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The Generalized Arc Routing Problem

Author

Listed:
  • Julián Aráoz

    (Universitat Politècnica de Catalunya-BcnTech)

  • Elena Fernández

    (Universitat Politècnica de Catalunya-BcnTech)

  • Carles Franquesa

    (IKIAM Universidad Regional Amazónica)

Abstract

This paper focuses on the generalized arc routing problem. This problem is stated on an undirected graph in which some clusters are defined as pairwise-disjoint connected subgraphs, and a route is sought that traverses at least one edge of each cluster. Broadly speaking, the generalized arc routing problem is the arc routing counterpart of the generalized traveling salesman problem, where the set of vertices of a given graph is partitioned into clusters and a route is sought that visits at least one vertex of each cluster. A mathematical programming formulation that exploits the structure of the problem and uses only binary variables is proposed. Facets and families of valid inequalities are presented for the polyhedron associated with the formulation and the corresponding separation problem studied. The numerical results of a series of computational experiments with an exact branch and cut algorithm are presented and analyzed.

Suggested Citation

  • Julián Aráoz & Elena Fernández & Carles Franquesa, 2017. "The Generalized Arc Routing Problem," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(3), pages 497-525, October.
    • Handle: RePEc:spr:topjnl:v:25:y:2017:i:3:d:10.1007_s11750-017-0437-4
    DOI: 10.1007/s11750-017-0437-4
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Bianchessi, Nicola & Corberán, Ángel & Plana, Isaac & Reula, Miguel & Sanchis, José M., 2022. "The min-max close-enough arc routing problem," European Journal of Operational Research, Elsevier, vol. 300(3), pages 837-851.
    2. Xiaoguang Bao & Xinhao Ni, 2024. "Approximation algorithms for two clustered arc routing problems," Journal of Combinatorial Optimization, Springer, vol. 47(5), pages 1-12, July.
    3. Ángel Corberán & Isaac Plana & Miguel Reula & José M. Sanchis, 2019. "A matheuristic for the Distance-Constrained Close-Enough Arc Routing Problem," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(2), pages 312-326, July.
    4. Rodríguez-Pereira, Jessica & Fernández, Elena & Laporte, Gilbert & Benavent, Enrique & Martínez-Sykora, Antonio, 2019. "The Steiner Traveling Salesman Problem and its extensions," European Journal of Operational Research, Elsevier, vol. 278(2), pages 615-628.
    5. Corberán, Ángel & Plana, Isaac & Reula, Miguel & Sanchis, José M., 2021. "On the Distance-Constrained Close Enough Arc Routing Problem," European Journal of Operational Research, Elsevier, vol. 291(1), pages 32-51.

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