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

Abstract

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.

Improved Black Widow Spider Optimization Algorithm Integrating Multiple Strategies

“…The best solutions for the BWOA, IBWOA, RO [ 24 ], CPSO [ 24 ], GWO [ 2 ], WOA [ 4 ], SSA [ 25 ]and HFBOA [ 26 ] regarding the design of welded beams are given in Table 10 . The optimal value of IBWOA is 1.706809, which means that the total cost of the welded beam design is minimized when and are set to 0.204300, 3.273201, 9.104938 and 0.205632, respectively.…”

“…The optimal solutions obtained for the BWOA, IBWOA, PSO [ 21 ], GWO [ 2 ], WOA [ 4 ], GSA [ 27 ]and HFBOA [ 26 ] regarding the design of tension/compression springs are given in Table 11 . The optimal value of the IBWOA is 0.012666, which means that the total cost of the tension/compression spring is minimized when , and are set as 0.051889, 0.361544 and 11.011088, respectively.…”

“…The optimal solutions obtained of IBWOA, BWOA, CS [ 5 ], SSA [ 25 ], HHO [ 28 ], MBA [ 29 ] and HFBOA [ 26 ] regarding the design of the three-bar truss are given in Table 12 . The optimal value of the IBWOA is 263.46343425, which means that the total cost of three-bar truss design is minimized when and are set as 0.786027200 and 0.407114772, respectively.…”

“…The optimal solutions obtained for the BWOA, IBWOA, CS [ 5 ], SSA [ 25 ], SOS [ 30 ], MMA [ 31 ] and HFBOA [ 26 ] regarding the cantilever beam design are given in Table 13 . The optimal value of the IBWOA is 1.307284, i.e., when and are set as 6.044796, 4.805171, 4.431811, 3.471760 and 2.196531, and the total cost of the cantilever beam is minimized.…”

Application of Heuristic Algorithms in the Tomography Problem for Pre-Mining Anomaly Detection in Coal Seams

“…The LSAM algorithm is presented in the scheme Algorithm 5. In the literature, there are many papers about the applications of the butterfly algorithm and its modifications (see [ 41 , 42 , 43 ]).…”