Metaheuristics Comparison for the Minimum Labelling Spanning Tree Problem

Cerulli, Raffaele; Fink, Andréas; Gentili, Monica; Voß, Stefan

doi:10.1007/0-387-23529-9_7

Cited by 47 publications

(92 citation statements)

References 11 publications

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“…The authors of (Cerulli et al, 2005), who kindly provided data for use in the experiments considered in this chapter, are strongly acknowledged. In the following computations, run on a Pentium Centrino microprocessor at 2.0 GHz with 512 MB RAM, different datasets are considered, each one containing 10 instances of the problem with the same set of values for the parameters n, , and m. For each dataset, solution quality is evaluated as the average objective function value for the 10 problem instances.…”

Section: Computational Resultsmentioning

confidence: 99%

“…The Pilot Method is a metaheuristic proposed by Duin and Voß (1999) The details of the Pilot Method proposed by Cerulli et al (2005) for the MLST problem are specified in Algorithm 3.3. It starts from the null solution Algorithm 3.3: The Pilot Method for the MLST problem (Cerulli et al, 2005) Input: A labelled, undirected, connected graph G = (V, E, L) with n vertices, m edges, labels; Output: A spanning tree T ; Initialisation: -Let M ← 0 be the initially empty master solution, -Let H = (V, E(M )) be the subgraph of G restricted to V and edges with labels in M , where…”

Section: Pilot Methodsmentioning

confidence: 99%

“…Subsequently, Cerulli et al (2005) applied the Pilot Method, a greedy heuristic developed by Duin and Voß (1999) and subsequently extended in (Voß et al, 2004), to the MLST problem. Considering different sets of instances of the MLST problem, Cerulli et al (2005) Cerulli et al (2005), this version can potentially reduce the computational running time by about 90%.…”

Section: Literature Reviewmentioning

confidence: 99%

“…Considering different sets of instances of the MLST problem, Cerulli et al (2005) Cerulli et al (2005), this version can potentially reduce the computational running time by about 90%. However, since a higher frequency label may not always be the best place to start, it may not perform as well as the Pilot Method.…”

Section: Literature Reviewmentioning

confidence: 99%

“…Several metaheuristics are proposed and evaluated. They outperform the Pilot Method (PILOT), which is the heuristic recommended by the literature for the MLSteiner problem (Cerulli et al, 2006). Further experimental analysis shows that some of the proposed heuristics (a Greedy Randomized Adaptive Search Procedure (GRASP), a Variable Neighbourhood Search (VNS), and a hybrid local search method (HYBRID) obtained by combining Variable Neighbourhood Search with Simulated Annealing (SA)) are effective approaches for the MLSteiner problem, obtaining high-quality solutions in short computational running times.…”

Section: Minimum Labelling Steiner Tree Problemmentioning

confidence: 99%

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We model and solve the Rainbow Cycle Cover Problem (RCCP). Given a connected and undirected graph G = ( V , E , L ) and a coloring function ℓ that assigns a color to each edge of G from the finite color set L , a cycle whose edges have all different colors is called a rainbow cycle. The RCCP consists of finding the minimum number of disjoint rainbow cycles covering G . The RCCP on general graphs is known to be NP-complete. We model the RCCP as an integer linear program, we derive valid inequalities and we solve it by branch-and-cut. Computational results are reported on randomly generated instances

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Heuristics for the strong generalized minimum label spanning tree problem

2019

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In this work we introduce and study the strong generalized minimum label spanning tree (GMLST), a novel optimization problem defined on edge-labeled graphs. Given a label set associated to each edge of the input graph, the aim is to look for the spanning tree using the minimum number of labels. Differently from the previously introduced GMLST problem, including a given edge in the solution means that all its labels are used. We present a mathematical formulation, as well as three heuristic approaches to solve the problem. Computational results compare the performances of the proposed algorithms. KEYWORDS carousel greedy, generalized problem, minimum label spanning tree, pilot method i=1 1 i , where b is the maximum number of occurrences of a label. The authors also showed this new bound to be tight. Metaheuristics for the problem were proposed in several works [4,7,11,19,22]. In [1], the authors presented a single-commodity flow mathematical model, and showed that the formulation obtained by relaxing integrality on the arc selection variables always provides the optimal solution value for the original unrelaxed problem.Several other problems defined on graphs with labeled edges have been defined and studied. Among them, we recall the colorful traveling salesman problem [6,13,14,17,24], the labeled perfect matching problem [16] and the rainbow spanning forest problem [2]. A survey on edge-labeled problems, as well as a variant of the maximum flow problem, are presented in [12].Networks. 2019;74:148-160.wileyonlinelibrary.com/journal/net

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Metaheuristics Comparison for the Minimum Labelling Spanning Tree Problem

Cited by 47 publications

References 11 publications

The development and application of metaheuristics for problems in graph theory: a computational study

The development and application of metaheuristics for problems in graph theory: a computational study

The Rainbow Cycle Cover Problem

Heuristics for the strong generalized minimum label spanning tree problem

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