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A matheuristic approach for the family traveling salesman problem

Author

Listed:
  • Abtin Nourmohammadzadeh

    (University of Hamburg)

  • Malek Sarhani

    (Al Akhawayn University in Ifrane)

  • Stefan Voß

    (University of Hamburg)

Abstract

In the family traveling salesman problem (FTSP), there is a set of cities which are divided into a number of clusters called families. The salesman has to find a shortest possible tour visiting a specific number of cities from each of the families without any restriction of visiting one family before starting the visit of another one. In this work, the general concept of the Partial OPtimization Metaheuristic Under Special Intensification Conditions is linked with the exact optimization by a classical solver using a mathematical programming formulation for the FTSP to develop a matheuristic. Moreover, a genetic and a simulated annealing algorithm are used as metaheuristics embedded in the approach. The method is examined on a set of benchmark instances and its performance is favorably compared with a state-of-the-art approach from literature. Moreover, a careful analysis of the specific components of the approach is undertaken to provide insights into the impact of their interplay.

Suggested Citation

  • Abtin Nourmohammadzadeh & Malek Sarhani & Stefan Voß, 2023. "A matheuristic approach for the family traveling salesman problem," Journal of Heuristics, Springer, vol. 29(4), pages 435-460, December.
    • Handle: RePEc:spr:joheur:v:29:y:2023:i:4:d:10.1007_s10732-023-09516-9
    DOI: 10.1007/s10732-023-09516-9
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    References listed on IDEAS

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    1. Bernardino, Raquel & Paias, Ana, 2018. "Solving the family traveling salesman problem," European Journal of Operational Research, Elsevier, vol. 267(2), pages 453-466.
    2. Taillard, Éric D. & Helsgaun, Keld, 2019. "POPMUSIC for the travelling salesman problem," European Journal of Operational Research, Elsevier, vol. 272(2), pages 420-429.
    3. Poojari, C.A. & Beasley, J.E., 2009. "Improving benders decomposition using a genetic algorithm," European Journal of Operational Research, Elsevier, vol. 199(1), pages 89-97, November.
    4. Taillard, Éric D., 2022. "A linearithmic heuristic for the travelling salesman problem," European Journal of Operational Research, Elsevier, vol. 297(2), pages 442-450.
    5. Doi, Tsubasa & Nishi, Tatsushi & Voß, Stefan, 2018. "Two-level decomposition-based matheuristic for airline crew rostering problems with fair working time," European Journal of Operational Research, Elsevier, vol. 267(2), pages 428-438.
    6. A Ostertag & K F Doerner & R F Hartl & E D Taillard & P Waelti, 2009. "POPMUSIC for a real-world large-scale vehicle routing problem with time windows," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(7), pages 934-943, July.
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