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In this paper, to solve the multi-objective problem of distribution feeder reconfiguration (DFR) in the presence of distributed generation (DG), the hybrid particle swarm optimization and gravitational search algorithm (PSOGSA) has been proposed, which is a combination of particle optimization (PSO) and gravitational (GSA) optimization algorithm. In this field, the power losses and operating costs are the two most used objective functions in the literature. In addition to the mentioned objective functions, this paper also considers the optimal generation capacity of DG resources and energy not supplied (ENS), which is one of the basic reliability indexes of distribution networks. In this paper, the values of different objective functions are normalized by the fuzzy method, and also the Fuzzy decision-maker is used to determine the most optimal solution among the Pareto-optimal solutions. The proposed algorithm is implemented on IEEE 70-bus and 119-bus test systems. The simulation results show the efficiency of the proposed PSOGSA in improving the considered objective functions. The proposed method, by establishing a suitable fit between different objective functions has introduced a more efficient structure with lower losses and operating costs, as well as greater reliability, compared to other optimization algorithms. [ABSTRACT FROM AUTHOR]