Heuristic Algorithms

Hertz, Alain; Mittaz, Michel

doi:10.1007/978-1-4615-4495-1_9

Cited by 12 publications

(3 citation statements)

References 33 publications

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“…However, applying both heuristics and selecting the best solution leads to a worst case ratio of 5/3, but it was not known if this new bound is sharp. The reader can find all the details in the survey by Hertz and Mittaz [96]. Twenty years later, Raghavachari and Veerasamy [135] proposed a modification to the Frederickson's Mixed Algorithm with a better worst case ratio of 3/2.…”

Section: The Mixed Chinese Postman Problem Given a Mixed Graph G = (mentioning

confidence: 98%

“…In Hertz et al [94] several improvement procedures are presented. These improvement routines can be used as basic tools for the design of more sophisticated constructive algorithms for the RPP (see also [96]) and can easily be adapted to handle directed or mixed graphs. Another local search framework is presented in Groves and van Vuuren [91].…”

Section: The Undirected Rppmentioning

confidence: 99%

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Recent results on Arc Routing Problems: An annotated bibliography

Corberán

Prins

2010

Networks

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Arc routing problems are vehicle routing problems in which the tasks to be performed are located on some arcs or edges of a network, e.g., spreading salt on a road or collecting municipal refuse in a street. They have been much less studied than node routing problems but impressive developments have been achieved in the last decade. The objective of this article is to survey these recent results and to provide an annotated bibliography. Except for a few references, the period surveyed starts from the publication of the book "Arc routing: theory, solutions and applications", edited by Dror in 2000. The article is made up of two main parts: one on uncapacitated (single vehicle) problems derived from the Chinese Postman Problem, the Rural Postman Problem, and the General Routing Problem; and one on multivehicle or capacitated problems such as the Capacitated Arc Routing Problem.

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Section: The Mixed Chinese Postman Problem Given a Mixed Graph G = (mentioning

confidence: 98%

Section: The Undirected Rppmentioning

confidence: 99%

Recent results on Arc Routing Problems: An annotated bibliography

Corberán

Prins

2010

Networks

View full text Add to dashboard Cite

show abstract

“…In Pearn and Li (1994) another heuristic for the WPP is proposed that, basically, consists of executing the phases of the Win's algorithm in a different order. The chapter by Hertz and Mittaz (2000) in the recent book edited by Dror (2000) gives a nice description of these algorithms. An integer formulation of the WPP and a cutting-plane procedure for its resolution were proposed in Grötschel and Win (1992).…”

Section: Introductionmentioning

confidence: 99%

Lower bounds and heuristics for the Windy Rural Postman Problem

Benavent

Carrotta

Corberán

et al. 2007

European Journal of Operational Research

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Pickup and Delivery Problems with Services on Nodes or Arcs of a Network

Hertz¹,

Mittaz²

2008

Operations Research and Networks

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Pickup and delivery are activities that appear frequently in numerous companies and communities. It generally concerns transporting merchandise from one depot to branch offices, delivering orders to clients, maintaining road networks, distributing mail, picking up rubbish, etc. These operations are often very costly and substantial savings can be made by reducing the length of the trips that must be made.According to the nature of the service furnished by the vehicles and in function of the geographical distribution of the clients, two large types of modelling emerge. The first consists in representing the clients by nodes of a network. The problem based on this model is called the node routing problem (NRP). Such a model is well adapted when the clients have precise distinct locations. The NRP has been and is still the object of many studies. Numerous variants of the NRP exist, going from the basic traveling salesman problem to problems with many more constraints, such as node routing problems with time windows.Another type of modelling associates the clients to the arcs of a network. We then speak of an arc routing problem (ARP). An arc is a direct link between two nodes in a network. Less present in the literature than the NRP, the ARP appears when the clients are located along the streets, or when the streets themselves need a service. Just as for the NRP, there are different variants of the ARP.

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Heuristic Algorithms

Cited by 12 publications

References 33 publications

Recent results on Arc Routing Problems: An annotated bibliography

Recent results on Arc Routing Problems: An annotated bibliography

Lower bounds and heuristics for the Windy Rural Postman Problem

Pickup and Delivery Problems with Services on Nodes or Arcs of a Network

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