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

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.

Keywords

• Lévy flight distribution
• Metaheuristics
• Nelder-Mead algorithm
• Benchmark functions

References

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