基于有限存储的简约空间序列二次规划算法研究

Study on reduced space SQP algorithm based on limited memory method

为了求解过程系统中自由度相对较大一些的大规模优化命题,对简约空间序列二次规划(reduced successive quadratic programming,RSQP)算法进行了改进和扩展,提出了基于有限存储的简约空间序列二次规划算法.该算法通过有限存储技术隐式的表示RSQP算法中的两个最大矩阵,大大减少了优化计算过程中的存储需求,并对有限存储技术应用到RSQP算法中后Hessian阵的更新和基变量的选择进行了特殊处理。该算法的求解性能通过benchmark算例进行了测试,并被应用到两个过程系统优化实例。计算结果表明,采用该方法求解自由度相对较大的问题可以大大减少内存消耗,从而可大大提高算法的优化求解效率。

To solve large-scale problems in process systems, a reduced space sequential quadratic programming （RSQP） algorithm based on Limited Memory method is presented. With Limited Memory method used, the RSQP algorithm is extended to solve problems with relatively large degrees of freedom. The biggest matrix reduced Hessian and cross item are not saved directly. Instead, they are created and used in the course of calculation. To make limited memory method more efficiently and apply it to RSQP, some special procedures are taken in the algorithm. The proposed limited memory RSQP is compared with normal SQP and RSQP algorithms by some small scale and large scale benchmark examples. Then it is applied to the optimization of real cases of chemical reaction process. Computational results demonstrate that the proposed method is more efficient in solving large-scale problems with relatively large degrees of freedom.