A novel extraction model optimization with effective separation coefficient for rare earth extraction process using improve differential evolution

The mechanistic model of the rare earth extraction process neglects the efficacy of the agitator within the extraction extractor. This oversight results in a significant discrepancy between the theoretical solute concentration at each stage and the actual process data. To rectify this issue, we introduce an effective separation coefficient, thereby enabling the creation of a model capable of accurately determining the concentration of rare earth elements (REE) within each extraction extractor. This model also facilitates the construction of an optimized objective function for determining the effective separation coefficient. Taking into account the multi-modal and multi-variable characteristics of the optimized objective function, we put forth an enhanced version of the improved differential evolution algorithm, the Linear-Chaos and Two Mutation Strategies of Adaptive Differential Evolution (LCTADE)with Covariance Matrix and Cauchy Perturbation(CC-LCTADE). First, a chaotic sequence is embedded into the improved algorithm to generate the initial population, enhancing population diversity. Next, during the mutation and crossover processes, a new feature coordinate system is established, and covariance matrices and Cauchy disturbances are added to enhance the algorithm's accuracy and its ability to avoid premature convergence. Additionally, recognizing the different performance requirements for mutation strategies at various stages of evolution, we introduce a dual-mutation strategy method based on DE/current-to-pbest/1 and DE/rand/1. Finally, a parameter-adaptive method is used to set the values of F, CR, and NP. In the simulation experiments, the proposed CC-LCTADE method and LCTADE method are first tested against the CEC2017 function and compared with other algorithms, demonstrating their superiority. CC-LCTADE is then used to solve the effective separation coefficient based objective function for rare earth extraction process. The experiments shows CC-LCTADE is effective and can be applied to the actual the rare earth extraction simulation system.