In this paper, an optimal adaptive robust pitch controller is proposed for variable speed wind turbines (VSWTs). The proposed pitch controller has stability analysis, while it simultaneously keeps the generated power of the wind turbine at the rated power and mitigates the mechanical loads on the gearbox. The proposed pitch controller in this paper has two terms. The first term is a radial basis function neural network (RBFNN), to approximate unknown nonlinear functions of the wind turbine. Another term is a chattering-free continuous robust structure, which can cope with the approximation error. The weights of RBFNN and the gain of the robust structure are derived via the Lyapunov synthesis approach. It is proved that the closed-loop signals are semi-globally uniformed and ultimately bounded. The optimal parameters of the proposed controller are derived by solving a proposed multi-objective optimization problem using non-dominated sorting genetic algorithm-II (NSGA-II) and multi-objective particle swarm optimization (MOPSO) algorithm. The effectiveness of the proposed controller is compared to the baseline PI controller designed by NREL. First, both the proposed and the baseline PI controllers are applied to the general model (2-mass model) of the wind turbine, and then they are validated via a highly reliable simulator called FAST. The results demonstrate the effectiveness and applicability of the proposed pitch controller.