Ant colony optimization with hill climbing for the bandwidth minimization problem

Authors:
Andrew Lim;Jing Lin;Brian Rodrigues;Fei Xiao
Affiliations:
Department of Industrial Engineering and Engineering Management, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong;Department of Computer Science, National University of Singapore, 3 Science Drive 2, Singapore 117543, Singapore;School of Business, Singapore Management University, 469 Bukit Timah Road, Singapore 259756, Singapore;Department of Computer Science, National University of Singapore, 3 Science Drive 2, Singapore 117543, Singapore
Venue:
Applied Soft Computing
Year:
2006

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Abstract

In this work, the problem of reducing the bandwidth of sparse matrices by permuting rows and columns is addressed and solved using a hybrid ant system to generate high-quality renumbering which is refined by a hill climbing local search heuristic. Computational experiments compare the algorithm with the well-known GPS algorithm, as well as recently proposed methods. These show the new approach to be as good as current best algorithms. In addition, an algorithm to randomly generate matrices with known optimal bandwidth is developed and used to evaluate results. Comparisons show that the new algorithm was able to find either the optimal solution or a solution very close to the optimal for most instances.