mLBOA: A Modified Butterfly Optimization Algorithm with Lagrange Interpolation for Global Optimization

Though the Butterfly Bptimization Algorithm (BOA) has already proved its effectiveness as a robust optimization algorithm, it has certain disadvantages. So, a new variant of BOA, namely mLBOA, is proposed here to improve its performance. The proposed algorithm employs a self-adaptive parameter setting, Lagrange interpolation formula, and a new local search strategy embedded with Levy flight search to enhance its searching ability to make a better trade-off between exploration and exploitation. Also, the fragrance generation scheme of BOA is modified, which leads for exploring the domain effectively for better searching. To evaluate the performance, it has been applied to solve the IEEE CEC 2017 benchmark suite. The results have been compared to that of six state-of-the-art algorithms and five BOA variants. Moreover, various statistical tests, such as the Friedman rank test, Wilcoxon rank test, convergence analysis, and complexity analysis, have been conducted to justify the rank, significance, and complexity of the proposed mLBOA. Finally, the mLBOA has been applied to solve three real-world engineering design problems. From all the analyses, it has been found that the proposed mLBOA is a competitive algorithm compared to other popular state-of-the-art algorithms and BOA variants.