串联系统动态规划的离散化寻优

DISPERSING OPTIMIZATION FOR DYNAMIC PROGRAMMING IN SERIAL SYSTEM

在炼油化工单元设备或过程构成的串联系统中,前后相邻两级单元之间的状态变量通常具有单调变化特性,每个单元的状态转移方程中的决策变量大多可以用反函数解析式表示。本文将整体多决策变量目标函数的动态规划问题转变为离散的各个状态变量对整体目标函数求偏优值的问题。离散化寻优法采用多变量函数的分段样条拟合或网格搜索方法,设计出一种用状态变量离散值直接计算目标函数值的嵌套循环程序,避免了解析方法中构造逐个子问题目标函数的困难和求导的不确定性。这种方法能自动缩小搜索步长和调整搜索区间,具有寻优速度快、精度高的优点。经实例验证,在实际工程最优化计算中比较可靠、实用。

In the serial system which consists of petroleum refining and petrochem- ical units and/or processes, the state variables between two neighbouring units have their monotropic character. The deciding variables in a state equation about each unit could be rep- resented as an inverse-function of state variables. The dynamic programming of objective function with poly-deciding variables about the total system would be turned into partial op- timization for the total system in which objective function is based on each dispersed state variable. In dispersing optimization, a sampler imitation of poly-variables and/or a network seeking method is used to design a loopcoupled program to calculate the value of objective function directly according to the value of dispersed state variable to avoid the indetermina- tion of derivative and the difficulty of building-up sub-objective function with analytics. In this method, the step length may be shortened automatically and the seeking interval may be regularized methodically.