9 research outputs found

    Performance Analysis of Evolutionary Algorithms for the Minimum Label Spanning Tree Problem

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    Some experimental investigations have shown that evolutionary algorithms (EAs) are efficient for the minimum label spanning tree (MLST) problem. However, we know little about that in theory. As one step towards this issue, we theoretically analyze the performances of the (1+1) EA, a simple version of EAs, and a multi-objective evolutionary algorithm called GSEMO on the MLST problem. We reveal that for the MLSTb_{b} problem the (1+1) EA and GSEMO achieve a b+12\frac{b+1}{2}-approximation ratio in expected polynomial times of nn the number of nodes and kk the number of labels. We also show that GSEMO achieves a (2ln(n))(2ln(n))-approximation ratio for the MLST problem in expected polynomial time of nn and kk. At the same time, we show that the (1+1) EA and GSEMO outperform local search algorithms on three instances of the MLST problem. We also construct an instance on which GSEMO outperforms the (1+1) EA

    Greedy Randomized Adaptive Search and Variable Neighbourhood Search for the minimum labelling spanning tree problem

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    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

    Constructive Heuristics for the Minimum Labelling Spanning Tree Problem: a preliminary comparison

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    This report studies constructive heuristics for the minimum labelling spanning tree (MLST) problem. The purpose is to find a spanning tree that uses edges that are as similar as possible. Given an undirected labeled connected graph (i.e., with a label or color for each edge), the minimum labeling spanning tree problem seeks a spanning tree whose edges have the smallest possible number of distinct labels. The model can represent many real-world problems in telecommunication networks, electric networks, and multimodal transportation networks, among others, and the problem has been shown to be NP-complete even for complete graphs. A primary heuristic, named the maximum vertex covering algorithm has been proposed. Several versions of this constructive heuristic have been proposed to improve its efficiency. Here we describe the problem, review the literature and compare some variants of this algorithm

    An effective genetic algorithm for the minimum-label spanning tree problem

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    Given a connected, undirected graph G with labeled edges, the minimum-label spanning tree problem seeks a spanning tree on G to whose edges are attached the smallest possible number of labels. A greedy heuristic for this NP-hard prob-lem greedily chooses labels so as to reduce the number of components in the subgraphs they induce as quickly as possi-ble. A genetic algorithm for the problem encodes candidate solutions as permutations of the labels; an initial segment of such a chromosome lists the labels that appear on the edges in the chromosome's tree. Three versions of the GA apply generic or heuristic crossover and mutation operators and a local search step. In tests on 27 randomly-generated instances of the minimum-label spanning tree problem, ver-sions of the GA that apply generic operators, with and with-out the local search step, perform less well than the greedy heuristic, but a version that applies the local search step and operators tailored to the problem returns solutions that require on average 10 % fewer labels than the heuristic's

    The Minimum Labeling Spanning Tree Problem and Some Variants

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    The focus of my dissertation research involves combinatorial optimization. This is a key area in operations research and computer science. It includes lots of problems that have a wide variety of real-world applications. In addition, most of these problems are inherently difficult to solve. My specific disseration topic is the minimum labeling spanning tree (MLST) problem and some variants, including the label-constrained minimum spanning tree (LC-MST) problem and the colorful travaling salesman problem (CTSP). All of the three problems are NP-hard. The MLST problem tries to find a spanning tree of a graph with the smallest number of labels. The LC-MST problem tries to find the minimum-cost spanning tree of a graph with no more than K labels. The CTSP tries to find a hamiltonian cycle of a graph with the smallest number of labels. For each of the problems, we use both heuristic and genetic algorithms to solve them. From the computational results, the genetic algorithm can always obtain a better tradeoff between the solution quality and the running time. My disseration research shows that the genetic algorithm can be successfully applied to solve many NP-hard problems

    Journal of Telecommunications and Information Technology, 2006, nr 4

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    Extensions of the minimum labelling spanning tree problem, Journal of Telecommunications and Information Technology, 2006, nr 4

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    In this paper we propose some extensions of the minimum labelling spanning tree problem. The main focus is on the minimum labelling Steiner tree problem: given a graph G with a color (label) assigned to each edge, and a subset Q of the nodes of G (basic vertices), we look for a connected subgraph of G with the minimum number of different colors covering all the basic vertices. The problem has several applications in telecommunication networks, electric networks, multimodal transportation networks, among others, where one aims to ensure connectivity by means of homogeneous connections. Numerical results for several metaheuristics to solve the problem are presented
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