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The objective of the present paper is to study the optimum installation of Non-dispatchable Distributed Generations (NDG) in the distribution network of given sizes under the given scheme. The uncertainty of various random (uncertain) parameters like load, wind and solar operated DG besides uncertainty of fuel prices has been investigated by the three-point estimate method (3-PEM) and Monte Carlo Simulation (MCS) based methods. Nearly twenty percent of the total number of buses are selected as candidate buses for NDG placement on the basis of system voltage profile to limit the search space. Weibull probability density function (PDF) is considered to address uncertain characteristics of solar radiation and wind speed under different scenarios. Load uncertainty is described by Standard Normal Distribution Function (SNDF). To investigate the solution of optimal probabilistic load flow (OPLF) three-point PEM-based technique was applied. For optimization, Genetic Algorithm (GA), Particle Swarm Optimization (PSO) and GA-PSO hybrid-based Artificial Intelligent (AI) based optimization techniques are employed to achieve the optimum value of the multi-objectives function. The proposed multi-objective function comprises loss and different costs. The proposed methods have been applied to IEEE 33- bus radial distribution network. Simulation results obtained by these techniques are compared based on loss minimization capability, enhancement of system bus voltage profile and reduction of cost and fitness functions. The major findings of the present study are the PEM-based method which provides almost similar results as MCS based method with less computation time and as far as loss minimization capacity, voltage profile improvement etc. is concerned, the hybrid-based optimization methods are compared with GA and PSO based optimization techniques. Full article