Aiming at the problem of butterfly optimization algorithm

this paper proposes a butterfly optimization algorithm which fuses the differential mutation strategy and adaptively adjusts the weight according to the evolutionary algebra. The nonlinear inertial weight is introduced in the global search stage to improve the update equation of butterfly position

the search range and granularity of the algorithm in different evolution periods are adjusted adaptively

and the convergence speed and optimization accuracy of the algorithm are improved. The global equation is further improved by adding F distribution global adaptive random mutation to improve the global search ergodicity of the algorithm

and prevent the occurrence of low precision precocious phenomenon. The bidirectional differential mutation strategy with decision coefficient and disturbance factor is integrated in the local search stage

which makes the exploration of butterfly individuals more directional without derogating the diversity of the population

which is beneficial to the algorithm to get rid of the local extremum points and speed up the convergence speed. The theoretical analysis proves that the time complexity of the improved algorithm is consistent with the basic butterfly optimization algorithm. The multi-dimensional test results of six representative contrast algorithms on benchmark functions of CEC 2017 show that the optimization accuracy and convergence speed of the improved algorithm is obviously better than those of other contrast algorithms in solving the optimization problem of high-dimensional complex functions

and the change of dimensions have less impact on the performance of the algorithm

and the optimization performance is better and more stable.