22,780 research outputs found
Greedy Randomized Adaptive Search and Variable Neighbourhood Search for the minimum labelling spanning tree problem
This paper studies heuristics for the minimum labelling spanning tree (MLST) problem. The purpose is to find a spanning tree using edges that are as similar as possible. Given an undirected labelled connected graph, the minimum labelling spanning tree problem seeks a spanning tree whose edges have the smallest number of distinct labels. This problem has been shown to be NP-hard. A Greedy Randomized Adaptive Search Procedure (GRASP) and a Variable Neighbourhood Search (VNS) are proposed in this paper. They are compared with other algorithms recommended in the literature: the Modified Genetic Algorithm and the Pilot Method. Nonparametric statistical tests show that the heuristics based on GRASP and VNS outperform the other algorithms tested. Furthermore, a comparison with the results provided by an exact approach shows that we may quickly obtain optimal or near-optimal solutions with the proposed heuristics
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Heuristics based on greedy randomized adaptive search and variable neighbourhood search for the minimum labelling spanning tree problem
This paper studies heuristics for the minimum labelling spanning tree (MLST) problem. The purpose is to find a spanning tree using edges that are as similar as possible. Given an undirected labelled connected graph, the minimum labelling spanning tree problem seeks a spanning tree whose edges have the smallest number of distinct labels. This problem has been shown to be NP-complete. A Greedy Randomized Adaptive Search Procedure (GRASP) and different versions of Variable Neighbourhood Search (VNS) are proposed. They are compared with other algorithms recommended in the literature: the Modified Genetic Algorithm and the Pilot Method. Nonparametric statistical tests show that the heuristics based on GRASP and VNS outperform the other algorithms tested. Furthermore, a comparison with the results provided by an exact approach shows that we may quickly obtain optimal or near-optimal solutions with the proposed heuristics
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Solving the minimum labelling spanning tree problem using hybrid local search
Given a connected, undirected graph whose edges are labelled (or coloured), the minimum
labelling spanning tree (MLST) problem seeks a spanning tree whose edges have the smallest
number of distinct labels (or colours). In recent work, the MLST problem has been shown
to be NP-hard and some effective heuristics (Modified Genetic Algorithm (MGA) and Pilot
Method (PILOT)) have been proposed and analyzed. A hybrid local search method, that we
call Group-Swap Variable Neighbourhood Search (GS-VNS), is proposed in this paper. It is
obtained by combining two classic metaheuristics: Variable Neighbourhood Search (VNS) and
Simulated Annealing (SA). Computational experiments show that GS-VNS outperforms MGA
and PILOT. Furthermore, a comparison with the results provided by an exact approach shows
that we may quickly obtain optimal or near-optimal solutions with the proposed heuristic
Transitions in spatial networks
Networks embedded in space can display all sorts of transitions when their
structure is modified. The nature of these transitions (and in some cases
crossovers) can differ from the usual appearance of a giant component as
observed for the Erdos-Renyi graph, and spatial networks display a large
variety of behaviors. We will discuss here some (mostly recent) results about
topological transitions, `localization' transitions seen in the shortest paths
pattern, and also about the effect of congestion and fluctuations on the
structure of optimal networks. The importance of spatial networks in real-world
applications makes these transitions very relevant and this review is meant as
a step towards a deeper understanding of the effect of space on network
structures.Comment: Corrected version and updated list of reference
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