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Revisiting dynamic programming for precedence-constrained traveling salesman problem and its time-dependent generalization

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  • Salii, Yaroslav

Abstract

The precedence constrained traveling salesman problem (TSP-PC), or the sequential ordering problem (SOP), consists of finding an optimal TSP tour that will also satisfy the namesake precedence constraints, typically specified as a partial order or a directed acyclic graph. Its dynamic programming (DP) solution was proposed as early as 1979, however, by late 1990s, it mostly fell out of use in plain TSP-PC. Revisiting this method, we are able to close one of the long-standing TSPLIB SOP problem instances, ry48p.3.sop, and provide improved bounds on its time complexity. Harnessing the “omnivorous” nature of DP, we prove the validity of DP optimality principle for TSP-PC with both (i) abstract cost aggregation function, which may be the arithmetic + operation as in “ordinary” TSP or max as in Bottleneck TSP, or any other left-associative nondecreasing in the first argument operation and (ii) travel cost functions depending on the set of pending tasks (“sequence dependence”). Using the latter generalization, we close several TD-SOP (time-dependent TSP-PC) instances based on TSPLIB SOP as proposed by Kinable et al., including rbg253a.sop. Through the restricted DP heuristic, which was originally formulated for time-dependent TSP by Malandraki and Dial, we improve the state-of-the-art upper bounds for all yet unsolved TSPLIB-based TD-SOP instances, including those with more than 100 cities. We also improve worst-case complexity estimates for DP in TSP-PC.

Suggested Citation

  • Salii, Yaroslav, 2019. "Revisiting dynamic programming for precedence-constrained traveling salesman problem and its time-dependent generalization," European Journal of Operational Research, Elsevier, vol. 272(1), pages 32-42.
    • Handle: RePEc:eee:ejores:v:272:y:2019:i:1:p:32-42
    DOI: 10.1016/j.ejor.2018.06.003
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    1. Allahverdi, Ali, 2015. "The third comprehensive survey on scheduling problems with setup times/costs," European Journal of Operational Research, Elsevier, vol. 246(2), pages 345-378.
    2. Ulrike Ritzinger & Jakob Puchinger & Richard Hartl, 2016. "Dynamic programming based metaheuristics for the dial-a-ride problem," Annals of Operations Research, Springer, vol. 236(2), pages 341-358, January.
    3. Thomas L. Morin & Roy E. Marsten, 1976. "Branch-and-Bound Strategies for Dynamic Programming," Operations Research, INFORMS, vol. 24(4), pages 611-627, August.
    4. Gerhard Reinelt, 1991. "TSPLIB—A Traveling Salesman Problem Library," INFORMS Journal on Computing, INFORMS, vol. 3(4), pages 376-384, November.
    5. Koulamas, Christos & Kyparisis, George J., 2008. "Single-machine scheduling problems with past-sequence-dependent setup times," European Journal of Operational Research, Elsevier, vol. 187(3), pages 1045-1049, June.
    6. Andre A. Cire & Willem-Jan van Hoeve, 2013. "Multivalued Decision Diagrams for Sequencing Problems," Operations Research, INFORMS, vol. 61(6), pages 1411-1428, December.
    7. Edward P. C. Kao & Maurice Queyranne, 1982. "On Dynamic Programming Methods for Assembly Line Balancing," Operations Research, INFORMS, vol. 30(2), pages 375-390, April.
    8. Letchford, Adam N. & Salazar-González, Juan-José, 2016. "Stronger multi-commodity flow formulations of the (capacitated) sequential ordering problem," European Journal of Operational Research, Elsevier, vol. 251(1), pages 74-84.
    9. Malandraki, Chryssi & Dial, Robert B., 1996. "A restricted dynamic programming heuristic algorithm for the time dependent traveling salesman problem," European Journal of Operational Research, Elsevier, vol. 90(1), pages 45-55, April.
    10. Anthony A. Mastor, 1970. "An Experimental Investigation and Comparative Evaluation of Production Line Balancing Techniques," Management Science, INFORMS, vol. 16(11), pages 728-746, July.
    11. Kinable, Joris & Cire, Andre A. & van Hoeve, Willem-Jan, 2017. "Hybrid optimization methods for time-dependent sequencing problems," European Journal of Operational Research, Elsevier, vol. 259(3), pages 887-897.
    12. Ghassan Shobaki & Jafar Jamal, 2015. "An exact algorithm for the sequential ordering problem and its application to switching energy minimization in compilers," Computational Optimization and Applications, Springer, vol. 61(2), pages 343-372, June.
    13. Escudero, L. F., 1988. "An inexact algorithm for the sequential ordering problem," European Journal of Operational Research, Elsevier, vol. 37(2), pages 236-249, November.
    14. Ulrike Ritzinger & Jakob Puchinger & Richard F. Hartl, 2016. "Dynamic programming based metaheuristics for the dial-a-ride problem," Annals of Operations Research, Springer, vol. 236(2), pages 341-358, January.
    15. Nathalie Caspard & Bruno Leclerc & Bernard Monjardet, 2012. "Finite Ordered Sets Concepts, Results and Uses," Post-Print halshs-00800193, HAL.
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