Abstract
This paper presents an application of Colonial Competitive Algorithm (CCA) in game theory and multi-objective optimization problems. The recently introduced CCA has proven its excellent capabilities, such as faster convergence and better global optimum achievement. In this paper CCA is used to find Nash Equilibrium points of nonlinear non-cooperative games. The proposed method can also be used as an alternative approach to solve multi-objective optimization problems. The effectiveness of the proposed method, in comparison to Genetic Algorithm, is proven through several static and dynamic example games and also multi-objective problems.
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References
Neumann, J., Morgenstern, O.: Theory of Games and Economic Behavior, 60th-Anniversary edn. Princeton University Press, Princeton (2007)
Nash, J.F.: Equilibrium points in n-person games. Proceedings of the National Academy of Sciences of the United States of America 36, 46–49 (1950)
Nash, J.F.: Non-Cooperative Games. The Annals of Mathematics 54, 286–295 (1951)
Varoufakis, Y.: General introduction: Game theory’s quest for a single, unifying framework for the social sciences. In: Varoufakis, Y. (ed.) Game Theory: Critical Concepts in the Social Sciences, vol. 1. Routledge, London (2001)
http://plato.stanford.edu/entries/game-evolutionary (January 2008)
Haurie, A., Krawczyk, J.: An Introduction to Dynamic Games (2000)
Basar, T., Olsder, G.J.: Noncooperative Game Theory, 2nd edn. Academic Press, London (1995)
Son, Y.S., Baldick, R.: Hybrid Coevolutionary Programming for Nash Equilibrium Search in Games with Local Optima. IEEE Trans. on evolutionary computation 8, 305–315 (2004)
Cau, T.D.H., Anderson, E.J.: A co-evolutionary approach to modeling the behavior of participants in competitive electricity markets. In: Proc. IEEE Power Engineering Soc. Summer Meeting, vol. 3, pp. 1534–1540 (2002)
Gaoping, W., Yongji, W.: A game model based co-evolutionary for constrained multiobjective optimization problems. In: IEEE International Symposium on Communications and Information Technology, vol. 1, pp. 187–190 (2005)
Daskalakis, C., Papadimitriou, C.: Computing Equilibria in Anonymous Games. In: 48th Annual IEEE Symposium on Foundations of Computer Science, pp. 83–93 (2007)
Sefrioui, M., Perlaux, J.: Nash genetic algorithms: examples and applications. In: Proceedings of the 2000 Congress on Evolutionary Computation, vol. 1, pp. 509–516 (2000)
Atashpaz-Gargari, E., Lucas, C.: Imperialist Competitive Algorithm: An algorithm for optimization inspired by imperialistic competition. In: IEEE Congress on Evolutionary Computation, Singapore (2007)
Rajabioun, R., Hashemzadeh, F., Atashpaz-Gargari, E., Mesgari, B., Rajaei Salmasi, F.: Identification of a MIMO Evaporator and Its Decentralized PID Controller Tuning Using Colonial Competitive Algorithm (accepted to be presented in IFAC World Congress 2008)
Biabangard-Oskouyi, A., Atashpaz-Gargari, E., Soltani, N., Lucas, C.: Application of Imperialist Competitive Algorithm for materials property characterization from sharp indentation test. International Journal of Engineering Simulation, under revision (submitted, 2008)
Sepehri Rad, H., Lucas, C.: Application of Imperialistic Competition Algorithm in Recommender Systems. In: 13th Int’l CSI Computer Conference (CSICC 2008), Kish Island, Iran (2008)
Muhlenbein, H., Schomisch, M., Born, J.: The parallel genetic algorithm as function optimizer. Parallel Computing 17(6-7), 619–632 (1991)
Deb, K.: Multi-objective genetic algorithms: Problem difficulties and construction of test problems. Technical report, Department of Computer Science / LS11, University of Dortmund (1998)
Dekel, E., Scotchmer, S.: On the Evolution of Optimizing Behavior. Journal of Economic Theory 57, 392–406 (1992)
Cunningham, L.B., Baldick, R., Baughman, M.L.: An Empirical Study of Applied Game Theory: Transmission Constrained Cournot Behavior. IEEE Transactions on Power Systems 17(1), 166–172 (2002)
Wood, A.J., Wollenberg, B.F.: Power Generation Operation and Control, 2nd edn. Wiley, Chichester (1996)
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Rajabioun, R., Atashpaz-Gargari, E., Lucas, C. (2008). Colonial Competitive Algorithm as a Tool for Nash Equilibrium Point Achievement. In: Gervasi, O., Murgante, B., Laganà, A., Taniar, D., Mun, Y., Gavrilova, M.L. (eds) Computational Science and Its Applications – ICCSA 2008. ICCSA 2008. Lecture Notes in Computer Science, vol 5073. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69848-7_55
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DOI: https://doi.org/10.1007/978-3-540-69848-7_55
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