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A unified matheuristic for solving multi-constrained traveling salesman problems with profits

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EURO Journal on Computational Optimization

Abstract

In this paper, we address a rich Traveling Salesman Problem with Profits encountered in several real-life cases. We propose a unified solution approach based on variable neighborhood search. Our approach combines several removal and insertion routing neighborhoods and efficient constraint checking procedures. The loading problem related to the use of a multi-compartment vehicle is addressed carefully. Two loading neighborhoods based on the solution of mathematical programs are proposed to intensify the search. They interact with the routing neighborhoods as it is commonly done in matheuristics. The performance of the proposed matheuristic is assessed on various instances proposed for the Orienteering Problem and the Orienteering Problem with Time Window including up to 288 customers. The computational results show that the proposed matheuristic is very competitive compared with the state-of-the-art methods. To better evaluate its performance, we generate a new testbed including instances with various attributes. Extensive computational experiments on the new testbed confirm the efficiency of the matheuristic. A sensitivity analysis highlights which components of the matheuristic contribute most to the solution quality.

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Acknowledgments

This work was partially supported by the International Campus on Safety and Intermodality in Transportation, the Nord-Pas-de-Calais Region, the European Community, the Regional Delegation for Research and Technology, the French Ministry of Higher Education and Research and the National Center for Scientific Research. This support is gratefully acknowledged. The authors thank Fabien Tricoire and Matteo Salani for their answers to our requests regarding the computational experiments. They also thank three anonymous referees whose comments have helped them to improve their paper.

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Authors and Affiliations

  1. College of Business, Al Faisal University, Riyadh, Kingdom of Saudi Arabia

    Rahma Lahyani

  2. College of Computer Engineering and Science, Prince Sattam Bin Abdulaziz University, Al Kharj, Kingdom of Saudi Arabia

    Mahdi Khemakhem

  3. UMR 9189-CRIStAL-Centre de Recherche en Informatique Signal et Automatique de Lille, Univ. Lille, CNRS, Centrale Lille, Inria, 59000, Lille, France

    Frédéric Semet

  4. LOGIQ Laboratory, ISGI, Sfax, Tunisia

    Rahma Lahyani

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  1. Rahma Lahyani
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Correspondence to Rahma Lahyani.

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Lahyani, R., Khemakhem, M. & Semet, F. A unified matheuristic for solving multi-constrained traveling salesman problems with profits. EURO J Comput Optim 5, 393–422 (2017). https://doi.org/10.1007/s13675-016-0071-1

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  • DOI: https://doi.org/10.1007/s13675-016-0071-1

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