The Modeling And Optimization Method For Electrolytic Aluminum Batching Problem

The aluminum smelting process can generally be divided into:electrolysis and casting stages.The optimal combination of materials and reasonable connection between electrolysis and casting stages are the key issues in the production management of aluminum smelting enterprises.Molten aluminum produced by electrolysis is transported to the casting foundry by crucibles.Each three cells of molten aluminum are fed into a crucible.An important decision problem involved in the aluminum smelting process is to batch molten aluminum in the different electrolysis cells into crucibles to improve the purity profit and the production efficiency and to reduce the energy consumption and emission.In addition,because the capacity of the melting furnace is generally larger than the capacity of the crucible,another important decision problem is to batch molten aluminum loaded in different crucibles into furnaces.The purity of the molten aluminum in furnace is directly related to the quality of the aluminum ingot.The cells batching problem and the crucibles batching problem are sequentially solved in practical.Both problems have significant impact to increase enterprise income and improve process matching.The main research contents of this thesis are as follows:(1)The multi-objective mix integer programming model for cells batching problem uses electrolysis cells clustering as the decision variable to optimize the driving distance of crane,the purity gain and the difference of test elements between the crucibles with the considering of the capacity of crucible and the requirement of impurity elements.The model is reformulated using D-W decomposition,and the reformulated model is solved by the multi-objective mathematical programming algorithm to get an optimized combination of cells.(2)The integer programming model based on P-median method for the crucibles batching problem uses crucibles clustering as the decision variable to optimize the purity gain with the considering of interval requirements of the furnace capacity and the piecewise linear function relationship between the purity profit and the purity of the molten aluminum.To solve the problem with actual scale,a heuristic algorithm based on column generation is designed.Numerical experiments show that the algorithm can obtain a high-quality approximate solution in a reasonable time.(3)In order to solve the crucibles batching problem precisely,a branch and price algorithm based on column generation is designed and some tailored improvement strategies are proposed to accelerate the convergence.For the master problem and the sub-problem,a column aggregation mechanism based on purity interval is proposed to reduce the redundant iteration caused by the symmetry between "column combinations".To construct the initial restricted master problem,a high-quality initial column generation strategy is proposed to reduce the number of column generation iterations.In terms of branching strategy,a guided branching mechanism based on key columns is proposed to achieve efficient solution space division.The numerical experiments show that the proposed improving strategy can break through the limitation of solving ability,and make the branch and price algorithm obtain the optimal solution for most practical scale instances in the acceptable calculation time.