基于二阶段随机规划的不确定条件下过程优化研究

在基于二阶段随机规划的不确定条件下过程优化研究中，Ierapetritou and Pistikopoulos(1994)提出了可行域求解策略，Liu and Sahinidis(1996)在此基础上用蒙特卡洛积分策略代替了高斯积分策略，但对于可行域的限定条件尚有欠缺。本文分析和比较了前人的工作，将蒙特卡罗积分策略与基于对偶理论的可行域限定条件相结合，提出了新的求解策略，不仅避免了可行域求解策略中求解一系列子问题而引起的计算负荷随不确定参数数目呈指数增加的不足，而且使蒙特卡洛积分策略算法中的可行域限定条件更加合理，应用文献中的算例进行了仿真实验，证明了该算法的有效性。

Study on process optimization under uncertainty based on 2S-SLP

In study of process optimization under uncertainty, it is important to use 2-stages stochastic linear programming (2S-SLP) based on Benders decomposition. Ierapetritou and Pistikopoulos (1994) proposed the feasible region (FR) algorithm, which sampling points are constrained in the feasible region by saving a series of feasibility subproblems, so the number of feasibility subproblems to be solved in each iteration increases exponentially with the number of uncertain parameters. Liu and Sahinidis(1996) using Monte Carlo (MC) integration schemes circumvents this problem by sampling from the entire domain of the distribution function, but it is too conservative in feasibility constraints aspects which adding the worst case scenario possible for feasibility constraints. In this paper, an improved algorithm of the MC algorithm for process optimization under uncertainty is proposed. We using Monte Carlo sampling from the entire domain of the distribution function, and using feasibility cuts based on dual theory in Benders decomposition. This is achieved by avoiding the solution of feasibility subproblems, and the feasibility constraints are more exact than before. The improved algorithm is more realistic, on the problems tested, than the former work.