Runge Kutta Optimization for Fixed Size Multimodal Test Functions

Öz

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.

Anahtar Kelimeler

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

Kaynakça

1. [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. [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. [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. [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. [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. [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. [7] Mirjalili, S., SCA: A sine cosine algorithm for solving optimization problems, Knowledge-Based Systems, 96, 120-133, 2016.
8. [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. [9] Formato, R., Central force optimization: A new metaheuristic with applications in applied electromagnetics, Progress in Electromagnetics Research, 77(1), 425-491, 2007.
10. [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. [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.