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Utilizing Distributed Generators (DGs) and Energy Storage Systems (ESSs) enhances power system reliability, drawing significant research attention. However, these systems pose challenges, compelling scientists to explore optimization methods. Our paper presents an innovative solution, Parallel Multi-Objective Multi-Verse Optimization (PMOMVO), aimed at optimizing DGs and Battery Energy Storage Systems (BESSs) allocation. This optimization addresses voltage violations and operation costs, crucial concerns for system operators and consumers. By leveraging a parallel approach, PMOMVO significantly accelerates the optimization process. We compared its results with a base case scenario, demonstrating the superior efficiency of our parallel method. It not only enhances the optimization performance but also proves its efficacy by generating optimal solutions from the Pareto front set. This research showcases the benefits of PMOMVO, offering a faster, more efficient, and reliable way to optimize power systems, benefiting both operators and consumers. • Introduces a novel bi-level optimization approach for DG and BESS allocation and operation. • Proposing a multi-objective formulation to identify Pareto optimal solutions, offering a balance between voltage stability and cost-effectiveness. • Optimizes asset operation strategies, considering both peak and off-peak load times, enhancing resource utilization. • Proposes a parallel processing method based on modified MOMVO, significantly accelerating computations for large distribution systems problems. • Achieves a substantial improvement in the speed-up index, ensuring swift and effective DG and BESS allocation and operation in complex systems. [ABSTRACT FROM AUTHOR]

• A new formulation comprising energy exchange between off-peak and peak load hours. • MOGOA comprising an additional stopping criteria. • Reduced Pareto solution space due to cost analysis at peak load hours. • Better performance than the other heuristic optimization algorithms. • Real load and DG data with site-specific constraints and incentives of Turkey. The penetration of small-scale generators (DGs) and battery energy storage systems (BESSs) into the distribution grid is growing rapidly and reaching a high percentage of installed generation capacity. These units can play a significant role in achieving various objectives if installed at suitable locations with appropriate sizes. In this paper, we present a new multi-objective optimization model to improve voltage profiles, minimize DG and BESS costs, and maximize energy transfer between off-peak and peak hours. We allocate and size DG and BESS units to achieve the first two objectives, while optimizing the operation strategy of BESS units for the last objective. The Multi-Objective Grasshopper Optimization Algorithm (MOGOA) is used to solve the formulated constrained optimization problem. The proposed formulation and solution algorithm are tested on 33-bus and 69-bus radial distribution networks. The advantages of the Pareto solutions are discussed from various aspects, and the Pareto solutions are subjected to cost analysis to identify the best solutions in the context of the worst voltage profiles at peak load times. Finally, the performance of the MOGOA algorithm is compared with the other heuristic optimization algorithms using two Pareto optimality indices. [ABSTRACT FROM AUTHOR]