) CPAIOR 2009. LNCS, vol. 5547, pp. 294–308. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-01929-6_22
VilÃm, 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). https://doi.org/10.1007/978-3-642-21311-3_22
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this paper
Cite this paper
Yang, M., Schutt, A., Stuckey, P.J. (2019). Time Table Edge Finding with Energy Variables. In: Rousseau, LM., Stergiou, K. (eds) Integration of Constraint Programming, Artificial Intelligence, and Operations Research. CPAIOR 2019. Lecture Notes in Computer Science(), vol 11494. Springer, Cham. https://doi.org/10.1007/978-3-030-19212-9_42
Download citation
DOI: https://doi.org/10.1007/978-3-030-19212-9_42
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-19211-2
Online ISBN: 978-3-030-19212-9
eBook Packages: Computer ScienceComputer Science (R0)