Multi-stage dynamic optimization method for long-term planning of the concentrate ingredient in copper industry

Abstract

As grade differences between concentrates increase, long-term concentrate ingredient planning (LCIP) becomes a crucial issue in ensuring continuous production and maximizing the concentrate utilization. Comparing with the existing studies, the number of LCIP ingredient stages is not deterministic and the decision variables and constraints are also will also change in accordance with the preceding ingredient list. Given these features of LCIP, this paper presents the concept of unpredictable multistage dynamic optimization (UMDO) and establishes an LCIP model that comprehensively considers production constraints, ingredient list duration, and concentrates inventories. A multistage stochastic object coding (MSOC) that establishes a mapping relationship between the coding sequence and the feasible solution space at each scheduling stage is further proposed. A multi-agent differential evolution (DE) algorithm based on the application of sequential simulation is proposed to optimize the high-dimensional population of the MSOC, enabling a globally optimal scheme in which the feasibility of the ingredient plan at each stage is ensured. Finally, the actual inventory concentration data collected from a copper industry in China are used to validate the effectiveness of the proposed planning methodology.