基于分片线性逼近的聚氯乙烯生产计划优化分解算法

聚氯乙烯全流程生产过程计划优化往往描述为复杂MINLP模型，求解难度非常大，为此引入分片线性技术逼近实际生产中的非线性特征，建立基于HH的MILP模型，进一步提出一种基于离线层级模型的分解算法来加速求解过程：第一层在对生产设备以最优能耗点进行层级划分得到离线层级模型的基础上优化一个等价MILP问题，确定表征设备操作状态的二值变量；第二层以HH模型为基础，在二值变量确定的情况下，代入计划优化模型调整设备的工作点，最终确定模型的最优操作决策方案。最后，以一个实际工厂规模的案例来验证模型和算法的有效性，结果表明本算法在基本不损失优化结果性能的前提下可以大大提高求解效率，缩短求解时间达99%以上。

Decomposition algorithm for PVC plant planning optimization based on piecewise linear approximation

In the previous work, the multiperiod planning optimization model of the whole production process has been presented. Due to the high energy consumption characteristics of PVC produced by calcium carbide method, the piecewise linear model to approximate the nonlinear items in real process was introduced and a mixed integer linear programming (MILP) model was established. However, it is difficult to solve it due to the large scale and the complex nonconvexity. Thus, a hierarchical decomposition algorithm is proposed to accelerate the computation progress. The problem is divided into two levels, in the first level, the operating states of equipment are optimized, which would be the hard-to-solve binary variables in the plantwide planning model; in the second level, the determined binary variables are embedded into the plantwide planning model, and thus a reduced scale scheduling optimization is executed. A case study was provided to verify the effectiveness of the proposed algorithm. Computational results show that the proposed algorithm can accelerate the computation greatly and the production costs are close to or even better than those given in the previous work.