Abstract
Most global optimization problems are nonlinear and thus difficult to solve, and they become even more challenging when uncertainties are present in objective functions and constraints. This paper provides a new two-stage hybrid search method, called Eagle Strategy, for stochastic optimization. This strategy intends to combine the random search using Lévy walk with the firefly algorithm in an iterative manner. Numerical studies and results suggest that the proposed Eagle Strategy is very efficient for stochastic optimization. Finally practical implications and potential topics for further research will be discussed.
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References
Ackley, D.H.: A connectionist machine for genetic hillclimbing. Kluwer Academic Publishers, Dordrecht (1987)
Barthelemy, P., Bertolotti, J., Wiersma, D.S.: A Lévy flight for light. Nature 453, 495–498 (2008)
Bental, A., El Ghaoui, L., Nemirovski, A.: Robust Optimization. Princeton University Press, Princeton (2009)
Bonabeau, E., Dorigo, M., Theraulaz, G.: Swarm Intelligence: From Natural to Artificial Systems. Oxford University Press, Oxford (1999)
Brown, C., Liebovitch, L.S., Glendon, R.: Lévy flights in Dobe Ju/’hoansi foraging patterns. Human Ecol. 35, 129–138 (2007)
Deb, K.: Optimisation for Engineering Design. Prentice-Hall, New Delhi (1995)
Goldberg, D.E.: Genetic Algorithms in Search, Optimisation and Machine Learning. Addison Wesley, Reading (1989)
Kennedy, J., Eberhart, R.C.: Particle swarm optimization. In: Proc. of IEEE International Conference on Neural Networks, Piscataway, NJ, pp. 1942–1948 (1995)
Kennedy, J., Eberhart, R., Shi, Y.: Swarm intelligence. Academic Press, London (2001)
Marti, K.: Stochastic Optimization Methods. Springer, Heidelberg (2005)
Nelder, J.A., Mead, R.: A simplex method for function minimization. Computer Journal 7, 308–313 (1965)
Pavlyukevich, I.: Lévy flights, non-local search and simulated annealing. J. Computational Physics 226, 1830–1844 (2007)
Pavlyukevich, I.: Cooling down Lévy flights. J. Phys. A:Math. Theor. 40, 12299–12313 (2007)
Reynolds, A.M., Frye, M.A.: Free-flight odor tracking in Drosophila is consistent with an optimal intermittent scale-free search. PLoS One 2, e354 (2007)
Shilane, D., Martikainen, J., Dudoit, S., Ovaska, S.J.: A general framework for statistical performance comparison of evolutionary computation algorithms. Information Sciences: an Int. Journal 178, 2870–2879 (2008)
Shlesinger, M.F., Zaslavsky, G.M., Frisch, U. (eds.): Lévy Flights and Related Topics in Phyics. Springer, Heidelberg (1995)
Shlesinger, M.F.: Search research. Nature 443, 281–282 (2006)
Urfalioglu, O., Cetin, A.E., Kuruoglu, E.E.: Levy walk evolution for global optimization. In: Proc. of 10th Genetic and Evolutionary Computation Conference, pp. 537–538 (2008)
Wallace, S.W., Ziemba, W.T.: Applications of Stochastic Programming. SIAM Mathematical Series on Optimization (2005)
Yang, X.S.: Firefly algorithms for multimodal optimization. In: Watanabe, O., Zeugmann, T. (eds.) SAGA 2009. LNCS, vol. 5792, pp. 169–178. Springer, Heidelberg (2009)
Yang, X.S., Deb, S.: Cuckoo search via Lévy flights. In: Proceedings of World Congress on Nature & Biologically Inspired Computing (NaBic 2009), pp. 210–214. IEEE Pulications, India (2009)
Yang, Z.Y., Tang, K., Yao, X.: Large Scale Evolutionary Optimization Using Cooperative Coevolution. Information Sciences 178, 2985–2999 (2008)
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Yang, XS., Deb, S. (2010). Eagle Strategy Using Lévy Walk and Firefly Algorithms for Stochastic Optimization. In: González, J.R., Pelta, D.A., Cruz, C., Terrazas, G., Krasnogor, N. (eds) Nature Inspired Cooperative Strategies for Optimization (NICSO 2010). Studies in Computational Intelligence, vol 284. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-12538-6_9
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DOI: https://doi.org/10.1007/978-3-642-12538-6_9
Publisher Name: Springer, Berlin, Heidelberg
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