Abstract
Firefly Algorithm (FA) is a stochastic population-based algorithm based on the flashing patterns and behavior of fireflies. Original FA was created and successfully applied to solve bound constrained optimization problems. In this paper we present extensions of FA for solving nonsmooth nonconvex constrained global optimization problems. To handle the constraints of the problem, feasibility and dominance rules and a fitness function based on the global competitive ranking, are proposed. To enhance the speed of convergence, the proposed extensions of FA invoke a stochastic local search procedure. Numerical experiments to validate the proposed approaches using a set of well know test problems are presented. The results show that the proposed extensions of FA compares favorably with other stochastic population-based methods.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Blum, C., Li, X.: Swarm intelligence in optimization. In: Blum, C., Merkle, D. (eds.) Swarm Intelligence: Introduction and Applications, pp. 43–86. Springer Verlag, Berlin (2008)
Tuba, M.: Swarm intelligence algorithms parameter tuning. In: Proceedings of the American Conference on Applied Mathematics (AMERICAN-MATH 2012), pp. 389–394, Harvard, Cambridge, USA (2012)
Holland, J.H.: Adaptation in Natural and Artificial Systems. University of Michigan Press, Ann Arbor (1975)
Kennedy, J., Eberhart, R.C.: Particle swarm optimization. In: IEEE International Conference on Neural Networks (Perth, Australia), pp. 1942–1948. IEEE Service Center, Piscataway (1995)
Geem, Z.W., Kim, J.H., Loganathan, G.V.: A new heuristic optimization algorithm: harmony search. Simulations 76, 60–68 (2001)
Yang, X. S.: Nature-Inspired Metaheuristic Algorithms. Luniver Press (2008)
Dorigo, M.: Optimization, learning and natural algorithms, Ph.D. Thesis, Dipartimento di Elettronica, Politecnico di Milano, Italy (1992)
Eberhart, R.C., Kennedy, J.: A new optimizer using particle swarm theory. In: Proceedings of the Sixth International Symposium on Micro Machine and Human Science, pp. 39–43. IEEE Press, Nagoya (1995)
Horng, M.H., Liou, R.J.: Multilevel minimum cross entropy threshold selection based on the firefly algorithm. Expert Syst. Appl. 38(12), 14805–14811 (2011)
Yang, X.S., Hosseini, S.S., Gandomi, A.H.: Firefly algorithm for solving non-convex economic dispatch problems with valve loading effect. Appl. Soft Comput. 12(3), 1180–1186 (2012)
Gandomi, A.H., Yang, X.S., Alavi, A.H.: Mixed variable structural optimization using Firefly Algorithm. Comput. Struct. 89(23–24), 2325–2336 (2011)
Costa, M.F.P., Rocha, A.M.A.C., Francisco, R.B., Fernandes, E.M.G.P.: Heuristic-based firefly algorithm for bound constrained nonlinear binary optimization. Adv. Oper. Res. 2014, Article ID 215182, 12 (2014)
Costa, M.F.P., Rocha, A.M.A.C., Francisco, R.B., Fernandes, E.M.G.P.: Firefly penalty-based algorithm for bound constrained mixed-integer nonlinear programming. Optimization 65(5), 1085-1104 (2016). doi:10.1080/02331934.2015.1135920
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.: Multiobjective firefly algorithm for continuous optimization. Eng. Comput. 29(2), 175–184 (2013)
Fister, I., Fister Jr., I., Yang, X.-S., Brest, J.: A comprehensive review of firefly algorithms. Swarm Evol. Comput. 13, 34–46 (2013)
Yang, X.-S., He, X.: Firefly algorithm: recent advances and applications. Int. J. Swarm Intell. 1(1), 36–50 (2013)
Ali, M., Zhu, W.X.: A penalty function-based differential evolution algorithm for constrained global optimization. Comput. Optim. Appl. 54(3), 707–739 (2013)
Barbosa, H.J.C., Lemonge, A.C.C.: An adaptive penalty method for genetic algorithms in constrained optimization problems. In: Iba, H. (ed.) Frontiers in Evolutionary Robotics, pp. 9–34. I-Tech Education Publications, Vienna (2008)
Mezura-Montes, E., Coello Coello, C.A.C.: Constraint-handling in nature-inspired numerical optimization: past, present and future. Swarm Evol. Comput. 1(4), 173–194 (2011)
Lemonge, A.C.C., Barbosa, H.J.C., Bernardino, H.S.: Variants of an adaptive penalty scheme for steady-state genetic algorithms in engineering optimization. Eng. Comput. Int. J. Comput.-Aided Eng. Softw. 32(8), 2182–2215 (2015)
Runarsson, T.P., Yao, X.: Constrained evolutionary optimization – the penalty function approach. In: Sarker, R., et al. (eds.) Evolutionary Optimization: International Series in Operations Research and Management Science, vol. 48, pp. 87–113. Springer, New York (2003)
Deb, K.: An efficient constraint-handling method for genetic algorithms. Comput. Methods Appl. Mech. Eng. 186(0045–7825), 311–338 (2000)
Birbil, S.I., Fang, S.-C.: An electromagnetism-like mechanism for global optimization. J. Global Optim. 25, 263–282 (2003)
Liang, J.J., Runarsson, T.P., Mezura-Montes, E., Clerc, M., Suganthan, P.N., Coello, C.A.C., Deb, K.: Problem definition and evolution criteria for the CEC 2006 special session on constrained real-parameter optimization. In: IEEE Congress on Evolutionary Computation, Vancouver, Canada, 17–21 July (2006)
Koziel, S., Michalewicz, Z.: Evolutionary algorithms, homomorphous mappings, and constrained parameter optimization. Evol. Comput. 7(1), 19–44 (1999)
Runarsson, T.P., Yao, X.: Stochastic ranking for constrained evolutionary optimization. IEEE Trans. Evol. Comput. 4(3), 284–294 (2000)
Farmani, R., Wright, J.: Self-adaptive fitness formulation for constrained optimization. IEEE Trans. Evol. Comput. 7(5), 445–455 (2003)
Silva, E.K., Barbosa, H.J.C., Lemonge, A.C.C.: An adaptive constraint handling technique for differential evolution with dynamic use of variants in engineering optimization. Optim. Eng. 12(1–2), 31–54 (2011)
Tessema, R, Yen, G.G.: A self adaptive penalty function based algorithm for constrained optimization. In: IEEE Congress on Evolutionary Computation (CEC 2006), pp. 246–253, Vancouver, Canada (2006)
Acknowledgements
This work has been supported by COMPETE: POCI-01-0145-FEDER-007043 and FCT – Fundação para a Ciência e Tecnologia within the projects UID/CEC/00319/2013 and UID/MAT/00013/2013.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this paper
Cite this paper
Francisco, R.B., Costa, M.F.P., Rocha, A.M.A.C. (2016). Extensions of Firefly Algorithm for Nonsmooth Nonconvex Constrained Optimization Problems. In: Gervasi, O., et al. Computational Science and Its Applications – ICCSA 2016. ICCSA 2016. Lecture Notes in Computer Science(), vol 9786. Springer, Cham. https://doi.org/10.1007/978-3-319-42085-1_31
Download citation
DOI: https://doi.org/10.1007/978-3-319-42085-1_31
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-42084-4
Online ISBN: 978-3-319-42085-1
eBook Packages: Computer ScienceComputer Science (R0)