Journal of Bionic Engineering (2022) 19:554–570  https://doi.org/10.1007/s42235-021-00143-3

Enhanced Butterfy Optimization Algorithm for Large-Scale Optimization Problems 

Yu Li1  · Xiaomei Yu2  · Jingsen Liu3 

1 Institute of Management Science and Engineering, and School of Business, Henan University, Kaifeng 475004, China
2 School of Business, Henan University, Kaifeng 475004, China
3 Institute of Intelligent Network Systems, and Software School, Henan University, Kaifeng 475004, China

Abstract  To solve large-scale optimization problems, Fragrance coefcient and variant Particle Swarm local search Butterfy Optimization Algorithm (FPSBOA) is proposed. In the position update stage of Butterfy Optimization Algorithm (BOA), the fragrance coefcient is designed to balance the exploration and exploitation of BOA. The variant particle swarm local search strategy is proposed to improve the local search ability of the current optimal butterfy and prevent the algorithm from falling into local optimality. 19 2000-dimensional functions and 20 1000-dimensional CEC 2010 large-scale functions are used to verify FPSBOA for complex large-scale optimization problems. The experimental results are statistically analyzed by Friedman test and Wilcoxon rank-sum test. All attained results demonstrated that FPSBOA can better solve more challenging scientifc and industrial real-world problems with thousands of variables. Finally, four mechanical engineering problems and one ten-dimensional process synthesis and design problem are applied to FPSBOA, which shows FPSBOA has the feasibility and efectiveness in real-world application problems. 

Keywords Butterfy optimization algorithm · Fragrance coefcient · Variant particle swarm local search · Large-scale optimization problems · Real-world application problems

Comparison of 2000-dimensional convergence curves