An Interactive Algorithm for Vehicle Routeing for Winter — Gritting

Li, Leon Y. O.; Eglese, Richard W.

doi:10.1057/jors.1996.20

Cited by 38 publications

(28 citation statements)

References 15 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%

Solving capacitated arc routing problems using a transformation to the CVRP

Longo

Aragão

Uchôa

2006

Computers & Operations Research

139

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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%

Solving capacitated arc routing problems using a transformation to the CVRP

Longo

Aragão

Uchôa

2006

Computers & Operations Research

139

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“…Summary results for Tabu-Guard on the six MM k-RPP instances adapted from Li and Eglese (1996) are shown in Table 8. We only report on the average results over k = 2, .…”

Section: Results For MM K-rpp Instancesmentioning

confidence: 99%

“…. , 10 of three Tabu-Guard (TG) setups on the MM k-RPP egl instances of Li and Eglese (1996). The average execution times reported are calculated over the total time taken to generate and improve five solutions for each k. please contact the authors.…”

Section: Results For MM K-rpp Instancesmentioning

confidence: 99%

“…For further evaluation of Tabu-Guard we tested the algorithm on networks of eight CARP instances from Li and Eglese (1996). The complete set contains 21 instances, but since the MM k-RPP and MM k-CPP do not model edge demand the problem set is reduced to eight instances with the others being duplicates.…”

Section: Further Algorithm Testingmentioning

confidence: 99%

“…Again, on average, all three Table 7: Computational results of three Tabu-Guard (TG) setups on the egl-s4-A instance of Li and Eglese (1996), with |V V V| = 140, |E E E| = 190 and |R R R| = 190. The execution times reported are the total time taken to generate and improve five solutions for each k. The average w max values are calculated in terms of lower bound gap values for each k. Tabu-Guard setups outperformed both T-10m and T-INF.…”

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confidence: 99%

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Applying min–maxkpostmen problems to the routing of security guards

Willemse¹,

Joubert

2012

Journal of the Operational Research Society

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The most essential and alluring characteristic of a security estate is the estate's ability to provide 24-hour security to its residents, of which the continual patrolling of roads and paths is vital. The objective of this paper is to address the lack of sufficient patrol route design procedures by presenting a tabu search algorithm capable of generating multiple patrol routes for an estate's security guards. The paper shows that the problem of designing these routes can be modelled as an Arc Routing Problem, specifically as min-max k postmen problems. The algorithm is illustrated with a real problem instance from an estate in Gauteng, South Africa. The patrol routes generated by the algorithm provide a significant improvement in the even patrolling of the road network, and a more balanced work distribution among guards. The algorithm is also tested on several benchmark problems from literature.

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

Maniezzo¹

2005

Networks

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An Interactive Algorithm for Vehicle Routeing for Winter — Gritting

Cited by 38 publications

References 15 publications

Solving capacitated arc routing problems using a transformation to the CVRP

Solving capacitated arc routing problems using a transformation to the CVRP

Applying min–maxkpostmen problems to the routing of security guards

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

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