The robust shortest path problem with interval data via Benders decomposition

Montemanni, Roberto; Gambardella, Luca Maria

doi:10.1007/s10288-005-0066-x

Cited by 68 publications

(54 citation statements)

References 20 publications

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“…This version of the robust shortest path problem, denoted ROBINTREG, is studied in [4,13,17,18,19,28]. Most results are based on the following property, established by Karaşan, Pinar and Yaman.…”

Section: With the Maximum Regret Criterionmentioning

confidence: 99%

“…Several algorithms for exactly solving ROBINTREG have been proposed [13,17,18,19]. In these studies, ROBINTREG is written as an integer linear program with variables y ij which represent a path µ as follows :…”

Section: Resolutionmentioning

confidence: 99%

“…In [18], authors propose to apply a Benders decomposition scheme on P 1 . A great number of experiments is carried out to compare these various approaches.…”

Section: Resolutionmentioning

confidence: 99%

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Robust Shortest Path Problems

and¹,

Murat²

2014

Paradigms of Combinatorial Optimization

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RésuméCet article constitue un état de l'art sur les problèmes de plus courts chemins pour lesquels il existe des éléments d'incertitude et d'indétermination sur les valeurs des arcs. Deux modèles d'incertitude sont distingués : celui dit par intervalle et celui dit par scénarios. Différentes mesures et approches de la robustesse sont présentées : celles issues de la théorie de la décison, celles issues de l'analyse multicritère et celles issues de la programmation mathématique. Elles donnent lieu à plusieurs versions distinctes du problème de plus court chemin robuste dont les complexités et les résolutions sont présentées. Mots-clefs : plus court chemin, optimisation robuste, incertitudes sur les données, scénario du pire cas, regret maximum AbstractThis paper is a state of the art on the shortest path problems for which it exists uncertainty and inaccuracy factors on arc values. Two uncertainty models are distinguished: the so-called interval model and the discrete set of scenarios model. Different measures and approaches of robustness are presented: those coming from decision theory, those coming from multicriteria analysis and those coming from mathematical programming. Each one leads to a particular version of robust shortest path problem for which complexity and resolution are studied.

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Section: With the Maximum Regret Criterionmentioning

confidence: 99%

Section: Resolutionmentioning

confidence: 99%

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Robust Shortest Path Problems

and¹,

Murat²

2014

Paradigms of Combinatorial Optimization

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“…and can not solve problem instances with |V| > 25 in reasonable time, where V(E) is the set of vertices (edges). In [13] and [14] a new exact method based on Benders decomposition was described with respect to the robust spanning tree and the robust shortest path problem respectively. It was shown that this approach gives very good computational results on all the benchmarks considered, and especially on those that were harder to solve for the methods previously known.…”

Section: Introductionmentioning

confidence: 99%

Simulated annealing algorithm for the robust spanning tree problem

Nikulin

2007

J Heuristics

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Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. This paper addresses the robust spanning tree problem with interval data, i.e. the case of classical minimum span ning tree problem whe n edge weights are not fixed but take their values from some intervals associated with edges. The problem c onsists in finding a spanning tree that minimizes so-called robust deviation, i.e. deviation from an optimal Solution under the worst case realization of interval weights. As it was proven in [8], the problem is NP-hard, therefore it is of great interest to tackle it with some metaheuristic approach, namely simulated annealing, in order to calculate an approximate Solution for large scale instances efficiently. We describe theoretical aspects and present the results of co mputational experiments. To the best of our knowledge, this is the first attempt to develop a metaheuristic approach for solving the robust spanning tree problem. Terms of use: Documents in EconStor may

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“…A more complex optimization criterion has then to be adopted. We consider here the relative robustness criterion, described in Kouvelis and Yu [14] and applied to many combinatorial optimization problems with interval data in [2][3][4]9,13,[21][22][23][24][25][28][29][30][31], although the list is by no means exhaustive.…”

Section: Introductionmentioning

confidence: 99%

A Benders decomposition approach for the robust spanning tree problem with interval data

Montemanni

2006

European Journal of Operational Research

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The robust spanning tree problem is a variation, motivated by telecommunications applications, of the classic minimum spanning tree problem. In the robust spanning tree problem edge costs lie in an interval instead of having a fixed value.Interval numbers model uncertainty about the exact cost values. A robust spanning tree is a spanning tree whose total cost minimizes the maximum deviation from the optimal spanning tree over all realizations of the edge costs. This robustness concept is formalized in mathematical terms and is used to drive optimization. This paper describes a new exact method, based on Benders decomposition, for the robust spanning tree problem with interval data. Computational results highlight the efficiency of the new method, which is shown to be very fast on all the benchmarks considered, and in particular on those that were harder to solve for the methods previously known.

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The robust shortest path problem with interval data via Benders decomposition

Cited by 68 publications

References 20 publications

Robust Shortest Path Problems

Robust Shortest Path Problems

Simulated annealing algorithm for the robust spanning tree problem

A Benders decomposition approach for the robust spanning tree problem with interval data

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