Global warming and environmental destruction are caused, in part by the mass consumption of energy by industries that use robotic manipulators. Many trajectories planning of the manipulators are determined by giving priority to the operation efficiency such as the operating time and controllability. And it may not be taking the consumption energy into consideration in the trajectory planning. The minimization of the energy under the equation of motion of the manipulator can be reduced to a two-point boundary value problem. This problem can be solved analytically if the equation of motion is linear. However, the equation of motion of a two-links manipulator is non-linear. This paper describes an application of the genetic algorithm based evolution strategy to solve minimizing the consumption energy of a manipulator with non-linear friction at the joints. When applying the genetic algorithm, it is necessary to define the relation between trajectory functions and genes. Fourier cosine series with Mth order are used in this paper. In this minimization problem of the consumption energy, there are many local minimum points due to the non-linearity. A major topic of this paper is to discuss the number of M to increase the accuracy of the solution without falling into the local minimum point. This paper has proposed to change M in the progress of evolution.