Evolutionary Algorithms (EAs) are widely used general-purpose optimization methods due to their domain independence. However, under a limited number of function evaluations (#FEs), the performance of EAs is quite sensitive to the quality of the initial population. Obtaining a high-quality initial population without problem-specific knowledge remains a significant challenge. To address this, this work proposes a general-purpose population initialization method, named mixture-of-experience for population initialization (MPI), for binary optimization problems where decision variables take values of 0 or 1. MPI leverages solving experiences from previously solved problems to generate high-quality initial populations for new problems using only a small number of FEs. Its main novelty lies in a general-purpose approach for representing, selecting, and transferring solving experiences without requiring problem-specific knowledge. Extensive experiments are conducted across six binary optimization problem classes, comprising three classic classes and three complex classes from real-world applications. The experience repository is constructed solely based on instances from the three classic classes, while the performance evaluation is performed across all six classes. The results demonstrate that MPI effectively transfers solving experiences to unseen problem classes (i.e., the complex ones) and higher-dimensional problem instances, significantly outperforming existing general-purpose population initialization methods.