Renewable energy-based distributed generators are widely embedded into distribution systems for several economical, technical, and environmental tasks. The main concern related to the renewable-based distributed generators, especially photovoltaic and wind turbine generators, is the continuous variations in their output powers due to variations in solar irradiance and wind speed, which leads to uncertainties in the power system. Therefore, the uncertainties of these resources should be considered for feasible planning. The main innovation of this paper is that it proposes an efficient stochastic framework for the optimal planning of distribution systems with optimal inclusion of renewable-based distributed generators, considering the uncertainties of load demands and the output powers of the distributed generators. The proposed stochastic framework depends upon the scenario-based method for modeling the uncertainties in distribution systems. In this framework, a multi-objective function is considered for optimal planning, including minimization of the expected total power loss, the total system voltage deviation, the total cost, and the total emissions, in addition to enhancing the expected total voltage stability. A novel efficient technique known as the Equilibrium Optimizer (EO) is actualized to appoint the ratings and locations of renewable-based distributed generators. The effectiveness of the proposed strategy is applied on an IEEE 69-bus network and a 94-bus practical distribution system situated in Portugal. The simulations verify the feasibility of the framework for optimal power planning. Additionally, the results show that the optimal integration of the photovoltaic and wind turbine generators using the proposed method leads to a reduction in the expected power losses, voltage deviations, cost, and emission rate and enhances the voltage stability by 60.95%, 37.09%, 2.91%, 70.66%, and 48.73%, respectively, in the 69-bus system, while in the 94-bus system these values are enhanced to be 48.38%, 39.73%, 57.06%, 76.42%, and 11.99%, respectively.