The issues of governance efficiency and cost caused by the stochastic fluctuations of harmonic sources in power-electronic distribution networks were addressed, and an optimal configuration strategy for shunt active power filters (SAPF) integrating the stochastic characterization of harmonic sources and the,multi-objective particle swarm optimization-genetic algorithm (MOPSO-GA) was proposed. Based on the central limit theorem, probability models for harmonic amplitude and phase were constructed using normal distribution and uniform distribution, and multi-objective optimization was achieved by combining the MOPSO-GA algorithm. Simulation results show that in the IEEE 18-bus system, when only 3 SAPFs are configured, the total harmonic distortion is reduced from 19.88% to 3.32%, and the voltage deviation is controlled from 10.4% to 4.5%. Compared with the traditional MOPSO algorithm, the number of SAPFs is reduced by one, the total capacity is more economical, and the convergence speed of the algorithm and the distribution of the Pareto front are significantly improved. Furthermore, the strategy was verified through an RT-Lab hardware-in-the-loop experimental platform. Under realistic harmonic source conditions, the voltage total harmonic distortion (THD) at the critical node is reduced from 25.24% to 2.12%. This strategy provides an efficient and economical solution for harmonic mitigation in complex distribution networks.