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The Generalized Arc Routing Problem

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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.

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Acknowledgements

This research has been partially supported by the Spanish Ministry of Economy and Competitiveness and EDRF funds through Grant MTM2015-63779-R (MINECO/FEDER). This support is gratefully acknowledged.

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Authors and Affiliations

  1. Department d’Estadística i Investigació Operativa, Universitat Politècnica de Catalunya-BcnTech, Barcelona, Spain

    Julián Aráoz & Elena Fernández

  2. Área de Matemáticas y Algoritmia, IKIAM Universidad Regional Amazónica, Tena, Ecuador

    Carles Franquesa

Authors
  1. Julián Aráoz
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  2. Elena Fernández
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  3. Carles Franquesa
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Correspondence to Carles Franquesa.

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Aráoz, J., Fernández, E. & Franquesa, C. The Generalized Arc Routing Problem. TOP 25, 497–525 (2017). https://doi.org/10.1007/s11750-017-0437-4

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