Improved Runge Kutta Optimizer with Fitness Distance Balance-Based Guiding Mechanism for Global Optimization of High-Dimensional Problems

Abstract

Runge Kutta (RUN) is an up-to-date and well-founded metaheuristic algorithm. The RUN algorithm aims to find the global best in solving problems by going beyond the traps of metaphors. For this purpose, enhanced solution quality mechanism is used to avoid local optimum solutions and increase the convergence speed. Although the RUN algorithm offers promising solutions, it is seen that this algorithm has shortcomings, especially in solving high dimensional multimodal problems. In this study, the solution candidates that guide the search process in the RUN algorithm are developed using the Fitness-Distance Balance (FDB) method. Thus, using the FDB-based RUN algorithm, the global optimum value of many optimization problems will be obtained in the future. CEC 2020 which has current benchmark problems was used to test the performance of the developed FDB-RUN algorithm. 10 different unconstrained benchmark problems taken from CEC 2020 were designed by arranging them in 30/50/100 dimensions. Experimental studies were carried out using the designed benchmark problems and analyzed with Friedman and Wilcoxon statistical test methods. According to the results of the analysis, it was seen that the FDB-RUN variations showed a superior performance compared to the base algorithm (RUN) in all experimental studies. In particular, it has been shown to provide more effective results for the continuous optimization of high-dimensional problems.

Keywords

• Meta-heuristic search
• runge kutta algorithm
• fitness-distance balance (FDB)
• benchmark problems

Yüksek Boyutlu Problemlerin Global Optimizasyonu için Uygunluk Mesafe Dengesi Tabanlı Rehber Mekanizmasıyla Runge Kutta Optimize Edicinin İyileştirilmesi

Abstract

Runge Kutta (RUN), güncel ve sağlam temellere sahip bir metasezgisel algoritmadır. RUN algoritması, metaforların tuzaklarının ötesine geçerek problemlerin çözümünde küresel en iyiyi bulmayı amaçlar. Bu amaçla, yerel optimum çözümlerden kaçınmak ve yakınsama hızını artırmak için geliştirilmiş çözüm kalitesi mekanizması kullanılmaktadır. RUN algoritması umut verici çözümler sunsa da bu algoritmanın özellikle yüksek boyutlu multimodal problemlerin çözümünde eksiklikleri olduğu görülmektedir. Bu çalışmada, Uygunluk-Mesafe Dengesi (FDB) yöntemi kullanılarak RUN algoritmasında arama sürecine rehberlik eden çözüm adayları geliştirilmiştir. Böylece FDB tabanlı RUN algoritması kullanılarak gelecekte birçok optimizasyon probleminin global optimum değeri elde edilecektir. Geliştirilen FDB-RUN algoritmasının performansını test etmek için güncel benchmark sorunları olan CEC 2020 kullanılmıştır. CEC 2020'den alınan 10 farklı kısıtsız kıyaslama problemi 30/50/100 boyutlarında düzenlenerek tasarlanmıştır. Deneysel çalışmalar tasarlanan kıyaslama problemleri kullanılarak gerçekleştirilmiş ve Friedman ve Wilcoxon istatistiksel test yöntemleri ile analiz edilmiştir. Analiz sonuçlarına göre FDB-RUN varyasyonlarının tüm deneysel çalışmalarda temel algoritmaya (RUN) göre daha üstün bir performans gösterdiği görülmüştür. Özellikle yüksek boyutlu problemlerin sürekli optimizasyonu için daha etkili sonuçlar sağladığı gösterilmiştir.

Keywords

• Meta-sezgisel arama
• Runge Kutta algoritması
• uygunluk-mesafe dengesi (FDB)
• kıyaslama problemleri

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