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An Adaptive Heuristic Approach to Compute Upper and Lower Bounds for the Close-Enough Traveling Salesman Problem

Author

Listed:
  • Francesco Carrabs

    (Department of Mathematics, University of Salerno, 84084 Fisciano, Italy;)

  • Carmine Cerrone

    (Department of Economics and Business Studies, University of Genova, 16126 Genova, Italy;)

  • Raffaele Cerulli

    (Department of Mathematics, University of Salerno, 84084 Fisciano, Italy;)

  • Bruce Golden

    (Robert H. Smith School of Business, University of Maryland, College Park, Maryland 20742)

Abstract

This paper addresses the close-enough traveling salesman problem, a variant of the Euclidean traveling salesman problem, in which the traveler visits a node if it passes through the neighborhood set of that node. We apply an effective strategy to discretize the neighborhoods of the nodes and the carousel greedy algorithm to appropriately select the neighborhoods that, step by step, are added to the partial solution until a feasible solution is generated. Our heuristic, based on these ingredients, is able to compute tight upper and lower bounds on the optimal solution relatively quickly. The computational results, carried out on benchmark instances, show that our heuristic often finds the optimal solution, on the instances where it is known, and in general, the upper bounds are more accurate than those from other algorithms available in the literature. Summary of Contribution: In this paper, we focus on the close-enough traveling salesman problem. This is a problem that has attracted research attention over the last 10 years; it has numerous real-world applications. For instance, consider the task of meter reading for utility companies. Homes and businesses have meters that measure the usage of gas, water, and electricity. Each meter transmits signals that can be read by a meter reader vehicle via radio-frequency identification (RFID) technology if the distance between the meter and the reader is less than r units. Each meter plays the role of a target point and the neighborhood is a disc of radius r centered at each target point. Now, suppose the meter reader vehicle is a drone and the goal is to visit each disc while minimizing the amount of energy expended by the drone. To solve this problem, we develop a metaheuristic approach, called ( lb/ub ) Alg , which computes both upper and lower bounds on the optimal solution value. This metaheuristic uses an innovative discretization scheme and the Carousel Greedy algorithm to obtain high-quality solutions. On benchmark instances where the optimal solution is known, ( lb/ub ) Alg obtains this solution 83% of the time. Over the remaining 17% of these instances, the deviation from the optimality is 0.05%, on average. On the instances with the highest overlap ratio, ( lb/ub ) Alg does especially well.

Suggested Citation

  • Francesco Carrabs & Carmine Cerrone & Raffaele Cerulli & Bruce Golden, 2020. "An Adaptive Heuristic Approach to Compute Upper and Lower Bounds for the Close-Enough Traveling Salesman Problem," INFORMS Journal on Computing, INFORMS, vol. 32(4), pages 1030-1048, October.
  • Handle: RePEc:inm:orijoc:v:32:y:4:i:2020:p:1030-1048
    DOI: 10.1287/ijoc.2020.0962
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    References listed on IDEAS

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    4. Walton Pereira Coutinho & Roberto Quirino do Nascimento & Artur Alves Pessoa & Anand Subramanian, 2016. "A Branch-and-Bound Algorithm for the Close-Enough Traveling Salesman Problem," INFORMS Journal on Computing, INFORMS, vol. 28(4), pages 752-765, November.
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    Cited by:

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    3. Wenda Zhang & Jason J. Sauppe & Sheldon H. Jacobson, 2023. "Results for the close-enough traveling salesman problem with a branch-and-bound algorithm," Computational Optimization and Applications, Springer, vol. 85(2), pages 369-407, June.
    4. Di Placido, Andrea & Archetti, Claudia & Cerrone, Carmine & Golden, Bruce, 2023. "The generalized close enough traveling salesman problem," European Journal of Operational Research, Elsevier, vol. 310(3), pages 974-991.
    5. Carrabs, Francesco, 2021. "A biased random-key genetic algorithm for the set orienteering problem," European Journal of Operational Research, Elsevier, vol. 292(3), pages 830-854.
    6. Yuan, Yuan & Cattaruzza, Diego & Ogier, Maxime & Semet, Frédéric & Vigo, Daniele, 2021. "A column generation based heuristic for the generalized vehicle routing problem with time windows," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 152(C).

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