The exploitation of wind energy is developed in recent year because it has a source of clean, non-polluting and renewable energy. Nevertheless, in the development of wind energy, the demand in research and development is always focus on the efficiency energy and minimized cost of wind turbine system. This paper describes the methodology to design, optimization and simulation of a 15kW at low wind speed (6m/s), the design will be focused to Permanent Magnet Synchronous Generator (PMSG) dedicated to wind turbine systems. Firstly, the model of wind turbine system direct-drive with wind speed, wind turbine will be presented. Secondly, a coupled electromagnetic, thermal model used in design of a PMSG will be demonstrated. The developed genetic algorithm (GA) approach is presented in three parts: the basic principles of the GAs, the constrained optimization conversion and the inultiobjective (power maximization and mass minimization) optimization method. Finally, an analysis of the multi-objective optimization method robustness is performed and applied in the case of 15 kW PMSG. According to the obtained results, the optimal design of a PMSG by genetic algorithms to solve the efficiency wind energy is simulated and analysis.