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Metaheuristic algorithms for the bandwidth reduction of large-scale matrices

Author

Listed:
  • S. L. Gonzaga de Oliveira

    (Universidade Federal de Lavras)

  • C. Carvalho

    (Universidade Federal de Lavras)

Abstract

This paper considers 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. Thus, the method places entries with a nonzero value as close to the main diagonal as possible. Bandwidth optimization is a critical issue for many scientific and engineering applications. This manuscript proposes two heuristics for the bandwidth reduction of large-scale matrices. The first is a variant of the Fast Node Centroid Hill-Climbing algorithm, and the second is an algorithm based on the iterated local search metaheuristic. This paper then experimentally compares the solutions yielded by the new reordering algorithms with the bandwidth solutions delivered by state-of-the-art heuristics for the problem, including tests on large-scale problem matrices. A considerable number of results for a range of realistic test problems showed that the performance of the two new algorithms compared favorably with state-of-the-art heuristics for bandwidth reduction. Specifically, the variant of the Fast Node Centroid Hill-Climbing algorithm yielded the overall best bandwidth results.

Suggested Citation

  • S. L. Gonzaga de Oliveira & C. Carvalho, 2022. "Metaheuristic algorithms for the bandwidth reduction of large-scale matrices," Journal of Combinatorial Optimization, Springer, vol. 43(4), pages 727-784, May.
    • Handle: RePEc:spr:jcomop:v:43:y:2022:i:4:d:10.1007_s10878-021-00801-6
    DOI: 10.1007/s10878-021-00801-6
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    References listed on IDEAS

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    1. Marti, Rafael & Laguna, Manuel & Glover, Fred & Campos, Vicente, 2001. "Reducing the bandwidth of a sparse matrix with tabu search," European Journal of Operational Research, Elsevier, vol. 135(2), pages 450-459, December.
    2. Lim, Andrew & Rodrigues, Brian & Xiao, Fei, 2006. "Heuristics for matrix bandwidth reduction," European Journal of Operational Research, Elsevier, vol. 174(1), pages 69-91, October.
    3. Mladenovic, Nenad & Urosevic, Dragan & Pérez-Brito, Dionisio & García-González, Carlos G., 2010. "Variable neighbourhood search for bandwidth reduction," European Journal of Operational Research, Elsevier, vol. 200(1), pages 14-27, January.
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