The stochastic resource allocation (SRA) problem is an extensive class of combinatorial optimization problems widely existing in complex systems such as communication networks and unmanned systems. In SRA, the ability of a resource to complete a task is described by certain probability, and the objective is to maximize the reward by appropriately assigning available resources to different tasks. This paper is aimed at an important branch of SRA, that is, stochastic SRA (SSRA) for which the probability for resources to complete tasks is also uncertain. Firstly, a general SSRA model with multiple independent uncertain parameters (GSSRA-MIUP) is built to formulate the problem. Then, a scenario-based reformulation which can address multi-source uncertainties is proposed to facilitate the problem-solving process. Secondly, in view of the superiority of the differential evolution algorithm in real-valued optimization, a discrete version of this algorithm was originally proposed and further combined with a specialized local search to create an efficient hybrid optimizer. The hybrid algorithm is compared with the discrete differential evolution algorithm, a pure random sampling method, as well as a restart local search method. Experimental results show that the proposed hybrid optimizer has obvious advantages in solving GSSRA-MIUP problems.