The increase in installed PV capacity worldwide and the intermittent nature of solar resources highlight the importance of power prediction for grid integration of this technology. Therefore, there is an urgent need for an effective prediction model, but the choice of model hyperparameters greatly affects the prediction performance. In this paper, a multi-strategy improved snowmelt algorithm (MISAO) is proposed for optimizing intrinsic computing-expressive empirical mode decomposition with adaptive noise (ICEEMDAN) and weighted least squares support vector machine for PV power forecasting. Firstly, a cyclic chaotic mapping initialization strategy is used to generate a uniformly distributed high-quality population, which facilitates the algorithm to enter the appropriate search domain quickly. Secondly, the Gaussian diffusion strategy enhances the local exploration ability of the intelligences and extends their search in the solution space, effectively preventing them from falling into local optima. Finally, a stochastic follower search strategy is employed to reserve better candidate solutions for the next iteration, thus achieving a robust exploration–exploitation balance. With these strategies, the optimization performance of MISAO is comprehensively improved. In order to comprehensively evaluate the optimization performance of MISAO, a series of numerical optimization experiments were conducted using IEEE CEC2017 and test sets, and the effectiveness of each improvement strategy was verified. In terms of solution accuracy, convergence speed, robustness, and scalability, MISAO was compared with the basic SAO, various state-of-the-art optimizers, and some recently developed improved algorithms. The results showed that the overall optimization performance of MISAO is excellent, with Friedman average rankings of 1.80 and 1.82 in the two comparison experiments. In most of the test cases, MISAO delivered more accurate and reliable solutions than its competitors. In addition, the altered algorithm was applied to the selection of hyperparameters for the ICEEMDAN-WLSSVM PV prediction model, and seven neural network models, including WLSSVM, ICEEMDAN-WLSSVM, and MISAO-ICEEMDAN-WLSSVM, were used to predict the PV power under three different weather types. The results showed that the models have high prediction accuracy and stability. The MAPE, MAE and RMSE of the proposed model were reduced by at least 25.3%, 17.8% and 13.3%, respectively. This method is useful for predicting the output power, which is conducive to the economic dispatch of the grid and the stable operation of the power system.