A Hybrid ACO Approach to the Matrix Bandwidth Minimization Problem

Pintea, Camelia-Mihaela; Crişan, Gloria-Cerasela; Chira, Camelia

doi:10.1007/978-3-642-13769-3_49

Cited by 9 publications

(10 citation statements)

References 13 publications

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“…Lim, Rodrigues and Xiao [32,33,35] NC-HC 2007 FNC-HC Lim, Lin and Xiao [30] PSO-HC 2007 Kaveh and Sharafi [23] Kaveh-Sharafi 2009 Mladenovic et al [39] VNS-band 2010 Koohestani and Poli [25] Koohestani-Poli 2010 Pintea, Crişa and Shira [42] ACO-PCS1 2010…”

Section: Heuristicmentioning

confidence: 98%

“…Czibula et al [9] proposed 3 heuristics that are not considered as the possible best for bandwidth reduction as well. Two of them are modifications of the ant-colony heuristic of Pintea et al [42] by introducing two local searches. Czibula et al [9] also applied a slight modification in the genetic-algorithm heuristic of Lim, Rodrigues e Xiao [31,34].…”

Section: Heuristicmentioning

confidence: 99%

See 1 more Smart Citation

Metaheuristic-based Heuristics for Symmetric-matrix Bandwidth Reduction: A Systematic Review

Chagas

Oliveira

2015

Procedia Computer Science

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Computational and storage costs of resolution of large sparse linear systems Ax = b can be performed by reducing the bandwidth of A. Bandwidth reduction consists of carrying out permutations of lines and columns so that they allow coefficients to remain near the main diagonal. When considering an adjacency matrix of a graph, bandwidth reduction can be considered in the sense of modifying the order in which the graph vertices are numbered. Heuristics for bandwidth reduction are revised in this study, aiming at determining which of them offers the higher bandwidth reduction with a reasonable computational cost. Specifically, metaheuristic-based heuristics are reviewed in this systematic review. Moreover, 29 metaheuristic-based heuristics tested for bandwidth reduction were found. Among them, 4 are recommended as possible state-of-the-art heuristics for addressing the problem.

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Section: Heuristicmentioning

confidence: 98%

Section: Heuristicmentioning

confidence: 99%

Metaheuristic-based Heuristics for Symmetric-matrix Bandwidth Reduction: A Systematic Review

Chagas

Oliveira

2015

Procedia Computer Science

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“…The algorithm proposed by Tello et al is based on three distinguished features including an original internal representation of solutions, a highly discriminating evaluation function and an effective neighborhood. More recently, the Ant Colony Optimization metaheuristic has been used in [13], [20] in order to solve the the MBMP.…”

Section: Marti Et Al Have Used Inmentioning

confidence: 99%

“…The hybrid ant algorithms [20] hACS and hMACS are implemented in Java. For each instance, both algorithms are executed 20 times.…”

Section: Computational Experimentsmentioning

confidence: 99%

Soft Computing Approaches on the Bandwidth Problem

et al. 2013

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The Matrix Bandwidth Minimization Problem (MBMP ) seeks for a simultaneous reordering of the rows and the columns of a square matrix such that the nonzero entries are collected within a band of small width close to the main diagonal. The MBMP is a NP-complete problem, with applications in many scientific domains, linear systems, artificial intelligence, and real-life situations in industry, logistics, information recovery. The complex problems are hard to solve, that is why any attempt to improve their solutions is beneficent. Genetic algorithms and ant-based systems are Soft Computing methods used in this paper in order to solve some MBMP instances. Our approach is based on a learning agent-based model involving a local search procedure. The algorithm is compared with the classical Cuthill-McKee algorithm, and with a hybrid genetic algorithm, using several instances from Matrix Market collection. Computational experiments confirm a good performance of the proposed algorithms for the considered set of MBMP instances. On Soft Computing basis, we also propose a new theoretical Reinforcement Learning model for solving the MBMP problem.

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“…The difficulty of obtaining optimum solutions for the MBMP has led to the development of several metaheuristics. The first such algorithms were the spectral analysis approach proposed by Bernard et al [6], the heuristic algorithm described by Dueck and Jeffs [7], the parallel heuristic algorithms introduced by Esposito and Tarricone [8], the Tabu Search (TS) heuristic proposed by Marti et al [9], the Greedy Randomized Adaptive Search Procedure (GRASP) combined with a Path Relinking (PR) method described by Pinana et al [10], the genetic algorithm (GA) suggested by Lim et al [11], the ant colony algorithm combined with hill climbing proposed by Lim et al [12], the particle swarm Downloaded by [The Aga Khan University] at 01: 18 20 February 2015 optimization combined with hill climbing described by Lim et al [13] and a hybrid ant colony optimization metaheuristic suggested by Pintea et al [14]. More recently, RodriguezTello et al [15] proposed an improved Simulated Annealing (SA) heuristic, Koohestani and Poli [16] described the first genetic programming approach and the same authors proposed a hyper-heuristic algorithm based on genetic programming [17] and finally, Mladenovic et al [18] elaborated a variable neighbourhood search (VNS)-based heuristic for reducing the bandwidth of a matrix.…”

Section: Introductionmentioning

confidence: 99%

Reducing the bandwidth of a sparse matrix with a genetic algorithm

2013

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The matrix bandwidth minimization problem (MBMP) consists in finding a permutation of the lines and columns of a given sparse matrix in order to keep the non-zero elements in a band that is as close as possible to the main diagonal. Equivalently in terms of graph theory, MBMP is defined as the problem of finding a labelling of the vertices of a given graph G such that its bandwidth is minimized. In this paper, we propose an improved genetic algorithm (GA)-based heuristic for solving the matrix bandwidth minimization problem, motivated by its robustness and efficiency in a wide area of optimization problems. Extensively computational results are reported for an often used set of benchmark instances. The obtained results on the different instances investigated show improvement of the quality of the solutions and demonstrate the efficiency of our GA compared to the existing methods in the literature.

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A Hybrid ACO Approach to the Matrix Bandwidth Minimization Problem

Cited by 9 publications

References 13 publications

Metaheuristic-based Heuristics for Symmetric-matrix Bandwidth Reduction: A Systematic Review

Metaheuristic-based Heuristics for Symmetric-matrix Bandwidth Reduction: A Systematic Review

Soft Computing Approaches on the Bandwidth Problem

Reducing the bandwidth of a sparse matrix with a genetic algorithm

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