Abstract: To solve large-scale optimization problems, Fragrance coefficient and variant Particle Swarm local search Butterfly Optimization Algorithm (FPSBOA) is proposed. In the position update stage of Butterfly Optimization Algorithm (BOA), the fragrance coefficient 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 butterfly 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 scientific 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 effectiveness in real-world application problems.

Key words: Butterfy optimization algorithm, Fragrance coefcient, Variant particle swarm local search, Large-scale optimization problems, Real-world application problems