Constrained dynamic multi-objective evolutionary optimization for operational indices of beneficiation process

Operational indices optimization of beneficiation process is a dynamic optimization problem in nature. It is difficult to solve because the related dynamic models of operational indices cannot be achieved easily. Focusing on the operational indices optimization under uncertain environments in production process, this paper first formulates a constrained dynamic multi-objective optimization problem based on the collected data, which considers the changing factors in production and the constraints of operational and production indices, and takes the production indices as optimization objectives and the operational indices as decision variables. To solve the established constrained dynamic multi-objective problem, a prediction with modification mechanism based dynamic multi-objective evolutionary optimization algorithm is proposed. The algorithm first divides the population into several sub-populations and then predicts each sub-population center of new environment independently. New population is generated by Gaussian and uniform distribution based on the estimated centers to improve the convergence speed. At the same time, to ensure the population diversity, a modification strategy is adopted to detect which reference point has no individual associated and produces some individuals around it. The proposed algorithm is applied to solve the dynamic operational indices optimization problem and compared with a constrained and a modified unconstrained dynamic multi-objective optimization algorithm. The statistical results demonstrate the efficiency and effectiveness of the proposed algorithm to solve the real-world dynamic operational indices optimization problem.