To address the issue of zebra optimization algorithm being prone to local optimum and poor robustness, a Multi-strategy combined zebra optimization algorithm is proposed. Utilizing a convergence factor based on logistic chaos as the step control parameter balances the algorithm's global exploration and local exploitation capabilities, thereby enhancing its optimization precision; Utilizing a position perturbation strategy avoid the decrease of population diversity in the iterative process and enhance the ability of the algorithm to jump out of local optimum; Utilizing a memory update strategy reduces the blindness of the location update strategy. Selecting Fourteen standard test functions examine the excellence of the improved algorithm in three aspects: convergence accuracy, convergence speed, and statistical tests. Experimental results show that the improved strategy effectively improves the optimization accuracy and the ability to jump out of the local optimal of the zebra optimization algorithm. The effectiveness and practicability of the algorithm in dealing with practical optimization problems are further verified by engineering optimization problems.