Abstract
The Cut width Minimization Problem is a NP-Hard problem that is found in the VLSI design, graph drawing, design of compilers and linguistics. Developing solutions that could solve it efficiently is important due to its impact in areas that are critical for society. It consists in finding the linear array of an undirected graph that minimizes the maximum number of edges that are cut. In this paper we propose a genetic algorithm applied to the Cut width Minimization Problem. As the configuration of a metaheuristic has a great impact on the performance, we also propose a Fuzzy Logic controller that is used to adjust the parameters of the GA during execution time to guide it during the exploration process.
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References
M. R. Garey, D. S. Johnson, and others, Computers and Intractability: A Guide to the Theory of NP-completeness. WH freeman San Francisco, 1979.
E. Korach and N. Solel, “Tree-width, path-width, and cutwidth,” Discret. Appl. Math., vol. 43, no. 1, pp. 97–101, 1993.
T. Ohtsuki, H. Mori, E. Kuh, T. Kashiwabara, and T. Fujisawa, “One-dimensional logic gate assignment and interval graphs,” Circuits Syst. IEEE Trans., vol. 26, no. 9, pp. 675–684, 1979.
M. Suderman, “Pathwidth and layered drawings of trees,” Int. J. Comput. Geom. Appl., vol. 14, no. 03, pp. 203–225, 2004.
H. Bodlaender, J. Gustedt, and J. A. Telle, “Linear-time register allocation for a fixed number of registers,” in Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms, 1998, pp. 574–583.
Z. Tuza, “Narrowness, Path-width, and their Application in Natural Language Processing.”
E. Pardo, N. Mladenović, J. Pantrigo, and A. Duarte, “Variable formulation search for the cutwidth minimization problem,” Appl. Soft Comput., vol. 13, pp. 2242–2252, 2013.
D. Andrade and M. Resende, “GRASP with path-relinking for network migration scheduling,” … Int. Netw. …, pp. 1–7, 2007.
D. Andrade and M. Resende, “GRASP with evolutionary path-relinking,” Proc. Seventh Metaheuristics …, pp. 6–9, 2007.
J. J. Pantrigo, R. Martí, A. Duarte, and E. G. Pardo, “Scatter search for the cutwidth minimization problem,” Ann. Oper. Res., vol. 199, no. 1, pp. 285–304, 2012.
V. Campos, E. Piñana, and R. Martí, “Adaptive memory programming for matrix bandwidth minimization,” Ann. Oper. Res., pp. 1–17, 2006.
J. H. Holland, Adaptation in Natural and Artificial Systems, vol. Ann Arbor. 1975.
L. A. Zadeh, “Fuzzy sets,” Inf. Control, vol. 8, no. 3, pp. 338–353, Jun. 1965.
A. Michael and H. Takagi, “Dynamic control of genetic algorithms using fuzzy logic techniques,” in Proceedings of the Fifth International Conference on Genetic Algorithms, 1993, pp. 76–83.
F. Valdez, P. Melin, and O. Castillo, “Fuzzy control of parameters to dynamically adapt the {PSO} and {GA} Algorithms,” in {FUZZ-IEEE} 2010, {IEEE} International Conference on Fuzzy Systems, Barcelona, Spain, 18-23 July, 2010, Proceedings, 2010, pp. 1–8.
F. Valdez and P. Melin, “A New Evolutionary Method with Particle Swarm Optimization and Genetic Algorithms Using Fuzzy Systems to Dynamically Parameter Adaptation,” in Soft Computing for Recognition Based on Biometrics, 2010, pp. 225–243.
R. Martí, J. Pantrigo, A. Duarte, and E. Pardo, “Branch and bound for the cutwidth minimization problem,” Comput. Oper. …, vol. 40, pp. 137–149, 2013.
L. Rutkowski, Flexible neuro-fuzzy systems: structures, learning and performance evaluation, vol. 771. Springer Science & Business Media, 2006.
D. A. Martí R. Pantrigo J.J. and P. E.G., “Optsicom Project.” 2010.
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Fraire-Huacuja, H.J., López-Locés, M.C., García, N.C., Pecero, J.E., Rangel, R.P. (2017). Solving the Cut Width Optimization Problem with a Genetic Algorithm Approach. In: Melin, P., Castillo, O., Kacprzyk, J. (eds) Nature-Inspired Design of Hybrid Intelligent Systems. Studies in Computational Intelligence, vol 667. Springer, Cham. https://doi.org/10.1007/978-3-319-47054-2_48
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DOI: https://doi.org/10.1007/978-3-319-47054-2_48
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