A cutting plane algorithm for the capacitated arc routing problem

Belenguer, José Manuel; Benavent, Enrique

doi:10.1016/s0305-0548(02)00046-1

Cited by 130 publications

(110 citation statements)

References 12 publications

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“…The current best bounds are those obtained by a cutting plane algorithm by Belenguer and Benavent [6]. Those bounds are much better than previous ones and matched the best heuristic solutions on 47 out of 87 instances tested from the literature.…”

Section: Introductionmentioning

confidence: 61%

“…The columns of both tables list the name of the instance and its characteristics, the number of vertices |V |, the number of required edges r, the minimum number of vehicles K * to cover the demands, the best known upper bound U B, the previous best lower bound (all of them obtained in [6]), the lower bound given by our transformation Our LB, and the corresponding CPU time RootT ime in seconds. Lower bounds in bold indicate a matching with the best upper bound.…”

Section: Computational Resultsmentioning

confidence: 99%

“…Moreover, we believe that the lower bounds can be further improved with the addition of cuts that take into account the specific structure of the CARP, for example, the ones proposed in Belenguer and Benavent [6]. Table 4: Results of the BCP algorithm for the kshs, gdb, bccm and egl instances.…”

Section: Computational Resultsmentioning

confidence: 99%

“…The approach proposed in this work, reducing the CARP to a CVRP that is given as input to a branch-and-cut-and-price algorithm, not only gives lower bounds even better than those by [6], it is already an exact algorithm that can solve many open instances from the literature.…”

Section: Introductionmentioning

confidence: 99%

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Solving capacitated arc routing problems using a transformation to the CVRP

Longo

Aragão

Uchôa

2006

Computers & Operations Research

134

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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 r edges are already fixed to 1. 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.Keywords: CARP, CVRP, Routing, Mixed-Integer Programming. ResumoO problema de roteamento de veículos em um grafo com demandas nas arestas (CARP -Capacitated Arc Routing Problem) pode ser transformado em um problema equivalente de roteamento com as demandas nos vértices (CVRP -Capacitated Vehicle Routing Problem), usando-se a transformação proposta por Pearn, Assad e Golden. Contudo, a utilização dessa transformaçãoé praticamente inviável, uma vez que uma instância do CARP com r arestas com demandasé transformada em um CVRP com 3r + 1 vértices. Nós propomos uma transformação similar que reduz esse grafo a 2r + 1 vértices, com a restrição adicional de que r arestas são previamente fixadas em 1. Usando-se um algoritmo recente de branch-and-cut-and-price para o CVRP, essa nova transformação mostrou-se eficaz na resolução do CARP, sendo significativamente melhor do que os métodos exatos criados especificamente para esse problema. As experiências computacionais melhoraram os limites inferiores no valor da soluçãoótima para quase todas as instâncias testadas. Muitas dessas instâncias da literatura puderam, pela primeira vez, ser resolvidas até a otimalidade.

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Section: Introductionmentioning

confidence: 61%

Section: Computational Resultsmentioning

confidence: 99%

Section: Computational Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Solving capacitated arc routing problems using a transformation to the CVRP

Longo

Aragão

Uchôa

2006

Computers & Operations Research

134

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“…In [19], Belenguer and Benavent present a Cutting Plane algorithm for the CARP, which is partly based on several classes of valid inequalities presented earlier by the same authors, [18]. Using their algorithm, the authors are able to reach the best existing lower bound for all test instances, and can improve the existing lower bounds for several instances.…”

Section: Exact Methods For the Carpmentioning

confidence: 99%

A Decade of Capacitated Arc Routing

Wøhlk

Operations Research/Computer Science Interfaces

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Summary. Arc Routing is the arc counterpart to node routing in the sense that focus regarding service and resource constraints are on the arcs and not on the nodes. The key problem within this area is the Capacitated Arc Routing Problem (CARP), which is the arc routing counterpart to the vehicle routing problem. During the last decade, arc routing has been a relatively active research area with respect to lower bounding procedures, solution approaches and modeling. Furthermore, several interesting variations of the problem have been studied. We survey the latest research within the area of arc routing focusing mainly on the CARP and its variants.

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Exact methods based on node‐routing formulations for undirected arc‐routing problems

Maniezzo¹

2005

Networks

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A cutting plane algorithm for the capacitated arc routing problem

Cited by 130 publications

References 12 publications

Solving capacitated arc routing problems using a transformation to the CVRP

Solving capacitated arc routing problems using a transformation to the CVRP

A Decade of Capacitated Arc Routing

Exact methods based on node‐routing formulations for undirected arc‐routing problems

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