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The m-Steiner Traveling Salesman Problem with online edge blockages

Author

Listed:
  • Henan Liu

    (Xi’an Jiaotong University)

  • Huili Zhang

    (Xi’an Jiaotong University
    State Key Lab for Manufacturing Systems Engineering)

  • Yi Xu

    (Xi’an University of Technology)

Abstract

We consider the online multiple Steiner Traveling Salesman Problem based on the background of the delivery of packages in an urban traffic network. In this problem, given an edge-weighted undirected graph $$G = (V, E)$$ G = ( V , E ) , a subset $$D\subset V$$ D ⊂ V of customer vertices, and m salesmen. For each edge in E, the weight w(e) is associated with the traversal time or the cost of the edge. The aim is to find m closed tours that visit each vertex of D at least once. We formulate the traffic congestion with k non-recoverable blocked edges revealed to the salesmen in real-time, meaning that the salesmen know about a blocked edge whenever it occurs. For the version to minimize the maximum cost of m salesmen (minmax mSTSP), we prove a lower bound and propose the ForestTraversal algorithm. The corresponding competitive ratio is proved to be linear with k. For the version to minimize the total cost of m salesmen (minsum mSTSP), we also propose a lower bound and the Retrace algorithm, where the competitive ratio of the algorithm is proved to be linear with k.

Suggested Citation

  • Henan Liu & Huili Zhang & Yi Xu, 2021. "The m-Steiner Traveling Salesman Problem with online edge blockages," Journal of Combinatorial Optimization, Springer, vol. 41(4), pages 844-860, May.
    • Handle: RePEc:spr:jcomop:v:41:y:2021:i:4:d:10.1007_s10878-021-00720-6
    DOI: 10.1007/s10878-021-00720-6
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    References listed on IDEAS

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    1. Xingang Wen & Yinfeng Xu & Huili Zhang, 2015. "Online traveling salesman problem with deadlines and service flexibility," Journal of Combinatorial Optimization, Springer, vol. 30(3), pages 545-562, October.
    2. Bektas, Tolga, 2006. "The multiple traveling salesman problem: an overview of formulations and solution procedures," Omega, Elsevier, vol. 34(3), pages 209-219, June.
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    4. Xu, Zhou & Rodrigues, Brian, 2017. "An extension of the Christofides heuristic for the generalized multiple depot multiple traveling salesmen problem," European Journal of Operational Research, Elsevier, vol. 257(3), pages 735-745.
    5. Yinfeng Xu & Maolin Hu & Bing Su & Binhai Zhu & Zhijun Zhu, 2009. "The canadian traveller problem and its competitive analysis," Journal of Combinatorial Optimization, Springer, vol. 18(2), pages 195-205, August.
    6. Zhang, Huili & Tong, Weitian & Xu, Yinfeng & Lin, Guohui, 2015. "The Steiner Traveling Salesman Problem with online edge blockages," European Journal of Operational Research, Elsevier, vol. 243(1), pages 30-40.
    7. Zhang, Huili & Tong, Weitian & Lin, Guohui & Xu, Yinfeng, 2019. "Online minimum latency problem with edge uncertainty," European Journal of Operational Research, Elsevier, vol. 273(2), pages 418-429.
    8. Bezalel Gavish & Kizhanathan Srikanth, 1986. "An Optimal Solution Method for Large-Scale Multiple Traveling Salesmen Problems," Operations Research, INFORMS, vol. 34(5), pages 698-717, October.
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    Cited by:

    1. Davood Shiri & Hakan Tozan, 2022. "Online routing and searching on graphs with blocked edges," Journal of Combinatorial Optimization, Springer, vol. 44(2), pages 1039-1059, September.

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