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http://dx.doi.org/10.11627/jkise.2013.36.2.8

A Continuous Optimization Algorithm Using Equal Frequency Discretization Applied to a Fictitious Play  

Lee, Chang-Yong (Department of Industrial and Systems Engineering, Kongju National University)
Publication Information
Journal of Korean Society of Industrial and Systems Engineering / v.36, no.2, 2013 , pp. 8-16 More about this Journal
Abstract
In this paper, we proposed a new method for the determination of strategies that are required in a continuous optimization algorithm based on the fictitious play theory. In order to apply the fictitious play theory to continuous optimization problems, it is necessary to express continuous values of a variable in terms of discrete strategies. In this paper, we proposed a method in which all strategies contain an equal number of selected real values that are sorted in their magnitudes. For comparative analysis of the characteristics and performance of the proposed method of representing strategies with respect to the conventional method, we applied the method to the two types of benchmarking functions: separable and inseparable functions. From the experimental results, we can infer that, in the case of the separable functions, the proposed method not only outperforms but is more stable. In the case of inseparable functions, on the contrary, the performance of the optimization depends on the benchmarking functions. In particular, there is a rather strong correlation between the performance and stability regardless of the benchmarking functions.
Keywords
Fictitious Play; Continuous Optimization Algorithm; Equal Frequency Discretization; Equal width Discretization;
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Times Cited By KSCI : 1  (Citation Analysis)
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1 Back, T. and Schwefel, H.-P., An overview of evolutionary algorithms for parameter optimization. Evolutionary Computation, 1993, Vol. 1, p 1-23.   DOI
2 Brown, G., Iterative Solutions of Games by Fictitious Play, in Activity Analysis of Production and Allocation, T. Koopmans (Ed.), New York : Wiley, 1951.
3 Das, K. and Vyas, P., A suitability study of discretization methods for associative classifiers. International Journal of Computer Applications, 2010, Vol. 5, p 46-51.   DOI
4 Dougherty, J., Kohavi, R., and Sahami, M., Supervised and unsupervised discretization of continuous features, in Machine Learning : Proceedings of the 12th International conference, A. Prieditis and S. Russell eds, Morgan Kaufmann Publisher, San Francisco, CA, 1995.
5 Fogel, D., Evolutionary Computation : Toward a New Philosophy of Machine Intelligence. IEEE Press, NY, 1995.
6 Fudenberg, D. and Kreps, D., Learning mixed equilibria, Games Econ. Behav., 1993, Vol. 5, p 320-367.   DOI
7 Fudenberg, D. and Levine, D., "The Theory of Learning in Games," Cambridge : MIT Press, 1998.
8 Garcia, A., Reaume, D., and Smith, R., Fictitious play for finding system optimal routings in dynamic traffic networks. Transportation Research Part B : Methodological, 2000, Vol. 34, p 147-156.   DOI
9 Garey, M. and Johnson, D., Computers and Intractability : A Guide to the Theory of NP-Completeness, W.H. Freeman, 1979.
10 Long, C., Zhang, Q., Li, B., Yang, H., and Guan, X., Non-Cooperative Power Control for Wireless Ad Hoc Networks with Repeated Games. IEEE Journal of selected areas in communications, 2007, Vol. 25, p 1101- 1112.   DOI
11 Lambert, T., Epelman, M., and Smith, R., A fictitious play approach to large-scale optimization. Operations Research, 2005, Vol. 53, p 477-489.   DOI
12 Lee, C. and Yao, X., Evolutionary programming using mutations based on the Levy probability distribution. IEEE Trans. Evol. Comput., 2004, Vol. 8, p 1-13.   DOI
13 Monderer, D. and Shapley, L., Fictitious play property for games with identical interests. Journal of Economic Theory, 1996, Vol. 68, p 258-265.   DOI
14 Lee, C., A study on a continuous optimization algorithm based on the fictitious play theory. Journal of KIISE : Software and Applications, 2012, Vol. 39, No. 10, p 787-795.
15 Lee, D. and Lee, C.-Y., Simulated Annealing Algorithm Using Cauchy-Gaussian Probability Distributions. Joural of the society of Korea industrial and systems engineering, 2010, Vol. 33, p 130-136.
16 Mitchell, M., An Introduction to Genetic Algorithms. Cambridge, MA : MIT Press, 1996.
17 Nash, J., Equilibrium points in n-person games. Proceedings of the National Academy of Sciences, 1950, Vol. 36, p 48-49.
18 Nash, J., Non-Cooperative Games. The Annals of Mathematics, 1951, Vol. 54, p 286-295.   DOI
19 Rezek, I., Leslie, D., Reece, S., Roberts, S., Rogers, A., Dash, R., and Jennings, N., On similarities between Inference in Game Theory and Machine Learning, Journal of Artificial Intelligence Research, 2008, Vol. 33, p 259-283.
20 Schaffer, J., Caruana, R., Eshelman, L., and Das, R., A study of control parameters affecting online performance of genetic algorithms for function optimization, in Proc. of the 3rd Int'l Conf. on GAs, edited by J. Schaffer. Morgan Kauffman, San Francisco, 1989, p 51-60.
21 Talbi, E.-G., Metaheuristics : from design to implementation (Wiley Series on Parallel and Distributed Computing) Wiley, Hoboken, 2009.