A genetic programming approach to the matrix bandwidth-minimization problem

Abstract

The bandwidth of a sparse matrix is the distance from the main diagonal beyond which all elements of the matrix are zero. The bandwidth minimisation problem for a matrix consists of finding the permutation of rows and columns of the matrix which ensures that the non-zero elements are located in as narrow a band as possible along the main diagonal. This problem, which is known to be NP-complete, can also be formulated as a vertex labelling problem for a graph whose edges represent the non-zero elements of the matrix. In this paper, a Genetic Programming approach is proposed and tested against two of the best-known and widely used bandwidth reduction algorithms. Results have been extremely encouraging. © 2010 Springer-Verlag.