New Metaheuristic Approaches for the Leaf-Constrained Minimum Spanning Tree Problem

Singh, Alok; Baghel, Anurag Singh

doi:10.1142/s0217595908001870

Cited by 9 publications

(7 citation statements)

References 8 publications

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“…The performance of the ML, KCB and LSoCV heuristics is compared in "Comparison of Heuristics on Standard Benchmark Instances" section on a set of standard benchmark graphs used widely in the literature [6,17,18]. These are comprised of forty-five complete Euclidean graphs, fifteen instances each having 50, 100 and 250 vertices, respectively.…”

Section: Computational Results and Discussionmentioning

confidence: 99%

“…A generational GA that encodes solutions using the Blob code [16], and another, better-performing subset-coded genetic algorithm (SCGA) that uses subset coding [16] are given by Julstrom [6]. Other meta-heuristic approaches that have been effectively applied for solving the problem include an ant colony optimization (ACO) algorithm given by [17], Tabu search [17] and an artificial bee colony (ABC) algorithm [18]. A quantum-inspired particle swarm optimization (QPSO) algorithm is also given for the problem [19].…”

Section: Introductionmentioning

confidence: 99%

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Novel Heuristics for the Euclidean Leaf-Constrained Minimum Spanning Tree Problem

Prakash

Patvardhan

2020

SN COMPUT. SCI.

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Given a graph G = (V, E) whose vertices are points in the two-dimensional Euclidean space and edge-weights are the Euclidean distances between those vertices, the Euclidean Leaf-Constrained Minimum Spanning Tree (e-LCMST) problem seeks a minimum cost spanning tree that has at least a specified number, L, of leaf vertices, 2 ≤ L ≤ |V| − 1. The problem is known to be NP-hard, and finds application in facilities location, circuit and network design. Extant heuristics for the problem take O(|V| 4) time to compute low-cost leaf-constrained spanning trees, thereby restricting their applicability to only small-sized problem instances. Several meta-heuristic strategies have also been applied for the problem. This paper proposes two novel heuristics that obtain good solutions for the e-LCMST problem in O(|V| 3) time and scale well with larger problem sizes. Some relevant theoretical results are also presented. In the course of several computational experiments, the proposed heuristics are shown to outperform the extant heuristics on a large set of benchmark instances for the problem. Results are also reported for the first time on much larger-sized problems than attempted hitherto in the literature. The proposed heuristics are also shown to obtain results that are competitive with those obtained by the best-known extant meta-heuristics for the problem. The computation time taken by the proposed heuristics is well bounded, unlike that for the meta-heuristics, and observed in the experiments to be relatively much lower. Further, the proposed heuristics also have the added advantage of being easily parallelizable, and are shown to obtain good computational speedups in the course of several experiments on large Euclidean benchmark instances.

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Section: Computational Results and Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Novel Heuristics for the Euclidean Leaf-Constrained Minimum Spanning Tree Problem

Prakash

Patvardhan

2020

SN COMPUT. SCI.

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“…This pheromone update rule has originally been used in an ant colony optimisation algorithm for the leaf-constrained minimum spanning tree problem [46]. In this formula, f is the best dominating set size for the current iteration and F is the best dominating set size found so far.…”

Section: Ant Colony Optimisation Algorithms With Local Search For Mdsmentioning

confidence: 99%

An order-based algorithm for minimum dominating set with application in graph mining

Chalupa

2018

Information Sciences

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Dominating set is a set of vertices of a graph such that all other vertices have a neighbour in the dominating set. We propose a new order-based randomised local search (RLS o ) algorithm to solve minimum dominating set problem in large graphs. Experimental evaluation is presented for multiple types of problem instances. These instances include unit disk graphs, which represent a model of wireless networks, random scale-free networks, as well as samples from two social networks and real-world graphs studied in network science. Our experiments indicate that RLS o performs better than both a classical greedy approximation algorithm and two metaheuristic algorithms based on ant colony optimisation and local search. The order-based algorithm is able to find small dominating sets for graphs with tens of thousands of vertices. In addition, we propose a multi-start variant of RLS o that is suitable for solving the minimum weight dominating set problem. The application of RLS o in graph mining is also briefly demonstrated.An Order-based Algorithm for Minimum Dominating Set studied in network science, instances from DIMACS series, as well as samples of anonymised publicly available data from social networks Google+ and Pokec. These results also confirm that RLS o provides results of better quality than the greedy approximation algorithm, ACO-LS and ACO-PP-LS, while maintaining solid scalability for large graphs. In addition, the solutions found by RLS o tend to be close to lower bounds, which have been computed as solutions to the linear programming relaxation of MDS. This relaxation represents the linear programming problem obtained from the formulation of MDS by assuming that decision variables can be any real values between 0 and 1, instead of binary variables.RLS o is also extended to a multi-start algorithm MSRLS o to solve the minimum weight dominating set (MWDS) problem. Finally, an application of RLS o in graph mining is briefly discussed.The structure of our paper is as follows. In Section 2, we review the background of the problem and related work. In Section 3, we describe our local search algorithm RLS o for MDS. In Section 4, the multi-start local search algorithm MSRLS o for MWDS is presented. In Section 5, we present the experimental results and provide a short discussion. Finally, in Section 6, we summarise the contributions and identify open problems.

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“…Eventually, we have compared our approach with SCGA, ML, Tabu-LCMST, ACO-LCMST and ABC-LCMST under the same conditions and the same test cases used by Julstrom (2004a), Singh and Baghel 2008;Singh 2008. Our approach has obtained better quality solutions on most of the test instances in shorter time.…”

mentioning

confidence: 94%

“…Singh has proposed three approaches for the LCMST problem Singh and Baghel 2008;Singh 2008. The first approach is based on ant-colony optimization (ACO) algorithm (ACO-LCMST) Singh and Baghel 2008.…”

mentioning

confidence: 99%

Leaf constrained minimal spanning trees solved by modified quantum-behaved particle swarm optimization

Farzi

Dastjerdi

2010

Artif Intell Rev

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Given an undirected, connected, weighted graph, the leaf-constrained minimum spanning tree (LCMST) problem seeks a spanning tree of minimum weight among all the spanning trees of the graph with at least l leaves. In this paper, we have proposed an approach based on Quantum-Behaved Particle Swarm Optimization (QPSO) for the LCMST problem. Particle swarm optimization (PSO) is a well-known population-based swarm intelligence algorithm. Quantum-behaved particle swarm optimization (QPSO) is also proposed by combining the classical PSO philosophy and quantum mechanics to improve performance of PSO. In this paper QPSO has been modified by adding a leaping behavior. When the modified QPSO (MQPSO), falls in to the local optimum, MPSO runs a leaping behavior to leap out the local optimum. We have compared the performance of the proposed method with ML, SCGA, ACO-LCMST, TS-LCMST and ABC-LCMST, which are reported in the literature. Computational results demonstrate the superiority of the MQPSO approach over all the other approaches. The MQPSO approach obtained better quality solutions in shorter time.

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New Metaheuristic Approaches for the Leaf-Constrained Minimum Spanning Tree Problem

Cited by 9 publications

References 8 publications

Novel Heuristics for the Euclidean Leaf-Constrained Minimum Spanning Tree Problem

Novel Heuristics for the Euclidean Leaf-Constrained Minimum Spanning Tree Problem

An order-based algorithm for minimum dominating set with application in graph mining

Leaf constrained minimal spanning trees solved by modified quantum-behaved particle swarm optimization

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