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Exact hybrid algorithms for solving a bi-objective vehicle routing problem

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  • Peter Reiter
  • Walter Gutjahr

Abstract

The paper investigates a capacitated vehicle routing problem with two objectives: (1) minimization of total travel cost and (2) minimization of the length of the longest route. We present algorithmic variants for the exact determination of the Pareto-optimal solutions of this bi-objective problem. Our approach is based on the adaptive ε-constraint method. For solving the resulting single-objective subproblems, we apply a branch-and-cut technique, using (among others) a novel implementation of Held-Karp-type bounds. Incumbent solutions are generated by means of a single-objective genetic algorithm and, alternatively, by the multi-objective NSGA-II algorithm. Experimental results for a benchmark of 54 test instances from the TSPLIB are reported. Copyright Springer-Verlag 2012

Suggested Citation

  • Peter Reiter & Walter Gutjahr, 2012. "Exact hybrid algorithms for solving a bi-objective vehicle routing problem," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 20(1), pages 19-43, March.
    • Handle: RePEc:spr:cejnor:v:20:y:2012:i:1:p:19-43
    DOI: 10.1007/s10100-010-0158-3
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    References listed on IDEAS

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    Cited by:

    1. Przybylski, Anthony & Gandibleux, Xavier, 2017. "Multi-objective branch and bound," European Journal of Operational Research, Elsevier, vol. 260(3), pages 856-872.
    2. Qingqing Qiao & Fengming Tao & Hailin Wu & Xuewei Yu & Mengjun Zhang, 2020. "Optimization of a Capacitated Vehicle Routing Problem for Sustainable Municipal Solid Waste Collection Management Using the PSO-TS Algorithm," IJERPH, MDPI, vol. 17(6), pages 1-22, March.
    3. Hongjie Liu & Tao Tang & Jidong Lv & Ming Chai, 2019. "A Dual-Objective Substation Energy Consumption Optimization Problem in Subway Systems," Energies, MDPI, vol. 12(10), pages 1-28, May.
    4. Halvorsen-Weare, Elin E. & Savelsbergh, Martin W.P., 2016. "The bi-objective mixed capacitated general routing problem with different route balance criteria," European Journal of Operational Research, Elsevier, vol. 251(2), pages 451-465.
    5. Ramos, Tânia Rodrigues Pereira & Gomes, Maria Isabel & Barbosa-Póvoa, Ana Paula, 2014. "Planning a sustainable reverse logistics system: Balancing costs with environmental and social concerns," Omega, Elsevier, vol. 48(C), pages 60-74.
    6. P. Matl & R. F. Hartl & T. Vidal, 2018. "Workload Equity in Vehicle Routing Problems: A Survey and Analysis," Transportation Science, INFORMS, vol. 52(2), pages 239-260, March.
    7. Karl F. Doerner & Vittorio Maniezzo, 2018. "Metaheuristic search techniques for multi-objective and stochastic problems: a history of the inventions of Walter J. Gutjahr in the past 22 years," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 26(2), pages 331-356, June.

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