Dynamic multi-objective optimization arising in iron precipitation of zinc hydrometallurgy

•A dynamic multi-objective optimization model for iron precipitation by goethite is established.•A discretization method based on control variables and control intervals is proposed.•A multi-objective optimization method based on state transition algorithm and constraint nondominated sorting is proposed.•An evaluation mechanism based on ions concentration and their trends is developed.•The effectiveness of the proposed methods and evaluation strategy is confirmed through industrial experiments.

The additions of oxygen and zinc oxide for the goethite process determine the cost and efficiency of the iron precipitation process. As the two production targets (cost and efficiency) are conflicting and the chemical reaction is a continuous process that changes over time, the amounts of additive need to be dynamically optimized to satisfy the requirement of industrial application. In this paper, a discretization method based on control variables and control intervals is proposed to transform the dynamic optimization problem to a nonlinear mathematical programming problem. Then, a multi-objective optimization approach based on the state transition algorithm and constrained nondominated sorting is proposed to find the Pareto optimal solutions. Finally, an evaluation mechanism is proposed to obtain the best solution for industrial applications. The results from a series of simulation experiments show the effectiveness of the proposed approach, e.g. the daily average additions of oxygen and zinc oxide are decreased by 778.0854 m3 and 4.9013 t, respectively.