Hybrid-Flash Butterfly Optimization Algorithm with Logistic Mapping for Solving the Engineering Constrained Optimization Problems.

Only the smell perception rule is considered in the butterfly optimization algorithm (BOA), which is prone to falling into a local optimum. Compared with the original BOA, an extra operator, i.e., color perception rule, is incorporated into the proposed hybrid-flash butterfly optimization algorithm (HFBOA), which makes it more in line with the actual foraging characteristics of butterflies in nature. Besides, updating the strategy of the control parameters by the logistic mapping is used in the HFBOA for enhancing the global optimal ability. The performance of the proposed method was verified by twelve benchmark functions, where the comparison experiment results show that the HFBOA converges quicker and has better stability for numerical optimization problems, which are compared with six state-of-the-art optimization methods. Additionally, the proposed HFBOA is successfully applied to six engineering constrained optimization problems (i.e., tubular column design, tension/compression spring design, cantilever beam design, etc.). The simulation results reveal that the proposed approach demonstrates superior performance in solving complex real-world engineering constrained tasks.