In order to effectively reduce the identification error for random loads under multi-point stationary excitation, a method based on genetic algorithm with two-sided weighting of frequency response function matrix and improved regularization parameter is proposed on the basis of the inverse pseudo excitation method. This method integrates genetic algorithm with two-sided matrix weighting, selecting elements of the two-sided weighting matrices as optimization variables. These parameters are encoded into the genetic algorithm population, with minimization of the condition number associated with the load identification equation serving as the global optimization objective. This approach effectively mitigates ill-conditioning near structural natural frequencies of the structure. Considering that noise is unavoidable in practical measurements, the Tikhonov regularization method is introduced during the solution of the load identification equation to reduce measurement noise-induced errors. However, the ill-conditioning of the frequency response matrix varies significantly across frequency points. Using a uniform regularization parameter readily prompts overfitting problems. Therefore, an self-adaptive regularization parameter adjustment strategy is developed based on the generalized cross-validation criterion. Numerical simulations and experimental validation demonstrate that the proposed method is less vulnerable to ill-conditioning and achieves higher accuracy compared to conventional methods such as the inverse pseudo excitation method and the traditional unilateral weighting method.