Identification of Vertex and Nonvertex Critical Points for Large-Scale Approximate Stochastic Optimization

This paper presents a strategy for optimal design of chemical processes with stochastic uncertain parameters defined inside bounded intervals. Strategy relies on approximate stochastic optimization at one single point, called the central basic point (CBP), while desired flexibility is achieved by simultaneous consideration of critical points. The CBP method has been extensively described elsewhere (Novak Pintari and Kravanja, 2004). The aim of this work is to develop a procedure for determining a minimal set of critical points, which can identify vertex and nonvertex critical points. In this procedure the uncertain parameters are transformed into continuous variables, and a special NLP problem is solved for each design variable in order to determine the most unfavourable combination of uncertain parameters which would force a given design variable to its maximum. The procedure avoids explicit enumeration of all vertices and is thus suitable for solving problems with several tens of uncertain parameters. Two examples are presented of heat exchanger network design with vertex and nonvertex critical points.