Quadratic and Lagrange interpolation-based butterfly optimization algorithm for numerical optimization and engineering design problem

This work proposes a novel and improved Butterfly Optimization Algorithm (BOA), known as LQBOA, to solve BOA’s inherent limitations. The LQBOA uses Lagrange interpolation and simple quadratic interpolation techniques with adapted parameter settings to enhance the search strategy of BOA and to achieve a better balance of diversification and intensification. LQBOA’s performance was examined on 45 traditional benchmark issues as well as the IEEE CEC 2017 benchmark suites with 10, 30 and 50 dimensions, and the results were compared against popular state-of-the-art and modified algorithms. It was discovered that in more than 85% of cases, the proposed LQBOA outperformed the compared algorithms. The Friedman rank test and Wilcoxon rank test were used to validate the suggested LQBOA’s rank and significance. Additionally, convergence and diversity analyses were performed to investigate its convergence speed and searching behavior, respectively. Furthermore, LQBOA has been successfully deployed to solve twelve real-world issues including several engineering design problems and two multiple gravity assist spacecraft trajectory problems. The results of these problems were compared to those of a wide range of algorithms, demonstrating the superior performance of the proposed LQBOA. In conclusion, LQBOA makes a significant addition to the optimization area, and its application could greatly improve the performance of numerous optimization jobs.