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

Montemanni, Roberto

doi:10.1016/j.ejor.2005.02.060

Cited by 62 publications

(54 citation statements)

References 24 publications

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“…We now analyze the Benders decomposition approach by Montemanni [53]. Mathematical programming formulation.…”

Section: Mmr-stmentioning

confidence: 99%

“…Let R be the feasible region (not empty) of the dual subproblem and let R P be the set of extreme points of R. By strong duality and by using the fact that R is a polytope, the primal subproblem is feasible and bounded. Since D(x) is a linear program, original RST can be written (see [53] for the details) in more compact way as follows:…”

Section: Mmr-stmentioning

confidence: 99%

“…Notice that as τ increases, M τ progressively looses unimodular property (true only for τ = 1), and it becames more and more difficult to solve in terms of integer programming. Montemanni [53] first applied the preprocessing procedure already discussed and then applied Benders decomposition.…”

Section: Mmr-stmentioning

confidence: 99%

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Minmax regret combinatorial optimization problems: an Algorithmic Perspective

2011

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Abstract. Uncertainty in optimization is not a new ingredient. Diverse models considering uncertainty have been developed over the last 40 years. In our paper we essentially discuss a particular uncertainty model associated with combinatorial optimization problems, developed in the 90's and broadly studied in the past years. This approach named minmax regret (in particular our emphasis is on the robust deviation criteria) is different from the classical approach for handling uncertainty, stochastic approach, where uncertainty is modeled by assumed probability distributions over the space of all possible scenarios and the objective is to find a solution with good probabilistic performance. In the minmax regret (MMR) approach, the set of all possible scenarios is described deterministically, and the search is for a solution that performs reasonably well for all scenarios, i.e., that has the best worst-case performance. In this paper we discuss the computational complexity of some classic combinatorial optimization problems using MMR approach, analyze the design of several algorithms for these problems, suggest the study of some specific research problems in this attractive area, and also discuss some applications using this model.

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“…We now analyze the Benders decomposition approach by Montemanni [53]. Mathematical programming formulation.…”

Section: Mmr-stmentioning

confidence: 99%

Section: Mmr-stmentioning

confidence: 99%

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Minmax regret combinatorial optimization problems: an Algorithmic Perspective

2011

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“…In addition, the interval model is applied to other combinatorial problems, for example the minimum spanning tree [16,26], the problem of selecting p elements among n with minimal total weight [3], or the assignment problem [1].…”

Section: The Interval Modelmentioning

confidence: 99%

Robust Shortest Path Problems

Gabrel

Murat

2013

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

Cited by 62 publications

References 24 publications

Minmax regret combinatorial optimization problems: an Algorithmic Perspective

Minmax regret combinatorial optimization problems: an Algorithmic Perspective

Robust Shortest Path Problems

Simulated annealing algorithm for the robust spanning tree problem

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