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Evolving reordering algorithms using an ant colony hyperheuristic approach for accelerating the convergence of the ICCG method

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Abstract

This paper proposes a novel ant colony hyperheuristic approach for reordering the rows and columns of symmetric positive definite matrices. This ant colony hyperheuristic approach evolves heuristics for bandwidth reduction applied to instances arising from specific application areas with the objective of generating low-cost reordering algorithms. This paper evaluates the resulting reordering algorithm in each application area against state-of-the-art reordering algorithms with the purpose of reducing the running times of the zero-fill incomplete Cholesky-preconditioned conjugate gradient method. The results obtained on a wide-ranging set of standard benchmark matrices show that the proposed approach compares favorably with state-of-the-art reordering algorithms when applied to instances arising from computational fluid dynamics, structural, and thermal problems.

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Acknowledgements

The Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) supported the development of this work. The ant colony image used in Fig. 1 is a free image taken from https://pixabay.com/photos/anthill-ant-insect-nature-colony-140643.

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  1. Departamento de Ciência da Computação, Universidade Federal de Lavras, Lavras, Brazil

    S. L. Gonzaga de Oliveira & L. M. Silva

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  1. S. L. Gonzaga de Oliveira
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  2. L. M. Silva
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Correspondence to S. L. Gonzaga de Oliveira.

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de Oliveira, S.L.G., Silva, L.M. Evolving reordering algorithms using an ant colony hyperheuristic approach for accelerating the convergence of the ICCG method. Engineering with Computers 36, 1857–1873 (2020). https://doi.org/10.1007/s00366-019-00801-5

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