The Capacitated Arc Routing Problem: Lower bounds

Benavent, Enrique; Campos, Vicente; Corberán, Ángel; Mota, Enrique

doi:10.1002/net.3230220706

Cited by 135 publications

(82 citation statements)

References 13 publications

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“…These datasets were originally used in Kiuchi et al [17] (kshs), DeArmon [10] and Golden et al [4](gdb), Belenguer et al [7](bccm), and Li [18] and Li and Eglese [19](egl), respectively. Except for the bccm instances, that are named 1.A, 1.B, ..., 10D, the remaining three sets have their names starting with the names of the sets.…”

Section: Computational Resultsmentioning

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: Computational Resultsmentioning

confidence: 99%

“…Algorithms yielding lower bounds for the CARP are presented by Golden and Wong [14], Assad et al [3], Pearn [22], Benavent et al [7], Amberg and Voß [1] and Wøhlk [30]. The current best bounds are those obtained by a cutting plane algorithm by Belenguer and Benavent [6].…”

Section: Introductionmentioning

confidence: 99%

Solving capacitated arc routing problems using a transformation to the CVRP

Longo

Aragão

Uchôa

2006

Computers & Operations Research

134

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“…Two different datasets are considered for the experiments. The first one, named Group A, is composed of instances taken from the known benchmark test sets egl (Eglese 1994), Beullen's C, D, E, F (Beullens et al 2003) and val (Benavent et al 1992). The second group (Group B) corresponds to the large scale CARP instances of the dataset EGL-G (Brandão and Eglese 2008).…”

Section: Experimental Studiesmentioning

confidence: 99%

Dynamic selection of evolutionary operators based on online learning and fitness landscape analysis

et al. 2016

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Self-adaptive mechanisms for the identification of the most suitable variation operator in evolutionary algorithms rely almost exclusively on the measurement of the fitness of the offspring, which may not be sufficient to assess the optimality of an operator (e.g., in a landscape with an high degree of neutrality). This paper proposes a novel adaptive operator selection mechanism which uses a set of four fitness landscape analysis techniques and an online learning algorithm, dynamic weighted majority, to provide more detailed information about the search space to better determine the most suitable crossover operator. Experimental analysis on the capacitated arc routing problem has demonstrated that different crossover operators behave differently during the search process, and selecting the proper one adaptively can lead to more promising results.

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“…In the Arc Routing Problems the demand occurs in each of the arcs (or edges) of the graph. An example of an Arc Routing Problem might be a postman who must visit each house along each street in a town [90]. Table 3 shows more details about the differences between Node Routing Problems and Arc Routing problems.…”

Section: Literature Review Sorted By Models Of Wcvrp With Relevant Mementioning

confidence: 99%