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A novel hybrid algorithm based on Stochastic Fractal Search Algorithm and CMA-ES

Year 2023, Volume: 11 Issue: 2, 868 - 907, 30.04.2023
https://doi.org/10.29130/dubited.1110725

Abstract

In this study, a novel hybridization approach, which is called CMASFS and is based on the covariance matrix adaptation evolution strategy (CMA-ES) and the stochastic fractal search (SFS) algorithms. To make the proposed algorithm dynamic, Gaussian walk equations involved in the diffusion process of SFS have been updated and the algorithm decide to use which the Gaussian walk equations. The effectiveness of the proposed algorithm is tested using CEC2017 benchmark functions having unimodal, multimodal, hybrid, and composition functions in 10, 30, 50, and 100 dimensions. The performance of the CMASFS algorithm is compared with 17 metaheuristic algorithms given in the literature over the CEC2017 benchmark functions. According to the results, it is seen that CMASFS is generally obtained better mean error values. Moreover, to show the superiority of the proposed algorithm, Friedman analysis and the Wilcoxon rank-sum test are applied to the test results of the algorithms. The results of the Wilcoxon signed-rank test show that the improvement with the CMASFS algorithm is statistically significant on the majority of the CEC2017. The results of Friedman test verify that the CMASFS is obtained the best rank compared to both the original SFS and other compared algorithms.

References

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Stokastik Fraktal Arama Algoritması ve CMA-ES tabanlı yeni bir hibrit algoritma

Year 2023, Volume: 11 Issue: 2, 868 - 907, 30.04.2023
https://doi.org/10.29130/dubited.1110725

Abstract

Bu çalışmada, kovaryans matris uyarlaması ile evrim stratejisi (CMA-ES) ve stokastik fraktal arama (SFA) algoritmalarına dayanan CMASFA adı verilen yeni bir hibritleştirme yaklaşımı geliştirilmiştir. Önerilen algoritmayı dinamik hale getirmek için, SFS'nin yayılım sürecinde yer alan Gauss yürüyüş eşitlikleri güncellenmiş ve hangi Gauss yürüyüş eşitliğinin kullanılacağına algoritmanın karar vermesi sağlanmıştır. Önerilen algoritmanın etkinliği, 10, 30, 50 ve 100 boyutlu tekmodlu, çokmodlu, melez ve komposizyon fonksiyonlarına sahip CEC2017 benchmark fonksiyonları kullanılarak test edilmiştir. CEC2017 benchmark fonksiyonları kullanılarak CMASFS algoritmasının performansı, literatürde verilen 17 metasezgisel algoritma ile karşılaştırılmıştır. Elde edilen sonuçlara göre, CMASFS'nin daha düşük bir ortalama hata değerleri elde ettiği görülmüştür. Ayrıca önerilen algoritmanın üstünlüğünü göstermek için algoritmaların elde ettiği sonuçlar üzerinde Friedman analizi ve Wilcoxon işaretli sıra testi uygulanmıştır. Wilcoxon işaretli sıra testinin sonuçlarına göre, CMASFA algoritmasıyla yapılan iyileştirmenin CEC2017 içerisindeki fonksiyonların büyük bir çoğunluğunda istatistiksel olarak anlamlı farklılık oluşturduğu ve daha uygun sonuçlar elde ettiği sonucuna ulaşılmıştır. Friedman testinin sonuçlarına göre de CMASFA'nin hem orijinal SFA’ya hem de diğer karşılaştırılan algoritmalara kıyasla en iyi sıralamayı elde ettiği görülmektedir.

References

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  • Eberhart, R., Kennedy, J., A new optimizer using particle swarm theory. In MHS'95. Proceedings of the Sixth International Symposium on Micro Machine and Human Science, 1995, 39-43, DOI: 10.1109/MHS.1995.494215.
  • Storn, R., Price, K., Differential evolution–a simple and efficient heuristic for global optimization over continuous spaces. Journal of global optimization, 11(4), 1997, pp. 341-359, DOI: 10.1023/A:1008202821328.
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  • Rashedi, E., Nezamabadi-Pour, H., Saryazdi, S., GSA: a gravitational search algorithm. Information sciences, 179(13), 2009, pp. 2232-2248. DOI: 10.1016/j.ins.2009.03.004.
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  • Mirjalili, S., SCA: a sine cosine algorithm for solving optimization problems. Knowledge-Based Systems, 96, 2016, pp. 120-133, DOI: 10.1016/j.knosys.2015.12.022.
  • Mirjalili, S., Lewis, A., 2016. The whale optimization algorithm. Advances in engineering software, 95, 51-67. DOI: 10.1016/j.advengsoft.2016.01.008
  • Mirjalili, S., Gandomi, A.H., Mirjalili, S.Z., Saremi, S., Faris, H., Mirjalili, S.M., 2017. Salp Swarm Algorithm: A bio-inspired optimizer for engineering design problems. Advances in Engineering Software, 114, 163-191. DOI: 10.1016/j.advengsoft.2017.07.002
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  • Arora, S., Singh, S., Butterfly optimization algorithm: a novel approach for global optimization. Soft Computing, 23(3), 2019, pp. 715-734, DOI: 10.1007/s00500-018-3102-4.
  • Zhao, W., Wang, L., Zhang, Z., Atom search optimization and its application to solve a hydrogeologic parameter estimation problem. Knowledge-Based Systems, 163, 2019, pp. 283-304, DOI: 10.1016/j.knosys.2018.08.030.
  • Salimi, H., Stochastic fractal search: a powerful metaheuristic algorithm. Knowledge-Based Systems, 75, 2015, pp. 1-18, DOI: 10.1016/j.knosys.2014.07.025.
  • Rahman, T.A. Parameters optimization of an SVM-classifier using stochastic fractal search algorithm for monitoring an aerospace structure. International Journal of Fluids and Heat Transfer, 1(1), 2016, pp. 69-79.
  • Mosbah, H., El-Hawary, M., Power system tracking state estimation based on stochastic fractal search technique under sudden load changing conditions. In 2016 IEEE Canadian Conference on Electrical and Computer Engineering (CCECE), 2016, pp. 1-6.
  • Chuan, S.U.N., WEI, Z.Q., ZHOU, C.J., Bin, W.A.N.G., Stochastic fractal search algorithm for 3d protein structure prediction. DEStech Transactions on Computer Science and Engineering. 2016, DOI: 10.12783/dtcse/aics2016/8189.
  • Luo, Q., Zhang, S., Zhou, Y., Stochastic Fractal Search Algorithm for Template Matching with Lateral Inhibition. Scientific Programming. 2017, DOI: 10.1155/2017/1803934.
  • Çelik, E., Incorporation of stochastic fractal search algorithm into efficient design of PID controller for an automatic voltage regulator system. Neural Computing and Applications, 30(6), 2018, pp. 1991-2002, DOI: 10.1007/s00521-017-3335-7.
  • Hinojosa, S., Dhal, K.G., Elaziz, M.A., Oliva, D., Cuevas, E., Entropy-based imagery segmentation for breast histology using the Stochastic Fractal Search. Neurocomputing, 321, 2018, pp. 201-215, DOI: 10.1016/j.neucom.2018.09.034.
  • Saha, D., Saikia, L.C., Automatic generation control of an interconnected CCGT‐thermal system using stochastic fractal search optimized classical controllers. International Transactions on Electrical Energy Systems, 28(5), 2018, pp. 2533. DOI: 10.1002/etep.2533.
  • Bingöl, O., Paçacı, S., Pişirir, O.M., Özkaya, B., Stochastic Fractal Search Algorithm for ANFIS Training, International Conference on Science and Technology (ICONST 2018), 2018, pp. 422-428.
  • Çelik, E., Gör, H., Enhanced speed control of a DC servo system using PI+ DF controller tuned by stochastic fractal search technique. Journal of the Franklin Institute, 356(3), 2019, pp. 1333-1359, DOI: 10.1016/j.jfranklin.2018.11.020.
  • Bhatt, R., Parmar, G., Gupta, R., Sikander, A., Application of stochastic fractal search in approximation and control of LTI systems. Microsystem Technologies, 25(1), 2019, pp. 105-114, DOI: 10.1007/s00542-018-3939-6.
  • Betka, A., Terki, N., Toumi, A., Hamiane, M., Ourchani, A., A new block matching algorithm based on stochastic fractal search. Applied Intelligence, 49(3), 2019, pp. 1146-1160, DOI: 10.1007/s10489-018-1312-1.
  • Mellal, M.A., Zio, E., A penalty guided stochastic fractal search approach for system reliability optimization. Reliability Engineering and System Safety, 152, 2016, pp. 213-227, DOI: 10.1016/j.ress.2016.03.019.
  • Awad, N.H., Ali, M.Z., Suganthan, P.N., Jaser, E., Differential evolution with stochastic fractal search algorithm for global numerical optimization. In 2016 IEEE Congress on Evolutionary Computation (CEC), 2016, pp. 3154-3161, DOI: 10.1109/CEC.2016.7744188.
  • Awad, N.H., Ali, M.Z., Suganthan, P.N., Jaser, E., A decremental stochastic fractal differential evolution for global numerical optimization. Information Sciences, 372, 2016, pp. 470-491, DOI: 10.1016/j.ins.2016.08.032.
  • Rahman, T.A., Tokhi, M.O., Enhanced stochastic fractal search algorithm with chaos. In 2016 7th IEEE Control and System Graduate Research Colloquium (ICSGRC), 2016, pp. 22-27, DOI: 10.1109/ICSGRC.2016.7813295.
  • Zhou, C., Sun, C., Wang, B., Wang, X., An improved stochastic fractal search algorithm for 3D protein structure prediction. Journal of molecular modeling, 24(6), 2018, pp. 125, DOI: 10.1007/s00894-018-3644-5.
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There are 68 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Serdar Paçacı 0000-0002-7191-7452

Okan Bingöl 0000-0001-9817-7266

Uğur Güvenç 0000-0002-5193-7990

Publication Date April 30, 2023
Published in Issue Year 2023 Volume: 11 Issue: 2

Cite

APA Paçacı, S., Bingöl, O., & Güvenç, U. (2023). A novel hybrid algorithm based on Stochastic Fractal Search Algorithm and CMA-ES. Düzce Üniversitesi Bilim Ve Teknoloji Dergisi, 11(2), 868-907. https://doi.org/10.29130/dubited.1110725
AMA Paçacı S, Bingöl O, Güvenç U. A novel hybrid algorithm based on Stochastic Fractal Search Algorithm and CMA-ES. DUBİTED. April 2023;11(2):868-907. doi:10.29130/dubited.1110725
Chicago Paçacı, Serdar, Okan Bingöl, and Uğur Güvenç. “A Novel Hybrid Algorithm Based on Stochastic Fractal Search Algorithm and CMA-ES”. Düzce Üniversitesi Bilim Ve Teknoloji Dergisi 11, no. 2 (April 2023): 868-907. https://doi.org/10.29130/dubited.1110725.
EndNote Paçacı S, Bingöl O, Güvenç U (April 1, 2023) A novel hybrid algorithm based on Stochastic Fractal Search Algorithm and CMA-ES. Düzce Üniversitesi Bilim ve Teknoloji Dergisi 11 2 868–907.
IEEE S. Paçacı, O. Bingöl, and U. Güvenç, “A novel hybrid algorithm based on Stochastic Fractal Search Algorithm and CMA-ES”, DUBİTED, vol. 11, no. 2, pp. 868–907, 2023, doi: 10.29130/dubited.1110725.
ISNAD Paçacı, Serdar et al. “A Novel Hybrid Algorithm Based on Stochastic Fractal Search Algorithm and CMA-ES”. Düzce Üniversitesi Bilim ve Teknoloji Dergisi 11/2 (April 2023), 868-907. https://doi.org/10.29130/dubited.1110725.
JAMA Paçacı S, Bingöl O, Güvenç U. A novel hybrid algorithm based on Stochastic Fractal Search Algorithm and CMA-ES. DUBİTED. 2023;11:868–907.
MLA Paçacı, Serdar et al. “A Novel Hybrid Algorithm Based on Stochastic Fractal Search Algorithm and CMA-ES”. Düzce Üniversitesi Bilim Ve Teknoloji Dergisi, vol. 11, no. 2, 2023, pp. 868-07, doi:10.29130/dubited.1110725.
Vancouver Paçacı S, Bingöl O, Güvenç U. A novel hybrid algorithm based on Stochastic Fractal Search Algorithm and CMA-ES. DUBİTED. 2023;11(2):868-907.