A multi-operator genetic algorithm for the generalized minimum spanning tree problem

Contreras‐Bolton, Carlos; Gatica, Gustavo; Barra, Carlos; Parada, Víctor

doi:10.1016/j.eswa.2015.12.014

Cited by 25 publications

(8 citation statements)

References 18 publications

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“…The different algorithms generated during the evolutionary process can be decoded manually from their tree structure to obtain their corresponding pseudocode. An illustrative case is presented in Algorithm 1 that builds a solution in 6 Scientific Programming Input: Graph Output: Generalized minimum spanning tree (1) repeat (2) condition-repeat1 ← false (3) condition-repeat2 ← false (4) if least-cluster-initial-connection () or tree-leaf-connection-improvement () (5) condition-repeat1 ← true (6) else (7) while1 [condition-repeat1 ← connect-cluster-with-fewer-vertices ()] = true do (8) tree-leaf-connection-improvement () (9) end while1 (10) end if (11) if condition-repeat1 = true (12) repeat (13) flag ← connection-cluster-improvement () (14) if internal-edge-connection-improvement () (15) while1 [flag2 ← subtree-4-cluster-connection-improvement ()] = true do (16) connect-smallest-edge-with-the-tree () (17) end while1 (18) else (19) flag2 ← false (20) end if (21) if flag = flag2 (22) condition-repeat2 ← true (23) while1 connect-cluster-with-fewer-vertices() do (24) connect-cluster-with-fewer-vertices () (25) end while1 (26) end if (27) until condition-repeat2 (28) end if (29) until condition-repeat1 (30) return GMSTP Algorithm 1: Pseudocode of GMSTP2. two stages.…”

Section: Resultsmentioning

confidence: 99%

“…The appropriate selection of genetic algorithm operators has several options [41]. In this study, operators are selected based on previous studies dealing with the automatic generation of algorithms and preliminary runs [14,27,29]. Thus, a selection operator used double tournament which consists in selecting four individuals that compete first in fitness and then in size [42,43].…”

Section: Operators Andmentioning

confidence: 99%

“…However, the best known value was not achieved by this approach [11]. Recently, Contreras-Bolton et al [14] proposed an approach based on a multioperator genetic algorithm by considering two crossover and five mutation operators, three of which are local searches. That allowed MGA to be competitive with respect to the best algorithms present in the literature, in terms of both quality of the solution and computing time.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Automatically Produced Algorithms for the Generalized Minimum Spanning Tree Problem

Contreras‐Bolton

Rey

Ramos-Cossio

et al. 2016

Scientific Programming

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The generalized minimum spanning tree problem consists of finding a minimum cost spanning tree in an undirected graph for which the vertices are divided into clusters. Such spanning tree includes only one vertex from each cluster. Despite the diverse practical applications for this problem, the NP-hardness continues to be a computational challenge. Good quality solutions for some instances of the problem have been found by combining specific heuristics or by including them within a metaheuristic. However studied combinations correspond to a subset of all possible combinations. In this study a technique based on a genotypephenotype genetic algorithm to automatically construct new algorithms for the problem, which contain combinations of heuristics, is presented. The produced algorithms are competitive in terms of the quality of the solution obtained. This emerges from the comparison of the performance with problem-specific heuristics and with metaheuristic approaches.

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Section: Resultsmentioning

confidence: 99%

Section: Operators Andmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Automatically Produced Algorithms for the Generalized Minimum Spanning Tree Problem

Contreras‐Bolton

Rey

Ramos-Cossio

et al. 2016

Scientific Programming

Self Cite

View full text Add to dashboard Cite

show abstract

“…Diverse metaheuristics have also been proposed, such as the variable neighborhood search (Hu et al., 2008), genetic algorithm (GA) (Golden et al., 2005), tabu search (Öncan et al., 2008), and greedy randomized adaptive search procedure (GRASP) (Ferreira et al., 2012), among others. In particular, two of the most effective metaheuristic algorithms so far are based on GA: a multioperator GA (Contreras‐Bolton et al., 2016) and a GA that uses a two‐level solution approach (Pop et al., 2018). For a complete revision of the GMSTP, see Pop (2020).…”

Section: Literature Reviewmentioning

confidence: 99%

An effective two‐level solution approach for the prize‐collecting generalized minimum spanning tree problem by iterated local search

Contreras‐Bolton

Parada

2020

Int Trans Operational Res

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The prize-collecting generalized minimum spanning tree problem consists of finding a minimum cost spanning tree in an undirected graph, considering that the vertices are divided into clusters, that there is a nonnegative cost associated with each edge, that there is a prize to be collected on each vertex, and that only one vertex of each cluster belongs to the tree. Due to its NP-hardness, this problem remains a computational challenge even for small instances, and the practical applications that arise in telecommunication networks can attain large dimensions. The state-of-the-art algorithm finds good solutions for several instances; however, the quality of solutions and the computing time for large instances remain to be improved. We propose an iterated local search algorithm that works on a two-level solution approach, taking advantage of the structure of the problem. The first-level subproblem aims to select a vertex for each cluster, and the second-level subproblem addresses the determination of the minimum spanning tree covering such vertices. The performance of the resulting algorithm is evaluated with the most challenging instances from the literature, comparing the results with the state-of-the-art algorithm. The computational experiment conducted shows that, both in existing instances and in a new group of instances presented in this paper, the proposed algorithm outperforms the state-of-the-art algorithm.

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“…If all prizes are equal to zero (or, if all prizes are simply equal for the vertices in each group of the vertex partition), then PC‐GMSTP can be reduced to the generalized minimum spanning tree problem (GMSTP) (Feremans et al., ; Pop, ; Golden et al., ; Contreras‐Bolton et al., ). Since the decision version of the latter was proved to be NP‐hard in Myung et al.…”

Section: Introductionmentioning

confidence: 99%

A GRASP with path‐relinking and restarts heuristic for the prize‐collecting generalized minimum spanning tree problem

Marzo

Ribeiro

2019

Int Trans Operational Res

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Given a graph with its vertex set partitioned into a set of groups, nonnegative costs associated to its edges, and nonnegative prizes associated to its vertices, the prize‐collecting generalized minimum spanning tree problem consists in finding a subtree of this graph that spans exactly one vertex of each group and minimizes the sum of the costs of the edges of the tree less the prizes of the selected vertices. It is a generalization of the NP‐hard generalized minimum spanning tree optimization problem. We propose a GRASP (greedy randomized adaptive search procedure) heuristic for its approximate solution, incorporating path‐relinking for search intensification and a restart strategy for search diversification. The hybridization of the GRASP with path‐relinking and restarts heuristic with a data mining strategy that is applied along with the GRASP iterations, after the elite set is modified and becomes stable, contributes to making the heuristic more robust. The computational experiments show that the heuristic developed in this work found very good solutions for test problems with up to 439 vertices. All input data for the test instances and detailed numerical results are made available from Mendeley Data.

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A multi-operator genetic algorithm for the generalized minimum spanning tree problem

Cited by 25 publications

References 18 publications

Automatically Produced Algorithms for the Generalized Minimum Spanning Tree Problem

Automatically Produced Algorithms for the Generalized Minimum Spanning Tree Problem

An effective two‐level solution approach for the prize‐collecting generalized minimum spanning tree problem by iterated local search

A GRASP with path‐relinking and restarts heuristic for the prize‐collecting generalized minimum spanning tree problem

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