A Critical Review of Moth-Flame Optimization Algorithm and Its Variants: Structural Reviewing, Performance Evaluation, and Statistical Analysis

A growing trend of introducing new metaheuristic algorithms and their improvements is observed with almost the same inherited weaknesses. The main reason is that a few studies have been performed to analyze the algorithms and their variants before improving them. This paper aims to review and analyze the moth-flame optimization (MFO) algorithm and its variants to show the structural reviewing, performance evaluation, and statistical analysis required before improving a metaheuristic algorithm. First, the MFO is described, and then its eligible variants are selected and reviewed in three categories: improved, hybrid, and adapted. Then, the outstanding developments of the eligible MFO variants are reviewed from a structural point of view. Next, to show the weaknesses and strengths of the MFO, its behavior, convergence, and balance ability are qualitatively analyzed. This paper quantitatively measures the performance of the MFO and its state-of-the-art variants. It also uses well-regarded criteria to conduct statistical tests among the algorithms. The results show that IMFO achieves the highest solution quality in dimensions 10 and 30, while m-DMFO achieves the highest in dimension 100. Overall, m-DMFO outperforms MFO and its state-of-the-art variants, with an overall effectiveness of 39.08%. Moreover, the results show that CMFO is the quickest MFO variant among the other algorithms regarding execution time. The findings of this study demonstrate that despite their claims, most MFO variants have not tackled the weaknesses and still inherently suffer from the same shortcomings. Thus, it is recommended to consider structural reviewing, performance evaluation, and statistical analysis performed in this study before improving other metaheuristic algorithms.