Annals of Operations Research

, Volume 199, Issue 1, pp 285–304 | Cite as

Scatter search for the cutwidth minimization problem

  • Juan J. Pantrigo
  • Rafael Martí
  • Abraham Duarte
  • Eduardo G. Pardo
Article

Abstract

The cutwidth minimization problem consists of finding a linear layout of a graph so that the maximum linear cut of edges is minimized. This NP-hard problem has applications in network scheduling, automatic graph drawing and information retrieval. We propose a heuristic method based on the Scatter Search (SS) methodology for finding approximate solutions to this optimization problem. This metaheuristic explores solution space by evolving a set of reference points. Our SS method is based on a GRASP constructive algorithm, a local search strategy based on insertion moves and voting-based combination methods. We also introduce a new measure to control the diversity in the search process. Empirical results with 252 previously reported instances indicate that the proposed procedure compares favorably to previous metaheuristics for this problem, such as Simulated Annealing and Evolutionary Path Relinking.

Keywords

Cutwidth Metaheuristics Scatter search 

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References

  1. Adolphson, D., & Hu, T. C. (1973). Optimal linear ordering. SIAM Journal on Applied Mathematics, 25(3), 403–423. CrossRefGoogle Scholar
  2. Andrade, D. V., & Resende, M. G. C. (2007a). GRASP with path-relinking for network migration scheduling. In Proceedings of international network optimization conference. Google Scholar
  3. Andrade, D. V., & Resende, M. G. C. (2007b). GRASP with evolutionary path-relinking. In Proceedings of seventh metaheuristics international conference (MIC). Google Scholar
  4. Botafogo, R. A. (1993). Cluster analysis for hypertext systems. In 16th annual international ACM-SIGIR conference on research and development in information retrieval (pp. 116–125). Google Scholar
  5. Cohoon, J., & Sahni, S. (1987). Heuristics for the board permutation problem. Journal of VLSI and Computer Systems, 2, 37–61. Google Scholar
  6. Feo, T. A., & Resende, M. G. C. (1989). A probabilistic heuristic for a computationally difficult set covering problem. Operations Research Letters, 8, 67–71. CrossRefGoogle Scholar
  7. Feo, T. A., & Resende, M. G. C. (1995). Greedy randomized adaptive search procedures. Journal of Global Optimization, 6, 109–133. CrossRefGoogle Scholar
  8. Gavril, F. (1977). Some NP-complete problems on graphs. In Proceedings of the 11th conference on information sciences and systems (pp. 91–95). Google Scholar
  9. Glover, F., & Laguna, M. (1997). Tabu search. Norwell: Kluwer Academic. CrossRefGoogle Scholar
  10. Karger, D. R. (1999). A randomized fully polynomial time approximation scheme for the all-terminal network reliability problem. SIAM Journal on Computing, 29(2), 492–514. CrossRefGoogle Scholar
  11. Laguna, M., & Martí, R. (2003). Scatter search: methodology and implementations in C. Boston: Kluwer Academic. CrossRefGoogle Scholar
  12. Makedon, F., & Sudborough, I. H. (1989). On minimizing width in linear layouts. Discrete Applied Mathematics, 23(3), 243–265. CrossRefGoogle Scholar
  13. Makedon, F., Papadimitriou, C., & Sudbourough, I. H. (1985). Topological bandwidth. SIAM Journal on Algebraic and Discrete Methods, 6(3), 418–444. CrossRefGoogle Scholar
  14. Martí, R., Campos, V., & Piñana, E. (2008). Branch and bound for the matrix bandwidth minimization. European Journal of Operational Research, 186, 513–528. CrossRefGoogle Scholar
  15. Piñana, E., Plana, I., Campos, V., & Martí, R. (2004). GRASP and path relinking for the matrix bandwidth minimization. European Journal of Operational Research, 153(1), 200–210. CrossRefGoogle Scholar
  16. Raspaud, A., Schröder, H., Sýkora, O., Török, L., & Vrt’o, I. (2009). Antibandwidth and cyclic antibandwidth of meshes and hypercubes. Discrete Mathematics, 309, 3541–3552. CrossRefGoogle Scholar
  17. Resende, M. G. C., & Andrade, D. V. (2009). Method and system for network migration scheduling. United States Patent Application Publication US2009/0168665. Google Scholar
  18. Resende, M. G. C., & Ribeiro, C. C. (2003). Greedy randomized adaptive search procedures. In F. Glover & G. Kochenberger (Eds.), Handbook of metaheuristics (pp. 219–250). Norwell: Kluwer Academic. Google Scholar
  19. Resende, M. G. C., & Werneck, R. F. (2004). A hybrid heuristc for the p-median problem. Journal of Heuristics, 10, 59–88. CrossRefGoogle Scholar
  20. Resende, M. G. C., Martí, R., Gallego, M., & Duarte, A. (2010). GRASP and path relinking for the max-min diversity problem. Computers & Operations Research, 37, 498–508. CrossRefGoogle Scholar
  21. Rolim, J., Sýkora, O., & Vrt’o, I. (1995). Cutwidth of the de Bruijn graph. RAIRO. Informatique Théorique et Applications, 29(6), 509–514. Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Juan J. Pantrigo
    • 1
  • Rafael Martí
    • 2
  • Abraham Duarte
    • 1
  • Eduardo G. Pardo
    • 1
  1. 1.Departamento de Ciencias de la ComputaciónUniversidad Rey Juan CarlosMostolesSpain
  2. 2.Departamento de Estadística e Investigación OperativaUniversidad de ValenciaValenciaSpain

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