A New Heuristic for Bandwidth and Profile Reductions of Matrices Using a Self-organizing Map

Oliveira, Sanderson L. Gonzaga de; Abreu, Alexandre A. A. M. de; Robaina, Diogo T.; Kischinhevsky, Mauricio

doi:10.1007/978-3-319-42085-1_5

Cited by 8 publications

(3 citation statements)

References 13 publications

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“…While traditional metaheuristic algorithms (e.g., Mladenovic et al (2010); Torres-Jimenez et al ( 2015)) for the problem showed remarkable bandwidth results when applied to very small-sized matrices (i.e., matrices with sizes of up to approximately 1,000) (Gonzaga de Oliveira et al, 2016Oliveira et al, , 2017, these metaheuristic algorithms are very slow (Gonzaga de Oliveira et al, 2018b;Gonzaga de Oliveira & Silva, 2020;Gonzaga de Oliveira & Carvalho, 2022). A traditional metaheuristic algorithm significantly reduces the bandwidth of very small-sized matrices at a high cost, whereas the other algorithms do not perform well.…”

Section: Metaheuristic Algorithmsmentioning

confidence: 99%

“…A traditional metaheuristic algorithm significantly reduces the bandwidth of very small-sized matrices at a high cost, whereas the other algorithms do not perform well. However, a conventional metaheuristic algorithm takes several orders of magnitude more running time than low-cost graph-theory heuristics for bandwidth reduction (Gonzaga de Oliveira et al, 2016Oliveira et al, , 2017Oliveira et al, , 2018bGonzaga de Oliveira & Silva, 2020;Gonzaga de Oliveira & Carvalho, 2022).…”

Section: Metaheuristic Algorithmsmentioning

confidence: 99%

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An Evaluation of Heuristic Methods for the Bandwidth Reduction of Large-Scale Graphs

Gonzaga de Oliveira

2023

Pesqui. Oper.

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This paper studies the bandwidth reduction problem for large-scale sparse matrices in serial computations. A heuristic for bandwidth reduction reorders the rows and columns of a given sparse matrix, placing entries with a non-null value as close to the main diagonal as possible. Recently, a paper proposed the FNCHC+ heuristic. The heuristic method is a variant of the Fast Node Centroid Hill-Climbing algorithm. The FNCHC+ heuristic presented better results than the other existing heuristics in the literature when applied to reduce the bandwidth of large-scale graphs (of the underline matrices) with sizes up to 18.6 million vertices and up to 57.2 million edges. The present paper provides new experiments with even larger graphs. Specifically, the present study performs experiments with test problems containing up to 24 million vertices and 130 million edges. The results confirm that the FNCHC+ algorithm is the state-of-the-art metaheuristic algorithm for reducing the bandwidth of large-scale matrices.

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Section: Metaheuristic Algorithmsmentioning

confidence: 99%

Section: Metaheuristic Algorithmsmentioning

confidence: 99%

An Evaluation of Heuristic Methods for the Bandwidth Reduction of Large-Scale Graphs

Gonzaga de Oliveira

2023

Pesqui. Oper.

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“…Metaheuristic-based algorithms for bandwidth reduction began to be proposed mainly in the 1990s [ 12 ]. As previously mentioned, since bandwidth reduction is a relevant problem in various scientific and engineering fields, practitioners have applied the best-known metaheuristics in the design of heuristics for bandwidth reduction [ 12 ], including tabu search [ 13 , 14 ], GRASP [ 15 ], genetic algorithm [ 16 , 17 ], ant colony optimization [ 6 , 7 , 18 – 21 ], particle swarm optimization [ 22 ], simulated annealing [ 23 , 24 ], variable neighbourhood search [ 25 ], genetic programming [ 26 – 28 ] and self-organizing maps [ 29 , 30 ].…”

Section: Introductionmentioning

confidence: 99%

A Biased Random-Key Genetic Algorithm for Bandwidth Reduction

Silva

Brandão

Morais

et al. 2020

Lecture Notes in Computer Science

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The bandwidth minimization problem is a well-known -hard problem. This paper describes our experience in implementing a biased random-key genetic algorithm for the bandwidth reduction problem. Specifically, this paper compares the results of the new algorithm with the results yielded by four approaches. The results obtained on a set of standard benchmark matrices taken from the SuiteSparse sparse matrix collection indicated that the novel approach did not compare favorably with the state-of-the-art metaheuristic algorithm for bandwidth reduction. The former seems to be faster than the latter. On the other hand, the design of heuristics for bandwidth reduction is a very consolidated research area. Thus, a paradigm shift seems necessary to design a heuristic with better results than the state-of-the-art meta-heuristic algorithm at shorter execution times.

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Iterated Local Search with Tabu Search for the Bandwidth Reduction Problem in Graphs

Abreu,

Gonzaga de Oliveira

2024

Lecture Notes in Computer Science

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A New Heuristic for Bandwidth and Profile Reductions of Matrices Using a Self-organizing Map

Cited by 8 publications

References 13 publications

An Evaluation of Heuristic Methods for the Bandwidth Reduction of Large-Scale Graphs

An Evaluation of Heuristic Methods for the Bandwidth Reduction of Large-Scale Graphs

A Biased Random-Key Genetic Algorithm for Bandwidth Reduction

Iterated Local Search with Tabu Search for the Bandwidth Reduction Problem in Graphs

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