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Metaheuristics for the distance constrained generalized covering traveling salesman problem

Author

Listed:
  • Prashant Singh

    (Indian Institute of Technology (BHU))

  • Ankush R. Kamthane

    (Indian Institute of Technology (BHU))

  • Ajinkya N. Tanksale

    (Indian Institute of Technology (BHU))

Abstract

In this work, we present an extension of the generalized covering salesman problem as distance constrained generalized m-covering salesman problem. Given a set of vertices including a depot, facilities, customer locations and demand associated with each customer location, the objective is to determine an optimal tour of each salesman such that the total covered demand is maximized and the tour length is minimized. A bi-objective mixed-integer programming model is formulated for the problem. The proposed model is solved using GUROBI 8.0 solver’s in-built hierarchical optimization approach. However, the computational complexity of the problem demands a specialized solution approach. To solve the problem efficiently, we propose two metaheuristics ant colony optimization (ACO) algorithm and greedy randomized adaptive search procedure (GRASP). Extensive computational experiments were performed using the benchmark instances from the literature. The results of computational experiments show the efficiency and effectiveness of the proposed metaheuristics algorithms. Although, the GRASP metaheuristics outperform the ACO algorithm in case of medium and large size instances.

Suggested Citation

  • Prashant Singh & Ankush R. Kamthane & Ajinkya N. Tanksale, 2021. "Metaheuristics for the distance constrained generalized covering traveling salesman problem," OPSEARCH, Springer;Operational Research Society of India, vol. 58(3), pages 575-609, September.
    • Handle: RePEc:spr:opsear:v:58:y:2021:i:3:d:10.1007_s12597-020-00503-3
    DOI: 10.1007/s12597-020-00503-3
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    References listed on IDEAS

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    1. Eduardo Álvarez-Miranda & Markus Sinnl, 2020. "A branch-and-cut algorithm for the maximum covering cycle problem," Annals of Operations Research, Springer, vol. 284(2), pages 487-499, January.
    2. Current, John R. & Schilling, David A., 1994. "The median tour and maximal covering tour problems: Formulations and heuristics," European Journal of Operational Research, Elsevier, vol. 73(1), pages 114-126, February.
    3. 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.
    4. Richard Church & Charles R. Velle, 1974. "The Maximal Covering Location Problem," Papers in Regional Science, Wiley Blackwell, vol. 32(1), pages 101-118, January.
    5. John R. Current & David A. Schilling, 1989. "The Covering Salesman Problem," Transportation Science, INFORMS, vol. 23(3), pages 208-213, August.
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    2. Shruti Maheshwari & Pramod Kumar Jain & Ketan Kotecha, 2023. "Route Optimization of Mobile Medical Unit with Reinforcement Learning," Sustainability, MDPI, vol. 15(5), pages 1-18, February.

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