Kaotik Harita Temelli Ağaç Tohum Algoritması

Öz

Kaotik haritalama tekniklerinin sezgisel algoritmalarda rastgele sayı üreteci olarak kullanımı giderek yaygınlaşan bir konudur. Geniş bir spekturuma sahip bu haritalama teknikler, sezgisel algoritmaların rastgele seçimlerindeki çeşitliliği arttırarak performans artışı sağlamaktadırlar. Ağaç tohum algoritması (TSA), son dönemde önerilmiş popülasyon temelli sezgisel algoritmalardan biridir. Doğadaki ağaç ve tohum gelişimini ilham alan bu algoritma, hesapsal süreci boyunca rastgele sayı dizilerini kullanan işlem basamaklarına sahiptir. Bu çalışmada, kaotik haritalama kullanılarak TSA ‘nın performansında iyileştirmeye odaklanılmıştır. Beş farklı kaotik harita temelli TSA (CTSA) metodu geliştirilmiştir. Geliştirilen metotların performansları 24 adet test fonksiyonu üzerinden karşılaştırılmıştır. Elde edilen sonuçlar, kaotik haritalamanın TSA’nın yakınsama ve lokal optimumdan kaçış performansına katkı sağladığını göstermektedir.

Anahtar Kelimeler

• Ağaç tohum algoritması,Kaotik haritalar,Sezgisel algoritmalar

Chaotic Map Based Tree Seed Algorithm

Öz

The use of chaotic maps as a random number generator in metaheuristics is a common issue. These methods, which have a spread spectrum, increase the diversity in the random selection of heuristic algorithms, resulting in increased performance. Tree seed algorithm (TSA) is one of the recently proposed population-based metaheuristic algorithms. Inspired by the growth of trees and seeds in nature, this algorithm has processing phases that use random numbers throughout the computational process. This paper focuses on improving the performance of the TSA using chaotic mapping. Five chaotic based TSA’s (CTSA’s) are developed. The developed methods are benchmarked on 24 test functions.  The obtained results show that chaotic mapping contributes to the performance of TSA in terms of both local optima avoidance and convergence speed.

Anahtar Kelimeler

• Tree seed algorithm,Chaotic maps,Metaheuristics

Kaynakça

1. [1] Kennedy, J., Eberhart, R. 1995. Particle Swarm Optimization. IEEE International Conference on Neural Networks, 27 November-1 December 1995, Perth, 1942-1948.
2. [2] Dorigo, M., Caro, G. D. 1999. The Ant Colony Optimization Meta-Heuristic. ss11-32. Corne, D., Dorigo, M., Glover, F., ed. 1999. New Ideas in Optimization, McGraw-Hill, New York, 493s.
3. [3] Karaboga, D., Basturk, B. 2007. A Powerful and Efficient Algorithm for Numerical Function Pptimization: Artificial Bee Colony (ABC) Algorithm. Journal of Global Optimization, 39(3), 459-471.
4. [4] Yang, X. S. 2012. Flower Pollination Algorithm for Global Optimization. Lecture Notes in Computer Science, 7445, 240-249.
5. [5] Yazdani, M., Jolai, F. 2016. Lion Optimization Algoritgm (LOA): A Nature-Inspired Metaheuristic Algorithm. Journal of Computational Design and Engineering, 3(1), 24-36.
6. [6] Gandomi, A. H., Yang, X. S., Talatahari, S., Alavi, A. H. 2013. Firefly Algorithm with Chaos. Communications in Nonlinear Science and Numerical Simulation, 18(1), 89-98.
7. [7] Han, X., Chang, X. 2012. A Chaotic Digital Secure Communication Based on A Modified Gravitational Search Algorithm Filter. Information Sciences, 208, 14-27.
8. [8] Wang, G. G., Guo, L., Gandomi, A. H., Hao, G. S., Wang, H. 2014. Chaotic Krill Herd Algorithm. Information Sciences, 274, 17-34.

9. [9] Alataş, B. 2010. Chaotic Harmony Search Algorithms. Applied Mathematics and Computation, 216(9), 2687-2699.
10. [10] Askarzadeh, A., Coelho, L. S. 2014. A Backtracking Search Algorithm Combined with Burger's Chaotic Map for Parameter Estimation of PEMFC Electrochemical Model. International Journal of Hydrogen Energy, 39(21), 11165-11174.
11. [11] Kaur, G., Arora, S. 2018. Chaotic Whale Optimization Algorithm. Journal of Computational Design and Engineering, 5(3), 275-284.
12. [12] Kohli, M., Arora, S. 2018. Chaotic Grey Wolf Optimization Algorithm for Constrained Optimization Problems. Journal of Computational Design and Engineering, 5(4), 458-472.
13. [13] Yüzgeç, U., Eser, M. 2018. Chaotic based Differential Evolution Algorithm for Optimization of Baker’s Yeast Drying Process. Egyptian Informatics Journal, 19(3),151-163.
14. [14] Feng, J., Zhang, J., Zhu, X., Lian, W. 2017. A Novel Chaos Optimization Algorithm. Multimedia Tools and Applications, 76(16),17405-17436.
15. [15] Saremi, S., Mirjalili, S., Lewis, A. 2014. Biogeography-based Optimisation with Chaos. Neural Computing and Applications, 25(5), 1077-1097.
16. [16] Kiran, M. S. 2015. TSA: Tree-Seed Algorithm for Continuous Optimization. Expert Systems with Applications, 42, 6686-6698.
17. [17] Cinar, A. C., Kiran M. S. 2018. Ağaç-Tohum Algoritmasının CUDA Destekli Grafik İşlem Birimi Üzerinde Paralel Uygulaması. Journal of Faculty of Engineering and Architecture of Gazi University, 33(4), 1397-1409.
18. [18] Babalık, A., Çınar, A. C., Kıran, M. S. 2018. A Modification of Tree-Seed Algorithm using Deb’s Rules for Constrained Optimization. Applied Soft Computing, 63, 289-305.
19. [19] Çınar, A. C., Kıran, M. S. 2018. Similarity and Logic Gate-Based Tree-Seed Algorithms for Binary Optimization. Computers & Industrial Engineering, 115, 631-646.
20. [20] Hilborn, R. C. 2004. Chaos and Nonlinear Dynamics: An Introduction for Scientists and Engineers. 2nd, Oxford University Press, New York, 672s.
21. [21] Mondragon, R. J., Pitts, J. M., Arrowsmith, D. K. 2000. Chaotic Intermittency-Sawtooth Map Model of Aggregate Self-Similar Traffic Streams. IEEE Electronics Letters, 36(2), 184-186.
22. [22] Li, Y., Deng, S., Xiao, D. 2011. A novel Hash Algorithm Construction Based on Chaotic Neural Network. Neural Computing and Application, 20, 133-141.
23. [23] Chirikov, B. V. 1979. A Universal Instability of Many-Dimensional Oscillator Systems. Physics Reports, 52(5), 263-379.
24. [24] Zaslavskii, G. M. 1978. The Simplest Case of A Strange Attractor. Physics Letters A, 69(3), 145-147.
25. [25] Karaboğa, D., Akay, B. 2009. A Comparative Study of Artificial Bee Colony Algorithm. Applied Mathematics and Computation, 214, 108-132.
26. [26] Boyer, D. O., Martfnez, C. H., Pedrajas, N. G. 2005. Crossover Operator for Evolutionary Algorithms Based on Population Features. Journal of Artificial Intelligence Research, 24, 1-48.
27. [27] Digalakis, J. G., Margaritis, K. G. 2002. An Experimental Study of Benchmarking Functions for Genetic Algorithms. International Journal of Computer Mathematics, 79(4), 403-416.
28. [28] Yao, X., Liu, Y., Lin, G. 1999. Evolutionary Programming Made Faster. IEEE Transactions on Evolutionary Computation, 3(2), 82-102.