THE CHAOS-BASED APPROACHES FOR ACTUAL METAHEURISTIC ALGORITHMS

Along with rapid developments in computational technologies, evolutionary/heuristic/metaheuristic algorithms have frequently used in many applications to solve optimization problems. Nowadays, new algorithms are being developed and improvements are being made to existing algorithms. In this study, chaos-based modifications have been proposed for recently developed metaheuristic algorithms: Backtracking Search (BS), Grey Wolf Optimizer (GWO) and Vortex Search (VS), and the algorithms have been analyzed by detailed comparisons. The proposed approaches are based on generating new values through chaos maps, rather than some random numbers normally used in the algorithms, to improve their solutions. In addition, some modifications are performed to the structural operations of the algorithms used in the optimization process by taking advantage of chaosbased values. The performances of the algorithms are evaluated by considering two metrics: convergence rates and statistical results. Experiments demonstrated that the performance of the algorithms with the proposed modifications based on the chaos approach, are better than, or at least comparable to, the original algorithms.

Güncel Metasezgisel Algoritmalar İçin Kaos Tabanlı Yaklaşımlar

Hesaplama teknolojilerindeki hızlı gelişmelerle orantılı olarak, optimizasyon problemlerinin çözümünde evrimsel/sezgisel/metasezgisel algoritmalardan birçok alandaki uygulamalarda sıklıkla faydalanılmaktadır. Günümüzde, yeni algoritmalar geliştirilmekte ve mevcut algoritmalara yenilikler uygulanmaya devam edilmektedir. Bu çalışmada, son zamanlarda geliştirilmiş olan metasezgisel algoritmalardan olan: Geri İzleme Arama (BS), Gri Kurt Optimizasyon (GWO) ve Girdap Arama (VS) algoritmalarına kaos tabanlı modifikasyonlar önerilmiş ve algoritmaların, kıyaslamalarla detaylı analizleri gerçekleştirilmiştir. Önerilen yaklaşımlar, algoritmaların çözümlerini geliştirmek için işlemlerinde kullandıkları bazı rassal değişkenler yerine, kaos haritalarına dayanan yeni değişkenlerin üretilmesi temeline dayanmaktadır. Bunun yanında, kaos tabanlı bu değişkenler kullanılarak algoritmaların optimizasyon sürecinde kullandıkları yapısal işlemlerinde modifikasyonlar gerçekleştirilmektedir. Algoritmaların performansları; istatistiksel ve yakınsama hızları açısından, iki yönlü olarak analiz edilmektedir. Kaotik haritalara dayanan yaklaşımların, orijinal algoritmalar üzerinde daha iyi veya en azından karşılaştırılabilir sonuçlar ürettiği, gerçekleştirilen deneylerde gösterilmiştir.

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Alatas, B., Akin, E. and Ozer, A. B. (2009) Chaos embedded particle swarm optimization algorithms, Chaos, Solitons Fractals, 40(4), 1715-1734. doi: 10.1016/j.chaos.2007.09.063

Civicioglu, P. (2013) Backtracking search optimization algorithm for numerical optimization problems, Applied Mathematics and Computation, 219(15), 8121-8144, 2013. doi: 10.1016/j.amc.2013.02.017

Dogan, B. and Olmez, T. A. (2015) A new metaheuristic for numerical function optimization: vortex search algorithm, Information Sciences, 293, 125-145. doi: 10.1016/j.ins.2014.08.053

Gandomi, A., Yang, X-S., Talatahari, S. and Alavi, A. (2013) Firefly algorithm with chaos, Communications in Nonlinear Science and Numerical Simulation., 18(1), 89-98. doi: 10.1016/j.cnsns.2012.06.009

Geem, Z., Kim, J. and Loganathan, G. (2001) A new heuristic optimization algorithm: harmony search, Simulation, 76(2), 60-68. doi: 10.1177/003754970107600201

Goldberg D. E. (1989) Genetic Algorithms in Search, Optimization and Machine Learning, Addison-Wesley Longman Publishing, USA.

Kellert, S. (1993) In the Wake of Chaos:Unpredictable Order in Dynamical Systems, University of Chicago Press, USA.

Kennedy J. and Eberhart R. (1995) Particle swarm optimization, IEEE International Conference on Neural Networks, 1942-1948. doi:10.1109/ICNN.1995.488968

Li, Y., Deng, S. and Xiao, D. (2011) A novel hash algorithm construction based on chaotic neural network, Neural Computing and Applications, 20(1), 133–141. doi: 10.1007/s00521- 010-0432-2

Li-Jiang, Y. and Tian-Lun, C. (2002) Application of chaos in genetic algorithms, Communications in Theoretical Physics, 38(2), 168. doi: 10.1088/0253-6102/38/2/168

Liang, J. J., Suganthan, P. N. and Hernandez-Diaz, A. G. (2013) Problem definitions and evaluation criteria for the CEC 2013 special session on real-parameter optimization, Zhengzhou University and Nanyang Technological University, 3-18. Technical report:201212

Mirjalili, S., Mirjalili, S. M. and Lewis, A. (2014) Grey wolf optimizer, Advances in Engineering Software, 69, 46-61. doi: 10.1016/j.advengsoft.2013.12.007

Pecora, L. and Carroll, T. (1990) Synchronization in chaotic system, Physical Review Letters, 64(8), 821-824. doi: 10.1103/PhysRevLett.64.821

Saremi, S., Mirjalili, S. M. and Mirjalili, S. (2014) Chaotic krill herd optimization algorithm, Procedia Techno, 12, 180-185. doi: 10.1016/j.protcy.2013.12.473

Schuster, H. G. and Just, W. (2006) Deterministic chaos: an introduction, John Wiley & Sons, Germany.

Storn, R. and Price K. (1995) Differential evolution: A simple and efficient adaptive scheme for global optimization over continuous spaces, International Computer Science Institute, 1- 12. Technical report:TR-95-012

Wang, N., Liu, L. M. and L. L. Liu. (2001) Genetic algorithm in chaos, Or Transactions, 5(5), 1-10.

Wang, L. and Zhong, Y. (2015) Cuckoo search algorithm with chaotic maps, Mathematical Problems in Engineering, 6(6), 546-554. doi: 10.1155/2015/715635

Wang,, G.-G., Guo, L., Gandomi, A., Hao, G.-S. and Wang, H. (2014) Chaotic krill herd algorithm, Information Sciences, 274, 17-34. doi: 10.1016/j.ins.2014.02.123

Wolpert, D. H. and Macready, W. G. (1997) No free lunch theorems for optimization, IEEE Transactions on Evolutionary Computation, 1(1), 67-82. doi: 10.1109/4235.585893

Yang, X-S. (2010) Nature-inspired Metaheuristic Algorithms, Luniver Press, UK.

Yang, X-S. and Deb, S. (2009) Cuckoo search via L´evy flights, Proceeding of World Congress on Nature Biologically Inspired Computing, 210-214, doi: 10.1109/NABIC.2009.5393690

Yao, J. F., Mei, C., Peng, X. Q., Hu, Z. K. and Hu, J (2001) A new optimization approachchaos genetic algorithm, Systems Engineering, 1, 1-5.

Zaharie, D. (2003) Control of population diversity and adaptation in differential evolution algorithms, Mendel 9th International Conference on Soft Computing, Brno, 41-46.

Zhenyu, G. Bo, Y. C. and Min, C. B. (2006) Self-adaptive chaos differential evolution, International Conference on Natural Computation, 972-975. doi: 10.1007/11881070_128