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Runge Kutta Optimization for Fixed Size Multimodal Test Functions

Year 2022, Volume: 6 Issue: 2, 144 - 155, 31.12.2022

Fatih Cantaş Serdar Özyön Celal Yaşar

https://doi.org/10.47897/bilmes.1219033

Abstract

In this study, it is aimed to increase the success of the Runge Kutta (RUN) algorithm, which is used in the solution of many optimization problems in the literature, on fixed-size test functions by changing the parameter values. Optimization can be defined as making a system most efficient at the least possible cost under certain constraints. For this process, many optimization algorithms have been designed in the literature and used to obtain the best solutions for certain problems. The most important parts in solving these problems are modeling the problem correctly, determining the parameters and constraints of the problem, and finally choosing a suitable meta-heuristic algorithm for the solution of the objective function. Not every algorithm is suitable for every problem structure. Therefore, in this study, the suitability of the RUN algorithm for the solution of fixed-size functions will be evaluated. Theoretically, Runge-Kutta methods used in numerical analysis are an important type of the family of closed and open iterative methods for solution approximations of ordinary differential equations. The RUN algorithm is also designed with inspiration from these methods. In order to evaluate the performance of the RUN algorithm on fixed-size functions in the study, 10 fixed-size multimodal test functions (Shekel's Foxholes, Kowalik, Six-Hump Camel-Back, Branin, Goldstein-Price, Hartman3, Hartman6, Shekel5, Shekel7, Shekel10) have been found in the literature before was selected. Solutions for each of the selected functions are obtained by changing the parameter values of the RUN algorithm. The obtained solution values were evaluated by comparing the solutions obtained with Slime Mold Algorithm (SMA) and Hunger Games Search (HGS) algorithms.

Keywords

Runge kutta algorithm (RUN) Slime mold algorithm (SMA) Hunger games search (HGS) Fixed size multimodal test functions.

References

  • [1] Özyön, S., Yaşar, C., Temurtaş, H., Test fonksiyonları için kaos tabanlı yerçekimsel arama algoritmaları (CbGSA-X), Düzce Üniversitesi Bilim ve Teknoloji Dergisi, 8(3),1771-1793, 2020.
  • [2] Ahmadianfar, I., Heidari, AA., Gandomi, AH., Chu, X., Chen, H. RUN beyond the metaphor: An efficient optimization algorithm based on Runge Kutta method, Expert Systems with Applications, 181, 2021, 115079.
  • [3] Yang, Y., Chen, H., Heidari, AA., Gandomi, AH., Hunger games search: Visions, conception, implementation, deep analysis, perspectives, and towards performance shifts, Expert Systems with Applications, 177, 2021, 114864.
  • [4] Çam, H., Yaşar, C., Özyön, S. Açlık oyunları arama algoritmasının değişken boyutlu test fonksiyonlarına uygulanması, 4. Uluslararası Palandöken Bilimsel Çalışmalar Kongresi, Erzurum, 880-891, 28-29.04.2022.
  • [5] Li, S., Chen, H., Wang, M., Heidari, AA., Mirjalili, S., Slime mould algorithm: a new method for stochastic optimization, Future generation computer systems, 111, 300-323, 2020.
  • [6] Kaya, MF., Yaşar, C., Özyön, S. Meta-Sezgisel Balçık Kalıp Algoritmasının Performans Analizi - Performance Analysis of Meta Heuristic Slime Mould Algorithm, 4. Uluslararası Palandöken Bilimsel Çalışmalar Kongresi, Erzurum, 910-921, 28.04.2022.
  • [7] Mirjalili, S., SCA: A sine cosine algorithm for solving optimization problems, Knowledge-Based Systems, 96, 120-133, 2016.
  • [8] Mirjalili, S., Mirjalili, SM., Hatamlou, A. Multi-verse optimizer: a natüre-inspired algorithm for global optimization, Neural Computing and Applications, 27, 495-513, 2016.
  • [9] Formato, R., Central force optimization: A new metaheuristic with applications in applied electromagnetics, Progress in Electromagnetics Research, 77(1), 425-491, 2007.
  • [10] Özyön, S., Durmuş, B., Kuvat, G. Özcan, G. Yüksek boyutlu problemlerin optimizasyonunda parametre seçiminin genetik algoritma performansına etkileri, International Multidisciplinary Congree of Eurasia (IMCOFE’15), Üsküp, 01.09.2015.
  • [11] Özyön, S., Yaşar, C. Temurtaş, H. Incremental gravitational search algorithm for high-dimensional benchmark functions, Neural Computing and Applications, 31(8), 3779-3803, 2019.

Runge Kutta Optimization for Fixed Size Multimodal Test Functions

Year 2022, Volume: 6 Issue: 2, 144 - 155, 31.12.2022

Fatih Cantaş Serdar Özyön Celal Yaşar

https://doi.org/10.47897/bilmes.1219033

Abstract

In this study, it is aimed to increase the success of the Runge Kutta (RUN) algorithm, which is used in the solution of many optimization problems in the literature, on fixed-size test functions by changing the parameter values. Optimization can be defined as making a system most efficient at the least possible cost under certain constraints. For this process, many optimization algorithms have been designed in the literature and used to obtain the best solutions for certain problems. The most important parts in solving these problems are modeling the problem correctly, determining the parameters and constraints of the problem, and finally choosing a suitable meta-heuristic algorithm for the solution of the objective function. Not every algorithm is suitable for every problem structure. Therefore, in this study, the suitability of the RUN algorithm for the solution of fixed-size functions will be evaluated. Theoretically, Runge-Kutta methods used in numerical analysis are an important type of the family of closed and open iterative methods for solution approximations of ordinary differential equations. The RUN algorithm is also designed with inspiration from these methods. In order to evaluate the performance of the RUN algorithm on fixed-size functions in the study, 10 fixed-size multimodal test functions (Shekel's Foxholes, Kowalik, Six-Hump Camel-Back, Branin, Goldstein-Price, Hartman3, Hartman6, Shekel5, Shekel7, Shekel10) have been found in the literature before was selected. Solutions for each of the selected functions are obtained by changing the parameter values of the RUN algorithm. The obtained solution values were evaluated by comparing the solutions obtained with Slime Mold Algorithm (SMA) and Hunger Games Search (HGS) algorithms.

Keywords

Runge kutta algorithm (RUN) Slime mold algorithm (SMA) Hunger games search (HGS) Fixed size multimodal test functions.

References

  • [1] Özyön, S., Yaşar, C., Temurtaş, H., Test fonksiyonları için kaos tabanlı yerçekimsel arama algoritmaları (CbGSA-X), Düzce Üniversitesi Bilim ve Teknoloji Dergisi, 8(3),1771-1793, 2020.
  • [2] Ahmadianfar, I., Heidari, AA., Gandomi, AH., Chu, X., Chen, H. RUN beyond the metaphor: An efficient optimization algorithm based on Runge Kutta method, Expert Systems with Applications, 181, 2021, 115079.
  • [3] Yang, Y., Chen, H., Heidari, AA., Gandomi, AH., Hunger games search: Visions, conception, implementation, deep analysis, perspectives, and towards performance shifts, Expert Systems with Applications, 177, 2021, 114864.
  • [4] Çam, H., Yaşar, C., Özyön, S. Açlık oyunları arama algoritmasının değişken boyutlu test fonksiyonlarına uygulanması, 4. Uluslararası Palandöken Bilimsel Çalışmalar Kongresi, Erzurum, 880-891, 28-29.04.2022.
  • [5] Li, S., Chen, H., Wang, M., Heidari, AA., Mirjalili, S., Slime mould algorithm: a new method for stochastic optimization, Future generation computer systems, 111, 300-323, 2020.
  • [6] Kaya, MF., Yaşar, C., Özyön, S. Meta-Sezgisel Balçık Kalıp Algoritmasının Performans Analizi - Performance Analysis of Meta Heuristic Slime Mould Algorithm, 4. Uluslararası Palandöken Bilimsel Çalışmalar Kongresi, Erzurum, 910-921, 28.04.2022.
  • [7] Mirjalili, S., SCA: A sine cosine algorithm for solving optimization problems, Knowledge-Based Systems, 96, 120-133, 2016.
  • [8] Mirjalili, S., Mirjalili, SM., Hatamlou, A. Multi-verse optimizer: a natüre-inspired algorithm for global optimization, Neural Computing and Applications, 27, 495-513, 2016.
  • [9] Formato, R., Central force optimization: A new metaheuristic with applications in applied electromagnetics, Progress in Electromagnetics Research, 77(1), 425-491, 2007.
  • [10] Özyön, S., Durmuş, B., Kuvat, G. Özcan, G. Yüksek boyutlu problemlerin optimizasyonunda parametre seçiminin genetik algoritma performansına etkileri, International Multidisciplinary Congree of Eurasia (IMCOFE’15), Üsküp, 01.09.2015.
  • [11] Özyön, S., Yaşar, C. Temurtaş, H. Incremental gravitational search algorithm for high-dimensional benchmark functions, Neural Computing and Applications, 31(8), 3779-3803, 2019.
There are 11 citations in total.

Details

Primary Language Turkish
Subjects Engineering
Journal Section Articles
Authors

Fatih Cantaş 0000-0001-5573-021X

Serdar Özyön 0000-0002-4469-3908

Celal Yaşar 0000-0002-1251-3562

Publication Date December 31, 2022
Acceptance Date December 30, 2022
Published in Issue Year 2022 Volume: 6 Issue: 2

Cite

APA Cantaş, F., Özyön, S., & Yaşar, C. (2022). Runge Kutta Optimization for Fixed Size Multimodal Test Functions. International Scientific and Vocational Studies Journal, 6(2), 144-155. https://doi.org/10.47897/bilmes.1219033
AMA Cantaş F, Özyön S, Yaşar C. Runge Kutta Optimization for Fixed Size Multimodal Test Functions. ISVOS. December 2022;6(2):144-155. doi:10.47897/bilmes.1219033
Chicago Cantaş, Fatih, Serdar Özyön, and Celal Yaşar. “Runge Kutta Optimization for Fixed Size Multimodal Test Functions”. International Scientific and Vocational Studies Journal 6, no. 2 (December 2022): 144-55. https://doi.org/10.47897/bilmes.1219033.
EndNote Cantaş F, Özyön S, Yaşar C (December 1, 2022) Runge Kutta Optimization for Fixed Size Multimodal Test Functions. International Scientific and Vocational Studies Journal 6 2 144–155.
IEEE F. Cantaş, S. Özyön, and C. Yaşar, “Runge Kutta Optimization for Fixed Size Multimodal Test Functions”, ISVOS, vol. 6, no. 2, pp. 144–155, 2022, doi: 10.47897/bilmes.1219033.
ISNAD Cantaş, Fatih et al. “Runge Kutta Optimization for Fixed Size Multimodal Test Functions”. International Scientific and Vocational Studies Journal 6/2 (December 2022), 144-155. https://doi.org/10.47897/bilmes.1219033.
JAMA Cantaş F, Özyön S, Yaşar C. Runge Kutta Optimization for Fixed Size Multimodal Test Functions. ISVOS. 2022;6:144–155.
MLA Cantaş, Fatih et al. “Runge Kutta Optimization for Fixed Size Multimodal Test Functions”. International Scientific and Vocational Studies Journal, vol. 6, no. 2, 2022, pp. 144-55, doi:10.47897/bilmes.1219033.
Vancouver Cantaş F, Özyön S, Yaşar C. Runge Kutta Optimization for Fixed Size Multimodal Test Functions. ISVOS. 2022;6(2):144-55.


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