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.

本文考虑了串行计算中大规模稀疏矩阵的带宽减少问题。带宽减少的启发式重新排序给定稀疏矩阵的行和列。因此，该方法将具有非零值的条目放置在尽可能靠近主对角线的位置。带宽优化是许多科学和工程应用的关键问题。这份手稿提出了两种减少大规模矩阵带宽的启发式方法。第一个是快速节点质心爬山算法的变体，第二个是基于迭代局部搜索元启发式的算法。然后，本文通过实验将新的重新排序算法产生的解决方案与最先进的启发式算法为该问题提供的带宽解决方案进行了比较，包括对大规模问题矩阵的测试。一系列实际测试问题的大量结果表明，这两种新算法的性能与最先进的带宽减少启发式算法相比具有优势。具体来说，快速节点质心爬山算法的变体产生了总体最佳带宽结果。