The need for energy and environmental sustainability drives the adoption of renewable energy systems to reduce greenhouse gas emissions. Efficient planning of energy sources is crucial for a reliable distribution network. This article solves the optimal allocation of hybrid energy sources (i.e., Renewable Distribution Generators (RDGs) and Battery Energy Storage System (BESS)) problem, aiming to minimize the annual energy loss and investment costs simultaneously. The proposed formulation includes the uncertainties such as forced outages of RDGs, intermittence in RDG power generation, Expected Energy Not Served (EENS) by DG units, and time-varying demand altogether in the existing formulation. To evaluate the effectiveness of the proposed formulation, a Multi-Objective Evolutionary Algorithm based on Decomposition with Dynamic Resource Allocation (MOEA/D-DRA) is used. Simulation studies are conducted on IEEE 33-node and TNEB 84-node Radial Distribution Systems (RDSs), comparing results with the Rider Optimization Algorithm (ROA) and Hybrid Nelder Mead-Particle Swarm Optimization (HNMPSO) respectively. The proposed formulation for a Multi-objective Optimization of Hybrid Energy Sources allocation problem solved by the MOEA/D-DRA algorithm provides improved benefits like minimum annual energy loss, investment cost, CO₂ emission, EENS by the DG units, and enhanced system voltage stability and voltage profile.