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New mixed integer linear programming models and an iterated local search for the clustered traveling salesman problem with relaxed priority rule

Author

Listed:
  • Thanh Tan Doan

    (Université de Nantes
    Phenikaa University)

  • Nathalie Bostel

    (Université de Nantes)

  • Minh Hoàng Hà

    (Phenikaa University)

  • Vu Hoang Vuong Nguyen

    (VNU University of Engineering and Technology)

Abstract

The Traveling Salesman Problem (TSP) is a well known problem in operations research with various studies and applications. In this paper, we address a variant of the TSP in which the customers are divided into several priority groups and the order of servicing groups can be flexibly changed with a rule called the d-relaxed priority rule. The problem is called the Clustered Traveling Salesman Problem with Relaxed Priority Rule (CTSP-d). We propose two new Mixed Integer Linear Programming (MILP) models for the CTSP-d and a metaheuristic based on Iterated Local Search (ILS) with operators designed for or adapted to the problem. The experimental results obtained on the benchmark instances show that two new models performs better than previous ones, and ILS also proves its performance with 13 new best known solutions found and significant stability compared to existing metaheuristics.

Suggested Citation

  • Thanh Tan Doan & Nathalie Bostel & Minh Hoàng Hà & Vu Hoang Vuong Nguyen, 2023. "New mixed integer linear programming models and an iterated local search for the clustered traveling salesman problem with relaxed priority rule," Journal of Combinatorial Optimization, Springer, vol. 46(1), pages 1-27, August.
    • Handle: RePEc:spr:jcomop:v:46:y:2023:i:1:d:10.1007_s10878-023-01066-x
    DOI: 10.1007/s10878-023-01066-x
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    References listed on IDEAS

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    1. Gerhard Reinelt, 1991. "TSPLIB—A Traveling Salesman Problem Library," INFORMS Journal on Computing, INFORMS, vol. 3(4), pages 376-384, November.
    2. G Laporte & U Palekar, 2002. "Some applications of the clustered travelling salesman problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 53(9), pages 972-976, September.
    3. Stefan Ropke & David Pisinger, 2006. "An Adaptive Large Neighborhood Search Heuristic for the Pickup and Delivery Problem with Time Windows," Transportation Science, INFORMS, vol. 40(4), pages 455-472, November.
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