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

Abstract

This paper aims to improve one of the recently proposed metaheuristic approaches known as Lévy flightdistribution (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 originalLFD algorithm. In the first strategy, NM was run twice as much the number of iterations of LFD after thelatter completes its task. In the second strategy, NM was applied after each iterations of LFD instead ofwaiting for the completion of the latter. Lastly, in the third strategy, NM was applied after each iterationsof LFD and run for the total number of current iterations of the latter algorithm. Well-known unimodaland multimodal benchmark functions were adopted, and statistical analysis was performed forperformance evaluation. Further assessment was carried out through a nonparametric statistical test. Theobtained results have shown the proposed versions of LFD algorithm provide significant performanceimprovement in general. In addition, the efficiency of the third strategy was found to be better for NMmodified LFD algorithm which has greater balance between global and local search stages and can beused as an effective tool for function optimization.