The installation of Distributed Generation (DG) units in the Radial Distribution Networks (RDNs) has significant potential to minimize active power losses in distribution networks. However, inaccurate size(s) and location(s) of DG units increase power losses and associated Annual Financial Losses (AFL). A comprehensive review of the literature reveals that existing analytical, metaheuristic and hybrid algorithms employed on DG allocation problems trap in local or global optima resulting in higher power losses. To address these limitations, this article develops a parallel hybrid Arithmetic Optimization Algorithm and Salp Swarm Algorithm (AOASSA) for the optimal sizing and placement of DGs in the RDNs. The proposed parallel hybrid AOASSA enables the mutual benefit of both algorithms, i.e., the exploration capability of the SSA and the exploitation capability of the AOA. The performance of the proposed algorithm has been analyzed against the hybrid Arithmetic Optimization Algorithm Particle Swarm Optimization (AOAPSO), Salp Swarm Algorithm Particle Swarm Optimization (SSAPSO), standard AOA, SSA, and Particle Swarm Optimization (PSO) algorithms. The results obtained reveals that the proposed algorithm produces quality solutions and minimum power losses in RDNs. The Power Loss Reduction (PLR) obtained with the proposed algorithm has also been validated against recent analytical, metaheuristic and hybrid optimization algorithms with the help of three cases based on the number of DG units allocated. Using the proposed algorithm, the PLR and associated AFL reduction of the 33-bus and 69-bus RDNs improved to 65.51% and 69.14%, respectively. This study will help the local distribution companies to minimize power losses and associated AFL in the long-term planning paradigm.