More Effective Reduction of the Bandwidth of Sparse Symmetric Matrices When Using Metaheuristics

Sparse matrices appear in a number of problems related to science and engineering. The performance of algorithms designed for solving such problems depends significantly on the bandwidth of the problem matrix.  The bandwidth of a sparse symmetric matrix is the distance from the main diagonal beyond which all elements of the matrix are zero. Minimizing the bandwidth of a matrix is an NP-complete problem. Considering the importance of this problem, numerous algorithms have so far been presented for its solution among which metaheuristic algorithms have performed much better than other algorithms. The issue with using metaheuristic algorithms for addressing this problem is that the bandwidth size, which has been employed for comparing the quality of solutions produced by these algorithms in almost all previous studies, is not an appropriate measure, and therefore cannot direct the search process towards high-quality solutions. In this research, the above-mentioned issue is investigated, and a new approach is presented for dealing with it.