A hyper-heuristic approach to evolving algorithms for bandwidth reduction based on genetic programming

Abstract

The bandwidth reduction problem is a well-known NP-complete graphlayout problem that consists of labeling the vertices of a graph with integer labels in such a way as to minimize the maximum absolute difference between the labels of adjacent vertices. The problem is isomorphic to the important problem of reordering the rows and columns of a symmetric matrix so that its non-zero entries are maximally close to the main diagonal - a problem which presents itself in a large number of domains in science and engineering. A considerable number of methods have been developed to reduce the bandwidth, among which graph-theoretic approaches are typically faster and more effective. In this paper, a hyper-heuristic approach based on genetic programming is presented for evolving graph-theoretic bandwidth reduction algorithms. The algorithms generated from our hyper-heuristic are extremely effective. We test the best of such evolved algorithms on a large set of standard benchmarks from the Harwell-Boeing sparse matrix collection against two state-of-the-art algorithms from the literature. Our algorithm outperforms both algorithms by a significant margin, clearly indicating the promise of the approach. © Springer-Verlag London Limited 2011.