The fleet size and mix problem for capacitated arc routing

Ulusoy, Gündüz

doi:10.1016/0377-2217(85)90252-8

Cited by 161 publications

(103 citation statements)

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“…This partitioning procedure based on solving the shortest path problem was presented by Beasley (1983) for solving the VRP and by Golden et al (1984) for the HFVRP. Since then, this partitioning approach has been used by several authors, including Ulusoy (1985) for the fleet size and mix problem for the capacitated arc routing problem, Ryan et 8 al. (1993) and Renaud et al (1996) for the VRP and Salhi and Sari (1997) for the multidepot HFVRP.…”

Section: Initial Solution (Step 0)mentioning

confidence: 99%

A variable neighborhood-based heuristic for the heterogeneous fleet vehicle routing problem

Imran

Salhi

Wassan

2009

European Journal of Operational Research

123

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The heterogeneous fleet vehicle routing problem is investigated using some adaptations of the variable neighborhood search (VNS). The initial solution is obtained by Dijkstra's algorithm based on a cost network constructed by the sweep algorithm and the 2-opt. Our VNS algorithm uses several neighborhoods which are adapted for this problem. In addition, a number of local search methods together with a diversification procedure are used. Two VNS variants, which differ in the order the diversification and Dijkstra's algorithm are used, are implemented. Both variants appear to be competitive and produce new best results when tested on the data sets from the literature. We also constructed larger data sets for which benchmarking results are provided for future comparison.

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Section: Initial Solution (Step 0)mentioning

confidence: 99%

A variable neighborhood-based heuristic for the heterogeneous fleet vehicle routing problem

Imran

Salhi

Wassan

2009

European Journal of Operational Research

123

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“…Several heuristics have been proposed for it. Among them we can cite Golden et al [4], Chapleau et al [9], Ulusoy [27], Pearn [23,24] and Hertz et al [15]. Many other heuristics are described in [2] [12] and [11].…”

Section: Introductionmentioning

confidence: 99%

Solving capacitated arc routing problems using a transformation to the CVRP

Longo

Aragão

Uchôa

2006

Computers & Operations Research

137

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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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“…b j ≥ 2). For each CARP instance, one can construct a Capacitated Arc Routing With Fixed Cost counterpart by simply adding a fixed cost F in the route costs, as first proposed in the literature of the 1980s [27]. We simply tried several F values (F = 5C, F = C, F = 0.2C and F = 0-pure CARP) and we applied them on some random instances from the four CARP instance classes above.…”

Section: Arc Routing Problems 421 Capacitated Arc-routing With Fixmentioning

confidence: 99%

Using dual feasible functions to construct fast lower bounds for routing and location problems

Porumbel

Gonçalves

2015

Discrete Applied Mathematics

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In cutting and packing problems, Dual Feasible Functions (DFFs) represent a well established tool for deriving high quality lower bounds in very short times. A well-known DFF lower bounding approach consists of using DFFs to rapidly generate feasible values for the dual variables of a Column Generation (CG) program (i.e., of an extended formulation commonly associated to CG). This paper presents a method for extending this approach to problems such as Capacitated p-Median, Distance Constrained General Routing and related variants (e.g., Capacitated Arc-Routing). In contrast to classical DFF bounds for cutting and packing, our extended DFF bounds deal with non-equal column costs, i.e., the column costs (primal objective function coefficients) have a more complex structure depending on some sums of distances. The general idea is to use a (reformulated) classical CG model in which a feasible dual solution is expressed as a linear combination of both DFF and non-DFF terms. In fact, one of the proposed approaches (the mixed CG-DFF bound for Capacitated p-Median in Section 2.2) still requires optimizing a restricted CG program, but with fewer variables and easier pricing sub-problems. The most refined bound version is the "DFF warm-started CG" from Section 2.2.2: it takes dual constraints generated while solving the above restricted CG program are re-uses them to warm-start a full CG phase. In the best cases, this can yield a speed-up between 2 and 3 relative to the pure CG. We present numerical experiments on Capacitated p-Median, Capacitated Arc-Routing (with fixed costs) and Distance Constrained Arc Routing; the numerical comparisons with the CG bound concern both the quality and the running time.

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The fleet size and mix problem for capacitated arc routing

Cited by 161 publications

References 10 publications

A variable neighborhood-based heuristic for the heterogeneous fleet vehicle routing problem

A variable neighborhood-based heuristic for the heterogeneous fleet vehicle routing problem

Solving capacitated arc routing problems using a transformation to the CVRP

Using dual feasible functions to construct fast lower bounds for routing and location problems

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