Journals / Dicle Üniversitesi Mühendislik Fakültesi Mühendislik Dergisi / 2026 / Cilt: 12 Sayı: 3

A Novel Modified Lévy Flight Distribution Algorithm based on Nelder-Mead Method for Function Optimization

Ahmet Dündar(MUŞ ALPARSLAN ÜNİVERSİTESİ)0000-0002-2123-0564
Davut İzci(BATMAN ÜNİVERSİTESİ)0000-0001-8359-0875
Serdar Ekinci(BATMAN ÜNİVERSİTESİ)0000-0002-7673-2553
Erdal Eker(MUŞ ALPARSLAN ÜNİVERSİTESİ)0000-0002-5470-8384
Pages
487–497
Publication Date
2021-06-29
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

In addition, the efficiency of the third strategy was found to be better for NM modified LFD algorithm which has greater balance between global and local search stages and can be used as an effective tool for function optimization.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:This paper aims to improve one of the recently proposed metaheuristic approaches known as Lévy flight distribution (LFD) algorithm by adopting a well-known simplex search algorithm named Nelder-Mead (NM) method.
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Key Findings & Data:Three new strategies were utilized to demonstrate the improved capability of the original LFD algorithm.
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Conclusion & Impact:In addition, the efficiency of the third strategy was found to be better for NM modified LFD algorithm which has greater balance between global and local search stages and can be used as an effective tool for function optimization.
🔬Design:Modeling & Simulation
📍Scope:Comprehensive Sample
⚙️Variables:Lévy flight distribution · Metaheuristics · Nelder-Mead algorithm

Abstract

This paper aims to improve one of the recently proposed metaheuristic approaches known as Lévy flight distribution (LFD) algorithm by adopting a well-known simplex search algorithm named Nelder-Mead (NM) method. Three new strategies were utilized to demonstrate the improved capability of the original LFD algorithm. In the first strategy, NM was run twice as much the number of iterations of LFD after the latter completes its task. In the second strategy, NM was applied after each iterations of LFD instead of waiting for the completion of the latter. Lastly, in the third strategy, NM was applied after each iterations of LFD and run for the total number of current iterations of the latter algorithm. Well-known unimodal and multimodal benchmark functions were adopted, and statistical analysis was performed for performance evaluation. Further assessment was carried out through a nonparametric statistical test. The obtained results have shown the proposed versions of LFD algorithm provide significant performance improvement in general. In addition, the efficiency of the third strategy was found to be better for NM modified LFD algorithm which has greater balance between global and local search stages and can be used as an effective tool for function optimization.

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Cite This Article

Dündar, A., İzci, D., Ekinci, S., Eker, E. (2021). A Novel Modified Lévy Flight Distribution Algorithm based on Nelder-Mead Method for Function Optimization. Dicle Üniversitesi Mühendislik Fakültesi Mühendislik Dergisi, Cilt: 12 Sayı: 3, 487–497. https://doi.org/10.24012/dumf.955645

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