Mixed-integer nonlinear programming problem process synthesis under uncertainty by reduced dimensional stochastic optimization

This paper presents the developments of a novel simultaneous method for the optimization and the synthesis of complex chemical problems under uncertainty with a fixed degree of flexibility. The approach approximates the stochastic method in using a weighted objective function calculated over a reduced set of the extreme points (vertices). The feasibility of the design is ensured simultaneously by the feasibility constraints at critical vertices. The main part of the proposed method which was called the method for reduced dimensional stochastic optimization (the RDS method) is a special setup procedure for determining the reduced set of vertices and their weights for the approximation of the expected value of the objective function. A very attractive feature of this method is that the sizes of mathematical models and the computational times are reduced by 1 or 2 orders of magnitude when compared to those of the stochastic methods. On the basis of the RDS method, a robust strategy for the synthesis of complex models under uncertainty is proposed (the RDS strategy). The steps of the RDS method and the RDS synthesis strategy are illustrated in detail by one simple and two more extensive example problems, respectively.