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

Abstract

The Butterfly Optimization Algorithm (BOA) is used widely in the field of optimization due to its proven effectiveness. However, the algorithm has certain limitations such as poor exploration-exploitation balance, lack of diversity, and entrapment into local solutions. To overcome these limitations, a new and improved modification of BOA, called LQBOA, is projected, which employs the Lagrange interpolation formula and simple quadratic interpolation technique to improve the searching strategy and achieve a enhanced equilibrium between diversification and intensification. One of the parameter of BOA, switch probability has also been adaptively adjusted within a specified range, which enables initial exploration of the domain and later exploitation to obtain the global optima. The performance of LQBOA has been evaluated on forty-five classical benchmark problems and IEEE CEC 2017 benchmark suite. The simulation results have judged against that of several state-of-the-art algorithms, and statistical tests such as the Friedman rank test and Wilcoxon rank test have been conducted to justify the rank and significance of the proposed LQBOA. Additionally, convergence and diversity analysis have been carried out to study its searching behaviour.Furthermore, LQBOA has successfully applied to solve eight real-world engineering design problems. The results have been compared with various state-of-the-art algorithms, which demonstrate superior performance of LQBOA with improved exploration-exploitation balance, diversity, and avoidance of local optima. In conclusion, LQBOA represents a significant contribution to the optimization field, and its use could significantly improve the performance of various optimization tasks.