Solving capacitated arc routing problems using a transformation to the CVRP

  • Authors:

  • Humberto Longo;Marcus Poggi de Aragão;Eduardo Uchoa

  • Affiliations:

  • Instituto de Informática, Universidade Federal de Goiás, Campus Samambaia, Goiania, GO 74001-970, Brazil;Departamento de Informática, Pontifícia Universidade Católica do Rio de Janeiro, R. Marquês de São Vicente 225, Rio de Janeiro, RJ 22453-900, Brazil;Departamento de Engenharia de Produção, Universidade Federal Fluminense, Rua Passo da Pátria 156, Niterói, RJ 24210-240, Brazil

  • Venue:
  • Computers and Operations Research
  • Year:
  • 2006

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Abstract

A well-known transformation by Pearn, Assad and Golden reduces a capacitated arc routing problem (CARP) into an equivalent capacitated vehicle routing problem (CVRP). However, that transformation is regarded as unpractical, since an original instance with r required edges is turned into a CVRP over a complete graph with 3r+1 vertices. We propose a similar transformation that reduces this graph to 2r+1 vertices, with the additional restriction that a previously known set of r pairwise disconnected edges must belong to every solution. Using a recent branch-and-cut-and-price algorithm for the CVRP, we observed that it yields an effective way of attacking the CARP, being significantly better than the exact methods created specifically for that problem. Computational experiments obtained improved lower bounds for almost all open instances from the literature. Several such instances could be solved to optimality. Scope and purpose The scope of this paper is transforming arc routing problems into node routing problems. The paper shows that this approach can be effective and, in particular, that the original instances may generate node routing instances that behave as if the size is not increased. This result is obtained by slightly modifying the well-known transformation by Pearn, Assad and Golden from capacitated arc routing problem (CARP) to the capacitated vehicle routing problem (CVRP), that is regarded as unpractical. The paper provides a computational experience using a recent branch-and-cut-and-price algorithm for the CVRP. The results are significantly better than the exact methods created specifically for that problem, improving lower bounds for almost all open instances from the literature. Several such instances could be solved to optimality.