Abstract
This paper studies heuristics for the bandwidth reduction of large-scale matrices in serial computations. Bandwidth optimization is a demanding subject for a large number of scientific and engineering applications. A heuristic for bandwidth reduction labels the rows and columns of a given sparse matrix. The algorithm arranges entries with a nonzero coefficient as close to the main diagonal as possible. This paper modifies an ant colony hyper-heuristic approach to generate expert-level heuristics for bandwidth reduction combined with a Hill-Climbing strategy when applied to matrices arising from specific application areas. Specifically, this paper uses low-cost state-of-the-art heuristics for bandwidth reduction in tandem with a Hill-Climbing procedure. The results yielded on a wide-ranging set of standard benchmark matrices showed that the proposed strategy outperformed low-cost state-of-the-art heuristics for bandwidth reduction when applied to matrices with symmetric sparsity patterns.
Highlights
The solution of large-scale sparse linear systems Ax = b, where A = [aij] is an n × n large-scale sparse matrix, x is the unknown n-vector solution, and b is a known n-vector, is essential in various application areas in science and engineering, such as computational fluid dynamics (CFD), electromagnetics, structural, thermal, and elsewhere
We compare the results yielded by the strategies with low-cost state-of-the-art heuristics for the bandwidth reduction of symmetric and nonsymmetric matrices arising from six application areas
We evaluate the results with the Reverse Cuthill–McKee (RCM), RBFS-GL, and KP-band heuristics and the resulting heuristics from the ant colony hyper-heuristic (ACHH) algorithm [17]
Summary
Practitioners employ heuristics for bandwidth reduction to provide low processing costs for solving large sparse linear systems by iterative methods [19,20]. Previous publications [5,15,17,19,20] have reviewed various heuristics and have indicated the most promising low-cost heuristics for bandwidth reduction so that they can be used in a preprocessing step when solving linear systems [17]. This article proposes an approach to reduce matrix bandwidth through low-cost heuristics, which are practical for large-scale problems, in tandem with an improved Hill-Climbing local search procedure. This paper evaluates the resulting heuristics together with the Hill-Climbing algorithm evolved by the modified ACHH system in each application area against the most promising low-cost heuristics for bandwidth reduction.
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