This paper proposes a probabilistic simulation-based multi-objective optimization approach for dimensioning robust renewable based Hybrid Power Systems. The method integrates an Optimization Module based on a multi-objective Genetic Algorithm, an Uncertainty Module that uses Latin Hypercube Sampling method and Monte Carlo Simulation to generate uncertainty scenarios and a Simulation Module to simulate the power system under real operating conditions. Uncertainties considered include the renewable resources availability, the load demand, and the probability of the components' failure. The performance of the proposed approach was assessed in a rural community of the Amazonian region of Brazil. Results show that a system configuration with the same level of reliability as in the deterministic scenario implies a higher economic cost; however, the configurations obtained probabilistically represent feasible robust solutions and guarantee a reliable source of generation. The proposed optimization method constitutes a useful decision making tool for dimensioning hybrid power systems that require both optimality and robustness.