Abstract
This paper presents a novel hybrid algorithm for combinatorial optimization problems based on mixing the cross-entropy (CE) method and a Hopfield neural network. The algorithm uses the CE method as a global search procedure, whereas the Hopfield network is used to solve the constraints associated to the problems. We have shown the validity of our approach in several instance of the generalized frequency assignment problem.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Talbi, E.: A taxonomy of hybrid metaheuristics. Journal of Heuristics 8, 541–564 (2002)
Blum, C., Roli, A.: Metaheuristics in combinatorial optimization: overview and conceptual comparison. ACM Computing Surveys 35, 268–308 (2003)
Krasnogor, N., Smith, J.: A tutorial for competent memetic algorithms: model, taxonomy, and design issues. IEEE Trans. Evol. Comput. 9(5), 474–488 (2005)
Rubinstein, R.Y.: The simulated entropy method for combinatorial and continous optimization. Methodology and computing in applied probability 2, 127–190 (2002)
Rubinstein, R.Y., Kroese, D.P.: The cross-entropy method: a unified approach to combinatorial optimization, Monte-carlo simulation and machine learning. Springer, NY (2004)
Hopfield, J.: Neurons and physical systems with emergent collective computational abilities. Proc. Natl. Acad. Sci. 79, 2554–2558 (1982)
De Boer, P., Kroese, D.P., Mannor, S., Rubinstein, R.Y.: A tutorial on the cross-entropy method. Annals of Operations Research 134, 19–67 (2005)
Shrivastava, Y., Dasgupta, S., Reddy, S.: Guaranteed convergence in a class of Hopfield networks. IEEE Trans. Neural Networks 3, 951–961 (1992)
Salcedo-Sanz, S., Bousoño-Calzón, C.: A portable and scalable algorithm for a class of constrained combinatorial optimization problems. Computers & Operations Research 32, 2671–2687 (2005)
Balicki, J., Stateczny, A., Zak, B.: Genetic algorithms and Hopfield neural networks to solve combinatorial optimization problems. Applied Mathematics and Computer Science 10(3), 568–592 (1997)
Watanabe, Y., Mizuguchi, N., Fujii, Y.: Solving optimization problems by using a Hopfield neural network and genetic algorithm combination. Systems and Computers in Japan 29(10), 68–73 (1998)
Salcedo-Sanz, S., Bousoño-Calzón, C.: A hybrid neural-genetic algorithm for the frequency assignment problem in satellite communications. Applied Intelligence 22, 207–218 (2005)
Bousoño-Calzón, C., Figueiras-Vidal, A.R.: Emergent techniques for dynamic frequency assignment: merging genetic algorithms and neural networks. In: Aerospace. Proc. of the RTO IST Symposium on Frequency Assignment, Sharing and Conservation in Systems, vol. 32, pp. 12/1–12/5 (1998)
Salcedo-Sanz, S., Santiago-Mozos, R., Bousoño-Calzón, C.: A hybrid Hopfield network-simulated annealing approach for frequency assignment in satellite communications systems. IEEE Trans. Systems, Man and Cybernetics, part B 34(2), 1108–1116 (2004)
Calderón-Macías, C., Sen, M.K., Stoffa, P.L.: Hopfield neural networks, and mean field annealing for seismic deconvolution and multiple attenuation. Geophysics 62(3), 992–1002 (1997)
Funabiki, N., Takefuji, Y.: A neural network parallel algorithm for channel assignment problems in cellular radio networks. IEEE Trans. Veh. Technol. 42(4), 430–437 (1992)
Goldberg, D.: Genetic algorithms in search, optimization and machine learning. Addison-Wesley, Reading, MA (1989)
Lai, W.K., Coghill, G.C.: Channel assignment through evolutionary optimization. IEEE Trans. Veh. Technol. 55(1), 91–95 (1996)
José-Revuelta, L.M.S.: A new adaptive genetic algorithm for fixed channel assignment. Information Sciences 177(13), 2655–2678 (2007)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Ortiz-García, E.G., Pérez-Bellido, Á.M. (2007). Hybrid Cross-Entropy Method/Hopfield Neural Network for Combinatorial Optimization Problems. In: Yin, H., Tino, P., Corchado, E., Byrne, W., Yao, X. (eds) Intelligent Data Engineering and Automated Learning - IDEAL 2007. IDEAL 2007. Lecture Notes in Computer Science, vol 4881. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-77226-2_116
Download citation
DOI: https://doi.org/10.1007/978-3-540-77226-2_116
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-77225-5
Online ISBN: 978-3-540-77226-2
eBook Packages: Computer ScienceComputer Science (R0)