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An Improved Heuristic for the Bandwidth Minimization Based on Genetic Programming

  • P. C. Pop
  • O. Matei
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6679)

Abstract

In this work we develop an improved heuristic based on genetic programming (GP) for the matrix bandwidth minimization problem (MBMP). This problem consists in rearranging the rows and columns of a sparse matrix such that the non-zero elements are in a band as close as possible to the main diagonal. We evaluated our heuristic on a set of 25 benchmark instances from the literature and compared with state-of-the-art algorithms. The obtained results are very encouraging and point out that GP is an appropriate method for solving the MBMP.

Keywords

bandwidth minimization problem heuristics genetic programming 

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References

  1. 1.
    Corso, G.D., Manzini, G.: Finding exact solutions to the bandwidth minimization problem. Computing 62(3), 189–203 (1999)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Cuthill, E., McKee, J.: Reducing the bandwidth of sparse symmetric matrices. In: Proc. 24-th Nat. Conf., pp. 157–172. ACM, New York (1969)Google Scholar
  3. 3.
    Koohestani, B., Poli, R.: A Genetic Programming Approach to the Matrix Bandwidth-Minimization Problem. In: Schaefer, R., Cotta, C., Kołodziej, J., Rudolph, G. (eds.) PPSN XI. LNCS, vol. 6239, pp. 482–491. Springer, Heidelberg (2010)Google Scholar
  4. 4.
    Koza, J.R.: Genetic Programming: On the Programming of Computers by Means of Natural Selection. The MIT Press, Cambridge (1992)zbMATHGoogle Scholar
  5. 5.
    Lim, A., Rodriguez, B., Xiao, F.: Heuristics for matrix bandwidth reduction. European Journal of Operational Research 174(1), 69–91 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Lim, A., Lin, J., Xiao, F.: Particle swarm optimization and hill climbing for the bandwidth minimization problem. Applied Intelligence 26, 175–182 (2007)CrossRefzbMATHGoogle Scholar
  7. 7.
    Marti, R., Campos, V., Pinana, E.: A branch and bound algorithm for the matrix bandwidth minimization. European Journal of Operational Research 186, 513–528 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Marti, R., Laguna, M., Glover, F., Campos, V.: Reducing the bandwidth of a sparse matrix with tabu search. European Journal of Operational Research 135(2), 211–220 (2001)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Matei, O.: Evolutionary Computation: Principles and Practices. Risoprint (2008)Google Scholar
  10. 10.
    Mladenovic, N., Urosevic, D., Perez-Brito, D., García-González, C.G.: Variable neighbourhood search for bandwidth reduction. European Journal of Operational Research 200, 14–27 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Papadimitriou, C.H.: The NP-completeness of the bandwidth minimization problem. Computing 16, 263–270 (1976)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Pinana, E., Plana, I., Campos, V., Marti, R.: GRASP and path relinking for the matrix bandwidth minimization. European Journal of Operational Research 153, 200–210 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Rodriguez-Tello, E., Jin-Kao, H., Torres-Jimenez, J.: An improved simulated annealing algorithm for bandwidth minimization. European Journal of Operational Research 185, 1319–1335 (2008)CrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • P. C. Pop
    • 1
  • O. Matei
    • 2
  1. 1.Dept. of Mathematics and InformaticsNorth University of Baia MareRomania
  2. 2.Dept. of Electrical EngineeringNorth University of Baia MareRomania

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