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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Adolphson, D., & Hu, T. C. (1973). Optimal linear ordering. SIAM Journal on Applied Mathematics, 25(3), 403–423.
Andrade, D. V., & Resende, M. G. C. (2007a). GRASP with path-relinking for network migration scheduling. In Proceedings of international network optimization conference.
Andrade, D. V., & Resende, M. G. C. (2007b). GRASP with evolutionary path-relinking. In Proceedings of seventh metaheuristics international conference (MIC).
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).
Cohoon, J., & Sahni, S. (1987). Heuristics for the board permutation problem. Journal of VLSI and Computer Systems, 2, 37–61.
Feo, T. A., & Resende, M. G. C. (1989). A probabilistic heuristic for a computationally difficult set covering problem. Operations Research Letters, 8, 67–71.
Feo, T. A., & Resende, M. G. C. (1995). Greedy randomized adaptive search procedures. Journal of Global Optimization, 6, 109–133.
Gavril, F. (1977). Some NP-complete problems on graphs. In Proceedings of the 11th conference on information sciences and systems (pp. 91–95).
Glover, F., & Laguna, M. (1997). Tabu search. Norwell: Kluwer Academic.
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.
Laguna, M., & Martí, R. (2003). Scatter search: methodology and implementations in C. Boston: Kluwer Academic.
Makedon, F., & Sudborough, I. H. (1989). On minimizing width in linear layouts. Discrete Applied Mathematics, 23(3), 243–265.
Makedon, F., Papadimitriou, C., & Sudbourough, I. H. (1985). Topological bandwidth. SIAM Journal on Algebraic and Discrete Methods, 6(3), 418–444.
Martí, R., Campos, V., & Piñana, E. (2008). Branch and bound for the matrix bandwidth minimization. European Journal of Operational Research, 186, 513–528.
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.
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.
Resende, M. G. C., & Andrade, D. V. (2009). Method and system for network migration scheduling. United States Patent Application Publication US2009/0168665.
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.
Resende, M. G. C., & Werneck, R. F. (2004). A hybrid heuristc for the p-median problem. Journal of Heuristics, 10, 59–88.
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.
Rolim, J., Sýkora, O., & Vrt’o, I. (1995). Cutwidth of the de Bruijn graph. RAIRO. Informatique Théorique et Applications, 29(6), 509–514.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Pantrigo, J.J., Martí, R., Duarte, A. et al. Scatter search for the cutwidth minimization problem. Ann Oper Res 199, 285–304 (2012). https://doi.org/10.1007/s10479-011-0907-2
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10479-011-0907-2