To overcome the shortcomings of the honey badger algorithm, such as low convergence accuracy and premature convergence, and enhance its optimization performance, a multi-strategy improved honey badger algorithm (PSWHBA) is proposed. Firstly, the iterative process is divided into three parts, and different search strategies are selected in different iterative periods to better balance exploration and development. Then, the stagnation threshold is introduced. Once the threshold is reached, a multiple mutation update strategy is performed to help the individual jump out of the local extremum. Finally, the wavelet mutation learning based on simulated annealing is performed on the poor solutions in the population to improve the overall population quality, thereby improving the convergence speed and optimization accuracy. To comprehensively evaluate the performance of the PSWHBA, it is tested on the IEEE CEC2022 test set with several representative comparison algorithms, including optimization accuracy, convergence performance, and difference analysis with comparison algorithms. Experiments show that the PSWHBA is superior to comparison algorithms, with excellent optimization performance and stability.