This research compared different sizing methods to improve the current autonomous hybrid system in the Galapagos Islands in 2031, analyzing the loss of power supply probability (LPSP). Firstly, the energy that will be consumed in islands in 2031 was obtained using artificial neural networks (ANN) with Matlab according to fundamental parameters in the design of a multilayer perceptron neural network model. Secondly, methods used for sizing the system were HOMER Pro and Simulink Design Optimization (SDO). The dynamic models of the different components of the hybrid system were created in MATLAB/Simulink. The proposed hybrid system was composed of photovoltaic (PV) and wind (WT), and lead–acid batteries, hydraulic pumping, and a diesel generator as the storage and support systems. Then, to design a sustainable system, a hybrid system was dimensioned with renewable energy sources of an appropriate size. The LPSP values obtained were below 0.09% and 0.22%, which showed that the system was optimally dimensioned. In addition, a cost analysis was carried out, and values obtained from NPC and COE according to HOMER Pro were $183 810 067 and 0.26$ per kW h, and $233 385 656 and 0.25$ per kW h and using SDO $148 523 110 and 0.25$ per kW h, $189 576 556 and 0.24$ per kW h for strategies I and II, respectively, of the proposed hybrid system. The data obtained showed that the Latin hypercube algorithm of SDO achieved better optimization compared to HOMER Pro.