The rare earth extraction process based on mechanism model does not consider mixer"s energy efficiency in the extraction tank leading to a large error with the solvable content at each level and the industrial production data. This paper introduces the concept of energy efficiency separation coefficient, establishes a model which meets the actual content of rare earth elements in each extraction tank, and construct an optimized objective function for solving the energy efficiency separation coefficient. Aiming at the multi-peak and multi-variable characteristics of the optimized objective function, an improved chaotic double mutation adaptive differential evolution algorithm LCTADE with linear population reduction is proposed. First, the chaotic sequence is embedded in the improved algorithm to generate the initial population, which enhances the diversity of the population; secondly, in view of the different performance requirements of the mutation strategy in different evolution stages, the method proposed in this paper is based on DE/current-to-pbest/1 and DE/rand/1 double mutation strategy method; finally, use different parameter adaptive methods to set the F, CR and NP values. In the simulation experiment, first, test the function of the improved LCTADE on CEC2017 and compare it with other algorithms. The results show that LCTADE is significantly better than other algorithms. Then use it to solve the energy efficiency separation coefficient of rare earth extraction process and optimize objective function, which shows the effectiveness of the method proposed in this paper.