The Chaos-Based Whale Optimization Algorithms Global Optimization

Year 2019, Volume: 1 Issue: 1, 51 - 63, 30.11.2019

Zeynep Garip Murat Erhan Cimen Durmuş Karayel Ali Fuat Boz

Abstract

Whale optimization algorithm (WOA) is one of the methods used effectively and efficiently to solve optimization problems in various fields. In the study, 5 different discrete chaotic maps were used in the aim of increasing the efficacy and efficiency of the WOA algorithm. CBWOA 1, CBWOA 2, CBWOA 3 and CBWOA 4 algorithms based on chaotic maps and whale optimization algorithm have been proposed for global optimization. In order to adjust the parameters contained in the WOA, random number sequences from Tinkerbell, Sine, Logistic, Tent and Henon chaotic maps were used. In order to test the accuracy of the developed algorithms and do the performance analysis, six different unimodal and multimodal benchmark functions were used. According to the simulation results, all the chaotic maps used in the study significantly improved the performance of the WOA algorithm.

Keywords

Chaos, Discrete time chaotic systems, Whale optimization algorithm

References

• [1] N. Aslimani and R. Ellaia, "A new chaos optimization algorithm based on symmetrization and levelling approaches for global optimization" , Numer Algo.,Vol.79, pp. 10211047, 2018.
• [2] J. D. Velsquez, "An introduction to chaos-based algorithms for numerical optimization", Avances en Sistemas e Informtica, Vol. 8, No. 3, 2011.
• [3] G. Kaur and S. Aror, "Chaotic whale optimization algorithm", Journal of Computational Design and Engineering Vol.5, pp. 275284, 2018.
• [4] R. Eberhart and J. Kennedy, " Particle swarm optimization", In Proceedings of IEEE inter- national conference on neural networks,pp. 19421948, 1995.
• [5] M. Dorigo and G. Di Caro, "Ant colony optimization: A new meta-heuristic", In CEC 99. Proceedings of the 1999 congress on evolutionary computation, Vol. 2, pp. 14701477, 1999.
• [6] X. S. Yang, "Firefly algorithm, Levy flights and global optimization", In Research and development in intelligent systems XXVI, pp. 209218, 2010.
• [7] D. Simon, "Biogeography-based optimization", IEEE Transactions on Evolutionary Compu- tation, Vol. 12, No. 6, pp. 702713, 2008.
• [8] A. H. Gandomi and X. S. Yang, "Chaotic bat algorithm", Journal of Computational Science, Vol. 5, No.2, pp. 224232 ,2014 .
• [9] A. H. Gandomi and A. H. Alavi,"Krill herd: A new bio-inspired optimization algorithm", Communications in Nonlinear Science and Numerical Simulation, Vol. 17,No. 12, pp. 48314845, 2012.
• [10] C. Shu-Chuan, T. Pei-Wei and P. Jeng-Shyang, "Cat swarm optimization", In 9th Pacific Rim international conference on artificial intelligence, LNAI Vol. 4099, pp. 854858, 2006.
• [11] S. Mirjalili, S. M. Mirjalili and A. Lewis, "Grey wolf optimizer", Advances in Engineering Software, Vol. 69, pp. 4661, 2014.
• [12] S. Mirjalili, "The ant lion optimizer", Advances in Engineering Software,Vol. 83,pp. 8098, 2015.
• [13] S. Arora and S. Singh, " Butterfly algorithm with Lvy Flights for global optimization. In 2015 International conference on signal processing, computing and control, pp. 220224, 2015.
• [14] S. Mirjalili and A. Lewis, "The whale optimization algorithm", Advances in Engineering Software, Vol. 95, pp. 5167, 2016.
• [15] R. Sheikholeslami and A. Kaveh , "A Survey Of Chaos Embedded Meta-Heurstc algorthms", Int. J. Optim. Civil Eng., Vol.3 No.4, pp. 617-633, 2013;
• [16] I. Fister, M. Perc and Sa.M. Kamal, "A review of chaos-based firefly algorithms: Perspectives and research challenges", Applied Mathematics and Computation, Vol. 252, pp.155165, 2015.
• [17] R. Hosseinpourfard and M.M. Javidi, "Chaotic PSO using the Lorenz System: An Effcient Approach for Optimizing Nonlinear Problems", Cankaya University Journal of Science and Engineering, Vol. 12, No. 1, pp. 040-059, 2015.
• [18] A. H. Abdullah , R. Enayatifar and M. Lee, "A hybrid genetic algorithm and chaotic function model for image encryption", Int. J. Electron. Commun.,Vol. 66, pp. 806816, 2012.
• [19] H. Afrabandpey, M. Ghaari, A. Mirzaei and M. Safayani ,"A Novel Bat Algorithm Based on Chaos for Optimization Tasks", Iranian Conference on Intelligent Systems,2014.
• [20] L. Huang, S. Ding, S. Yu, J.Wang and K. Lu ," Chaos-enhanced Cuckoo search optimization algorithms for global optimization", Applied Mathematical Modelling Vol. 40, pp. 38603875, 2016.
• [21] Q. V. Lawande , B. R. Ivan and S. D. Dhodapkar, "Chaos based ryptography: a new approach to secure communications", Barc new letter, Vol. 258,2005.
• [22] L. M. Pecora and T. L. Carroll, Synchronization in chaotic systems, Phys. Rev. Lett. Vol. 64,No. 821, 1990.
• [23] F. S. Gharehchopogh and H. Gholizadeh," A comprehensive survey: Whale Optimization Algorithm and its applications", Swarm and Evolutionary Computation,Vol. 48,pp. 124, 2019.