An algorithm for the ranking of shortest paths

Azevedo, JoséAugusto; Costa, Maria Emília O. Santos; Madeira, Joaquim; Martins, Ernesto de Queirós Vieira

doi:10.1016/0377-2217(93)90095-5

Cited by 185 publications

(90 citation statements)

References 13 publications

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“…So, for example, if we have the paths A, B and C with cost vectorsā = [5,9,3], b = [2, 1, 3] andc = [5,3,2] respectively, then A is dominated by both B and C. The paths B and C, on the other hand, form a set of Pareto optimal paths within the set {A, B,C}.…”

Section: Definition 2 (Pareto Optimality)mentioning

confidence: 99%

Speeding up Martins’ algorithm for multiple objective shortest path problems

et al. 2013

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The latest transportation systems require the best routes in a large network with respect to multiple objectives simultaneously to be calculated in a very short time. The label setting algorithm of Martins efficiently finds this set of Pareto optimal paths, but sometimes tends to be slow, especially for large networks such as transportation networks. In this article we investigate a number of speedup measures, resulting in new algorithms. It is shown that the calculation time to find the Pareto optimal set can be reduced considerably. Moreover, it is mathematically proven that these algorithms still produce the Pareto optimal set of paths.

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Section: Definition 2 (Pareto Optimality)mentioning

confidence: 99%

Speeding up Martins’ algorithm for multiple objective shortest path problems

et al. 2013

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“…In Section 2.2, we introduce algorithms of Martins [18] and Azevedo et al [19] that closely relate to our algorithm. We present our algorithm with an example, and show the complexity of the algorithm in Section 2.3.…”

Section: The Problem and Solutionmentioning

confidence: 99%

“…Since the algorithms proposed by Martins [18] and Azevedo et al [19] form the basis of our algorithm, we will describe their algorithms and complexities before we proceed. For each network N , Martins' algorithm [18] executes two algorithms: (1) a shortest path algorithm to ÿnd the shortest path p, and (2) a path deletion algorithm to generate a new network N .…”

Section: The Algorithms By Martins and Azevedo Et Almentioning

confidence: 99%

“…Later, this worst case time was improved to be O(K 2 |A|) by Azevedo et al [19] using an e cient computational implementation. According to Azevedo et al [19], however, comparative computational experiments showed that their algorithm outperformed that of Dreyfus [16] despite its worse complexity. For a given pair of nodes, Eppstein [11] used an implicit representation of paths to signiÿcantly improve the time to be O(|A| + |V | log|V | + K|V |).…”

Section: Introductionmentioning

confidence: 99%

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Finding K shortest looping paths in a traffic-light network

Yang

Chen

2005

Computers & Operations Research

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In this paper we consider a tra c-light network where every node in the network is associated with the constraint consisting of a repeated sequence of time windows. The constraint aims to simulate the operations of tra c-light control in an intersection of roads. With this kind of constraints in place, directions of routes when passing through the intersections can be formally modeled. The objective of this paper is to ÿnd the ÿrst K shortest looping paths in the tra c-light network. An algorithm of time complexity of O(rK 2 |V 1 | 3 ) is developed, where r is the number of di erent windows of a node and |V 1 | is the number of nodes in the original network. ?

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“…Different heuristics have been proposed to generate subsets of paths, commonly referred to as consideration sets (e.g. Ben-Akiva et al, 1984;Azevedo et al, 1993;de la Barra et al, 1993;van der Zijpp and Fiorenzo Catalano, 2005;Friedrich et al, 2001;Hoogendoorn-Lanser, 2005;Prato and Bekhor, 2006), to which the observed path is subsequently added . The values of the parameter estimates are dependent on the definition of the choice sets (Frejinger et al, 2009) and may vary significantly for different instances of sampled sets.…”

Section: Introductionmentioning

confidence: 99%

Operational route choice methodologies for practical applications

2018

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Understanding the route choice of individuals is a key question in travel behavior research and fundamental to transportation demand management. Modeling route choice involves several challenges, pertaining to both data availability and accuracy, and model structure and computational efficiency. The main challenge related to the route choice problem, namely the generation of the choice set, has been circumvented by Fosgerau et al. (2013) through a Markovian link choice problem that is equivalent to a path-based logit model. It is called the recursive logit (RL) model and it is directly applicable for analysis at a disaggregate level. Recent methodologies are designed to simplify the structure of the model and reduce the data requirements. Kazagli et al. (2016) propose a representation of routes that is based on aggregate elements, inspired by the environmental images of the physical world formed by the individuals (Lynch, 1960), instead of links. It is called the mental representation items (MRI) model and is useful for analysis at an aggregate level. From an application point of view, both disaggregate and aggregate route choice indicators are useful. In this paper, we describe how the RL and the MRI models can be used in practice to derive link and route flows, that are the most relevant indicators for route choice applications. Our analysis identifies the advantages and the limitations of each model and allows to draw insights into the use of a specific model, depending on the needs of the application and the data availability. Finally, we investigate the performance of the two models on real data and discuss specific features of the MRI model. The results demonstrate the validity of the MRI model for the purposes of an aggregate analysis.

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An algorithm for the ranking of shortest paths

Cited by 185 publications

References 13 publications

Speeding up Martins’ algorithm for multiple objective shortest path problems

Speeding up Martins’ algorithm for multiple objective shortest path problems

Finding K shortest looping paths in a traffic-light network

Operational route choice methodologies for practical applications

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