To tackle complex numerical optimization problems, this paper proposes an improved hiking optimization algorithm based on Cauchy distribution operator and random differential mutation strategy (CDHOA). The algorithm enhances diversity through effective population initialization, balances global search with local exploitation using the inverse cumulative Cauchy distribution operator, and employs a random differential mutation strategy to boost exploitation and reduce local optima risks. Experimental results show the average performance of CDHOA on the CEC2017 test set is better than that of eight comparison algorithms. The statistical test further confirmed that the performance difference was significant. Nine representative test functions are selected from the CEC2017 test set, and the effectiveness of the three enhancement strategies in the algorithm is verified by comparative experiments. Additionally, it is applied to the parameter identification of photovoltaic model, and a small root mean square error of 2.43×10-3 is achieved, which has the best result of all comparison algorithms. In two kinds of engineering design problems, the algorithm achieves the minimum objective function value, which is better than the comparison algorithms. Overall，CDHOA performs well in global search ability, convergence speed and accuracy, which effectively improves the performance of solving complex numerical optimization problems.