Wind energy is an abundant renewable energy resource that has been extensively used worldwide in recent years. The present work proposes a new Multi-Objective Optimization (MOO) based genetic algorithm (GA) model for a wind energy system. The proposed algorithm consists of non-dominated sorting which focuses to maximize the power extraction of the wind turbine, minimize the cost of generating energy, and the lifetime of the battery. Additionally, the performance characteristics of the wind turbine and battery energy storage system (BESS) are analyzed specifically torque, current, voltage, state of charge (SOC), and internal resistance. The complete analysis is carried out in the MATLAB/Simulink platform. The simulated results are compared with existing optimization techniques such as single-objective, multi-objective, and non-dominating sorting GA II (Genetic Algorithm-II). From the observed results, the non-dominated sorting genetic algorithm (NSGA III) optimization algorithm offers superior performance notably higher turbine power output with higher torque rate, lower speed variation, reduced energy cost, and lesser degradation rate of the battery. This result attested to the fact that the proposed optimization tool can extract a higher rate of power from a self-excited induction generator (SEIG) when compared with a conventional optimization tool.