Minimum spanning tree with conflicting edge pairs: a branch-and-cut approach

Carrabs, Francesco; Cerulli, Raffaele; Pentangelo, Rosa; Raiconi, Andrea

doi:10.1007/s10479-018-2895-y

Cited by 23 publications

(25 citation statements)

References 10 publications

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“…The first five columns of these tables show the characteristics of the instances. The column Opt reports the optimal solution value computed by the branch‐and‐cut (BC) proposed in [4]. When a certified optimal solution is not found within the time limit of 5000 s, the best solution found is shown, if available, and a “*” symbol is added near the related value.…”

Section: Computational Testsmentioning

confidence: 99%

“…To further investigate the effectiveness of HDA + , we compare the upper bounds with the optimal solutions provided by B&C on the set of small instances proposed in [4]. The results of this comparison are reported in Table 5.…”

Section: Computational Testsmentioning

confidence: 99%

“…Moreover, they introduced a preprocessing technique to possibly reduce the instance size. Very recently, a branch‐and‐cut approach was introduced in [4], based on a new set of valid inequalities. It outperforms previous branch‐and‐cut methods.…”

Section: Introductionmentioning

confidence: 99%

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A Lagrangian approach for the minimum spanning tree problem with conflicting edge pairs

Carrabs

Gaudioso

2020

Networks

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This article addresses the minimum spanning tree problem with conflicting edge pairs, a variant of the classical minimum spanning tree where, given a list of conflicting edges, the goal is to find the cheapest spanning tree with no edges in conflict. We adopt a Lagrangian relaxation approach together with a dual ascent and a subgradient procedure to find tight lower bounds on the optimal solution. The algorithm is also equipped with a heuristic approach which provides an upper bound by removing the conflicts from possible infeasible solutions met during the calculation of the lower bounds. The computational results, carried out on benchmark instances, show that the proposed algorithm finds the optimal solutions on several instances. Moreover, the lower bounds it provides are much more accurate than ones provided by other Lagrangian approaches available in the literature and they are computed in much less time.

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Section: Computational Testsmentioning

confidence: 99%

Section: Computational Testsmentioning

confidence: 99%

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A Lagrangian approach for the minimum spanning tree problem with conflicting edge pairs

Carrabs

Gaudioso

2020

Networks

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“…For instance, let us consider again the graph G in Figure 1A with P = {{(1,2), (2,6)}}. An upper bound W(T max ) can be easily computed by adding the five highest edge weight of G obtaining W(T max ) = 28.…”

Section: Chromosome Definition and Fitness Functionmentioning

confidence: 99%

“…Moreover, the authors introduced a preprocessing phase that results very effective on some sets of instances. Finally, very recently, another branch-and-cut algorithm for MSTC was introduced in [2]. Thanks to a new set of valid inequalities, based on combined properties belonging to any feasible solution, this last algorithm outperforms the ones proposed in [17].…”

Section: Introductionmentioning

confidence: 99%

A multiethnic genetic approach for the minimum conflict weighted spanning tree problem

2019

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This paper addresses a variant of the minimum spanning tree problem in which, given a list of conflicting edges, the primary goal is to find a spanning tree with the minimum number of conflicting edge pairs and the secondary goal is to minimize the weight of spanning trees without conflicts. The problem is NP-hard and it finds applications in the design of offshore wind farm networks. We propose a multiethnic genetic algorithm for the problem in which the fitness function is designed to simultaneously manage the two goals of the problem. Moreover, we introduce three local search procedures to improve the solutions inside the population during the computation. Computational results performed on benchmark instances reveal that our algorithm outperforms the other heuristic approach, proposed in the literature, for this problem.

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Minimum cost flow problem with conflicts

2021

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The minimum cost flow problem with conflicts is a recent extension of the ordinary minimum cost flow problem. It includes flow compatibility restrictions in addition to flow balance equalities and capacity constraints: at most one of the conflicting arcs can have positive flow. In this work we study this extension of the minimum cost flow problem, which can be faced in many real‐world applications. We give mixed‐integer programming formulations of the problem after briefly analyzing its complexity and propose two exact solution algorithms. One of them is a branch‐and‐bound procedure with combinatorial branching rules based on conflicts in an optimal solution of the relaxations. The other one is a Russian Doll Search method exploring the maximal stable sets of the conflict graph, which is obtained from the original network with the purpose of representing the conflict relations among arcs. Also, a set of preprocessing procedures is introduced with the aim of reducing the size of the problem. We can say that the new algorithms are very efficient according to the results of extensive computational experiments realized on a large set of test problems.

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Minimum spanning tree with conflicting edge pairs: a branch-and-cut approach

Cited by 23 publications

References 10 publications

A Lagrangian approach for the minimum spanning tree problem with conflicting edge pairs

A Lagrangian approach for the minimum spanning tree problem with conflicting edge pairs

A multiethnic genetic approach for the minimum conflict weighted spanning tree problem

Minimum cost flow problem with conflicts

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