A Multi-Stage Differential-Multifactorial Evolutionary Algorithm for Ingredient Optimization in the Copper IndustryOACSTPCDEI

Ingredient optimization plays a pivotal role in the copper industry,for which it is closely related to the concentrate utilization rate,stability of furnace conditions,and the quality of copper production.To acquire a practical ingredient plan,which should exhibit long duration time with sufficient utilization and feeding stability for real applications,an ingredient plan opti-mization model is proposed in this study to effectively guarantee continuous production and stable furnace conditions.To address the complex challenges posed by this integer programming model,including multiple coupling feeding stages,intricate constraints,and significant non-linearity,a multi-stage differential-multifac-torial evolution algorithm is developed.In the proposed algo-rithm,the differential evolutionary(DE)algorithm is improved in three aspects to efficiently tackle challenges when optimizing the proposed model.First,unlike traditional time-consuming serial approaches,the multifactorial evolutionary algorithm is utilized to optimize multiple complex models contained in the population of evolutionary algorithm caused by the feeding stability in a par-allel manner.Second,a repair algorithm is employed to adjust infeasible ingredient lists in a timely manner.In addition,a local search strategy taking feedback from the current optima and considering the different positions of global optimum is devel-oped to avoiding premature convergence of the differential evolu-tionary algorithm.Finally,the simulation experiments consider-ing different planning horizons using real data from the copper industry in China are conducted,which demonstrates the superi-ority of the proposed method on feeding duration and stability compared with other commonly deployed approaches.It is prac-tically helpful for reducing material cost as well as increasing pro-duction profit for the copper industry.