Optimization problem of complex system under uncertainty

Design of chemical processes (CP) is usually performed in a condition of some uncertainty of original physical and chemical information. In connection with this the important problem of the evaluation of flexibility of CP (the ability of CP to preserve its capacity for work) arises. Halemane and Grossmann (1983) (Optimal process design under uncertainty. A.I.Ch.E. J., 29 (3), 425–433.) introduced the flexibility (feasibility) function which permits evaluation of CP flexibility. But direct calculation of the flexibility function is reduced to solving very hard nondifferentiable and multiextremal optimization problems. In connection with this we give an effective method of calculation of the flexibility function. It is reduced to an iteration procedure on each iteration of which usual nonlinear programming problems are solved. On the basis of this method we consider two algorithms for solving the two stage optimization problem.