Search for the best compromise solution on Multiobjective shortest path problem

Sauvanet, Gaël; Néron, Emmanuel

doi:10.1016/j.endm.2010.05.078

Cited by 9 publications

(8 citation statements)

References 3 publications

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“…In this paper, we propose an efficient label-correcting algorithm called "Label-Correcting with Dynamic update of Pareto Frontier" (LCDPF), which provides an exact resolution of the MOSP problem. This work is an extension of previous works [50]. The LCDPF algorithm rapidly computes all non-dominated solutions, even for large graphs; its performance is even competitive with that of the best benchmark algorithms.…”

Section: Introductionmentioning

confidence: 84%

“…The MOSP problem is to find a set of paths between two given points that minimizes several objective functions. This problem arises in many applications, including the design of transportation networks [13], transportation problems [2], transport risk management [14], tourist trip design [27], satellite scheduling [24], bike tour planning [50], and evacuation planning [44].…”

Section: Introductionmentioning

confidence: 99%

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An Efficient Label-Correcting Algorithm for the Multiobjective Shortest Path Problem

Kergosien

Giret

Néron

et al. 2022

INFORMS Journal on Computing

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This paper proposes an exact algorithm to solve the one-to-one multiobjective shortest path problem. The solution involves determining a set of nondominated paths between two given nodes in a graph that minimizes several objective functions. This study is motivated by the application of this solution method to determine cycling itineraries. The proposed algorithm improves upon a label-correcting algorithm to rapidly solve the problem on large graphs (i.e., up to millions of nodes and edges). To verify the performance of the proposed algorithm, we use computational experiments to compare it with the best-known methods in the literature. The numerical results confirm the efficiency of the proposed algorithm. Summary of Contribution: The paper deals with a classic operations research problem (the one-to-one multiobjective shortest path problem) and is motivated by a real application for cycling itineraries. An efficient method is proposed and is based on a label-correcting algorithm into which several additional improvement techniques are integrated. Computational experiments compare this algorithm with the best-known methods in the literature to validate the performance on large-size graphs (Center for Discrete Mathematics and Theoretical Computer Science (DIMACS) instances from the ninth DIMACS challenge). New instances from the context of cycling itineraries are also proposed.

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Section: Introductionmentioning

confidence: 84%

Section: Introductionmentioning

confidence: 99%

An Efficient Label-Correcting Algorithm for the Multiobjective Shortest Path Problem

Kergosien

Giret

Néron

et al. 2022

INFORMS Journal on Computing

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“…Pangilinan and Janssens (2007) have addressed the problem of multiobjectives path aiming to find all effective ways (nondominated or Pareto-optimal) from a source node to a destination node with multiple objectives. Sauvanet et al (2011) addressed as well the multi-objective path problem for the benefit of cyclists, where several criteria such as distance, insecurity and stress are considered (Néron and Sauvanet, 2010).…”

Section: K-shortest Paths Problemmentioning

confidence: 99%

Establishing an Evacuation Network: A Path Ranking Approach

Alaeddine¹,

Serrhini²,

Maïzia³

et al. 2019

Journal of Computer Science

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The evacuation of population exposed to flood hazard requires the establishment of a specific transportation network. This is to compute escape routes to be taken by affected population. At evacuation time, inhabitants of affected area must be evacuated through transportation network to safety area. The main objective of this work is to provide assistance to rescue forces in terms of accessibility by providing itinieraries between buildings at risk of flooding and safety points equipped for this purpose. Technically, the problem of k-shortest paths between two nodes in network has been extensively studied in the literature offering several efficient algorithms for different applications. Those algorithms so-called ranking methods aim to compute the first shortest path then the second one and so on. It's well known that the computation in ranking methods is based only on one criterion which is generally distance or time. Often a single criterion is not sufficient in some real-world problems (road network, internet, etc.,) where one or several supplementary criteria (such as cost, capacity, security, etc.,) must also be taken into consideration. This multi-criteria optimization so-called labeling method aims to compute a Pareto front that represents a set of non-dominated paths. However it is very difficult to take a decision on which k-paths to select among this set and especially when selected paths are served as a data input for a sensitive problem such as the evacuation. We contribute in this paper to establish an evacuation network dedicated to the evacuation of population exposed to natural hazards and more particularly to flood hazard. Two ranking methods to compute paths between each origin (building)-destination (shelter) pair are presented. The criteria free-flow travel time, capacity and number of lanes of road are considered in computing paths. Thus we aim in the proposed ranking approach to simulate a multi-criteria aspect by combining travel time and number of lanes as weight function. The establishment of network (determination of k-paths between each building and shelter associated) is then performed according to several measures we introduce in this paper.

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“…As an example, consider the problem of finding optimized routes for cyclists in a road network: While edges may be associated with different categories like asphalt, gravel or sand-or, when related to safety considerations, very safe (there is a bicycle path), neutral (a quiet road) or unsafe (a main road without bicycle path)-such categories do not immediately translate into monetary or cost values. Bi-objective shortest path problems with route safety criteria are addressed, for example, in the web application geovelo and in the associated publications Kergosien et al (2021); Sauvanet & Néron (2010). In these references, only two categories are considered (safe or unsafe edges), and the safety criterion is translated into a cost function that evaluates the total length of unsafe route segments.…”

Section: Introductionmentioning

confidence: 99%

Ordinal Optimization Through Multi-objective Reformulation

Klamroth¹,

Stiglmayr²

2022

Preprint

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We analyze combinatorial optimization problems with ordinal, i.e., non-additive, objective functions that assign categories (like good, medium and bad) rather than cost coefficients to the elements of feasible solutions. We review different optimality concepts for ordinal optimization problems and discuss their similarities and differences. We then focus on two prevalent optimality concepts that are shown to be equivalent. Our main result is a bijective linear transformation that transforms ordinal optimization problems to associated standard multi-objective optimization problems with binary cost coefficients. Since this transformation preserves all properties of the underlying problem, problemspecific solution methods remain applicable. A prominent example is dynamic programming and Bellman's principle of optimality, that can be applied, e.g., to ordinal shortest path and ordinal knapsack problems. We extend our results to multi-objective optimization problems that combine ordinal and real-valued objective functions.

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Search for the best compromise solution on Multiobjective shortest path problem

Cited by 9 publications

References 3 publications

An Efficient Label-Correcting Algorithm for the Multiobjective Shortest Path Problem

An Efficient Label-Correcting Algorithm for the Multiobjective Shortest Path Problem

Establishing an Evacuation Network: A Path Ranking Approach

Ordinal Optimization Through Multi-objective Reformulation

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