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Uncertain multiobjective traveling salesman problem

Author

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  • Wang, Zutong
  • Guo, Jiansheng
  • Zheng, Mingfa
  • Wang, Ying

Abstract

Traveling salesman problem is a fundamental combinatorial optimization model studied in the operations research community for nearly half a century, yet there is surprisingly little literature that addresses uncertainty and multiple objectives in it. A novel TSP variation, called uncertain multiobjective TSP (UMTSP) with uncertain variables on the arc, is proposed in this paper on the basis of uncertainty theory, and a new solution approach named uncertain approach is applied to obtain Pareto efficient route in UMTSP. Considering the uncertain and combinatorial nature of UMTSP, a new ABC algorithm inserted with reverse operator, crossover operator and mutation operator is designed to this problem, which outperforms other algorithms through the performance comparison on three benchmark TSPs. Finally, a new benchmark UMTSP case study is presented to illustrate the construction and solution of UMTSP, which shows that the optimal route in deterministic TSP can be a poor route in UMTSP.

Suggested Citation

  • Wang, Zutong & Guo, Jiansheng & Zheng, Mingfa & Wang, Ying, 2015. "Uncertain multiobjective traveling salesman problem," European Journal of Operational Research, Elsevier, vol. 241(2), pages 478-489.
  • Handle: RePEc:eee:ejores:v:241:y:2015:i:2:p:478-489
    DOI: 10.1016/j.ejor.2014.09.012
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    References listed on IDEAS

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    1. Çela, Eranda & Deineko, Vladimir & Woeginger, Gerhard J., 2012. "The x-and-y-axes travelling salesman problem," European Journal of Operational Research, Elsevier, vol. 223(2), pages 333-345.
    2. Patrick Jaillet, 1988. "A Priori Solution of a Traveling Salesman Problem in Which a Random Subset of the Customers Are Visited," Operations Research, INFORMS, vol. 36(6), pages 929-936, December.
    3. Dimitris J. Bertsimas & David Simchi-Levi, 1996. "A New Generation of Vehicle Routing Research: Robust Algorithms, Addressing Uncertainty," Operations Research, INFORMS, vol. 44(2), pages 286-304, April.
    4. Rego, César & Gamboa, Dorabela & Glover, Fred & Osterman, Colin, 2011. "Traveling salesman problem heuristics: Leading methods, implementations and latest advances," European Journal of Operational Research, Elsevier, vol. 211(3), pages 427-441, June.
    5. G. Dantzig & R. Fulkerson & S. Johnson, 1954. "Solution of a Large-Scale Traveling-Salesman Problem," Operations Research, INFORMS, vol. 2(4), pages 393-410, November.
    6. Erdogan, Günes & Cordeau, Jean-François & Laporte, Gilbert, 2010. "The Attractive Traveling Salesman Problem," European Journal of Operational Research, Elsevier, vol. 203(1), pages 59-69, May.
    7. Szeto, W.Y. & Wu, Yongzhong & Ho, Sin C., 2011. "An artificial bee colony algorithm for the capacitated vehicle routing problem," European Journal of Operational Research, Elsevier, vol. 215(1), pages 126-135, November.
    8. Chang, Tsung-Sheng & Wan, Yat-wah & OOI, Wei Tsang, 2009. "A stochastic dynamic traveling salesman problem with hard time windows," European Journal of Operational Research, Elsevier, vol. 198(3), pages 748-759, November.
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    Cited by:

    1. Hughes, Michael S. & Lunday, Brian J. & Weir, Jeffrey D. & Hopkinson, Kenneth M., 2021. "The multiple shortest path problem with path deconfliction," European Journal of Operational Research, Elsevier, vol. 292(3), pages 818-829.
    2. Mingfa Zheng & Yuan Yi & Zutong Wang & Tianjun Liao, 2017. "Relations among efficient solutions in uncertain multiobjective programming," Fuzzy Optimization and Decision Making, Springer, vol. 16(3), pages 329-357, September.
    3. Mercier, Quentin & Poirion, Fabrice & Désidéri, Jean-Antoine, 2018. "A stochastic multiple gradient descent algorithm," European Journal of Operational Research, Elsevier, vol. 271(3), pages 808-817.

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