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.

An Improved Artificial Atom Algorithm With the Operator of Shuffled Frog Leaping Algorithm

“…Considering the performanceruntime balance, Improved A 3 is clearly superior to all other methods. In addition to these applications, two comparison were made with the variants of the Krill Held Algorithm [32] and Levy Flight Distribution Algorithm [33] in recent studies in the literature for 7 selected test functions. In the first of these comparison, the Improved A 3 method achieved the best results for all test functions except the Rosenbrock function.…”

“…In Table 7, the Improved A 3 method is presented in comparison with four methods based on the Modified Levy Flight Distribution Algorithm (LFD) [33]. The Improved A 3 method was tested with the same parameter values using 7 test functions preferred in the relevant study in the literature.…”

“…In this study, the number of parameters was determined as 30, the population size was 50, and the maximum number of iterations was 1000. The results were compared in terms of best and mean values [33].…”