Abstract
The Dial a Ride family of Problems (DARP) consists in routing a fleet of vehicles to satisfy transportation requests with time-windows. This problem is at the frontier between routing and scheduling. The most successful approaches in dealing with DARP are often tailored to specific variants. A generic state-of-the-art constraint programming model consists in using a sequence variable to represent the ordering of visits in a route. We introduce a possible representation for the domain called Insertion Sequence Variable that naturally extends the standard subset bound for set variables with an additional insertion operator after any element already sequenced. We describe the important constraints on the sequence variable and their filtering algorithms required to model the classical DARP and one of its variants called the Patient Transportation Problem (PTP). Our experimental results on a large variety of instances show that the proposed approach is competitive with existing sequence based approaches.
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References
Aggoun, A., Beldiceanu, N.: Extending chip in order to solve complex scheduling and placement problems. Math. Comput. Modell. 17(7), 57–73 (1993)
Braekers, K.: Dial-a-Ride Problems Instances. http://alpha.uhasselt.be/kris.braekers/ (2019). Accessed 2 Dec 2019
Cappart, Q., Thomas, C., Schaus, P., Rousseau, L.-M.: A constraint programming approach for solving patient transportation problems. In: Hooker, J. (ed.) CP 2018. LNCS, vol. 11008, pp. 490–506. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-98334-9_32
Cordeau, J.F.: A branch-and-cut algorithm for the dial-a-ride problem. Oper. Res. 54(3), 573–586 (2006)
Cordeau, J., Laporte, G.: The dial-a-ride problem (DARP): variants, modeling issues and algorithms. 4OR 1(2), 89–101 (2003). https://doi.org/10.1007/s10288-002-0009-8
Cordeau, J.F., Laporte, G.: A Tabu search heuristic for the static multi-vehicle dial-a-ride problem. Transp. Res. Part B: Methodol. 37(6), 579–594 (2003)
Cordeau, J.F., Laporte, G.: The dial-a-ride problem: models and algorithms. Ann. Oper. Res. 153(1), 29–46 (2007)
Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. W. H. Freeman (1979)
Gervet, C.: Interval propagation to reason about sets: definition and implementation of a practical language. Constraints 1(3), 191–244 (1997)
Hartert, R., Schaus, P., Vissicchio, S., Bonaventure, O.: Solving segment routing problems with hybrid constraint programming techniques. In: Pesant, G. (ed.) CP 2015. LNCS, vol. 9255, pp. 592–608. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-23219-5_41
Ho, S.C., Szeto, W., Kuo, Y.H., Leung, J.M., Petering, M., Tou, T.W.: A survey of dial-a-ride problems: Literature review and recent developments. Transp. Res. Part B: Methodol. 111, 395–421 (2018)
IBM Knowledge Center: Interval variable sequencing in CP Optimizer. https://www.ibm.com/support/knowledgecenter/SSSA5P_12.9.0/ilog.odms.ide.help/refcppopl/html/interval_sequence.html (2019). Accessed 22 Nov 2019
IBM Knowledge Center: Search API for scheduling in CP Optimizer. https://www.ibm.com/support/knowledgecenter/SSSA5P_12.9.0/ilog.odms.cpo.help/refcppcpoptimizer/html/sched_search_api.html?view=kc#85 (2019). Accessed 22 Nov 2019
Jain, S., Van Hentenryck, P.: Large neighborhood search for dial-a-ride problems. In: Lee, J. (ed.) CP 2011. LNCS, vol. 6876, pp. 400–413. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-23786-7_31
Laborie, P.: Objective landscapes for constraint programming. In: van Hoeve, W.-J. (ed.) CPAIOR 2018. LNCS, vol. 10848, pp. 387–402. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-93031-2_28
Laborie, P., Godard, D.: Self-adapting large neighborhood search: application to single-mode scheduling problems. In: Proceedings MISTA-07, Paris, vol. 8 (2007)
Laborie, P., Rogerie, J.: Reasoning with conditional time-intervals. In: FLAIRS conference. pp. 555–560 (2008)
Laborie, P., Rogerie, J., Shaw, P., VilÃm, P.: Reasoning with conditional time-intervals. part ii: an algebraical model for resources. In: Twenty-Second International FLAIRS Conference (2009)
Laborie, P., Rogerie, J., Shaw, P., VilÃm, P.: IBM ILOG CP optimizer for scheduling. Constraints 23(2), 210–250 (2018)
Liu, C., Aleman, D.M., Beck, J.C.: Modelling and solving the senior transportation problem. In: van Hoeve, W.-J. (ed.) CPAIOR 2018. LNCS, vol. 10848, pp. 412–428. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-93031-2_30
OscaR Team: OscaR: Scala in OR (2012). https://bitbucket.org/oscarlib/oscar
Perron, L., Furnon, V.: Or-tools (2019). https://developers.google.com/optimization/
Perron, L., Furnon, V.: OR-Tools Sequence Var. https://developers.google.com/optimization/reference/constraint_solver/constraint_solver/SequenceVar (2019). Accessed 22 Nov 2019
de Saint-Marcq, V.l.C., Schaus, P., Solnon, C., Lecoutre, C.: Sparse-sets for domain implementation. In: CP Workshop on Techniques for Implementing Constraint Programming Systems (TRICS), pp. 1–10 (2013)
Shaw, P.: Using constraint programming and local search methods to solve vehicle routing problems. In: Maher, M., Puget, J.-F. (eds.) CP 1998. LNCS, vol. 1520, pp. 417–431. Springer, Heidelberg (1998). https://doi.org/10.1007/3-540-49481-2_30
Thomas, C., Cappart, Q., Schaus, P., Rousseau, L.M.: CSPLib problem 082: patient transportation problem (2018). http://www.csplib.org/Problems/prob082
Cauwelaert, S.V., Lombardi, M., Schaus, P.: How efficient is a global constraint in practice? Constraints 23(1), 87–122 (2017). https://doi.org/10.1007/s10601-017-9277-y
VilÃm, P., Laborie, P., Shaw, P.: Failure-directed search for constraint-based scheduling. In: Michel, L. (ed.) CPAIOR 2015. LNCS, vol. 9075, pp. 437–453. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-18008-3_30
Acknowledgments
This research is financed by the Walloon Region (Belgium) as part of PRESupply Project. We thank Siddhartha Jain and Pascal Van Hentenryck for sharing with us their implementation of the LNS-FFPA algorithm.
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Thomas, C., Kameugne, R., Schaus, P. (2020). Insertion Sequence Variables for Hybrid Routing and Scheduling Problems. In: Hebrard, E., Musliu, N. (eds) Integration of Constraint Programming, Artificial Intelligence, and Operations Research. CPAIOR 2020. Lecture Notes in Computer Science(), vol 12296. Springer, Cham. https://doi.org/10.1007/978-3-030-58942-4_30
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