Nonlinear Chance-Constrained Process Optimization under Uncertainty

Optimization under uncertainty is considered necessary for robust process design and operation. In this work, a new approach is proposed to solve a kind of nonlinear optimization problem under uncertainty, in which some dependent variables are to be constrained with a predefined probability. Such problems are called optimization under chance constraints. By employment of the monotony of these variables to one of the uncertain variables, the output feasible region will be mapped to a region of the uncertain input variables. Thus, the probability of holding the output constraints can be simply achieved by integration of the probability density function of the multivariate uncertain variables. Collocation on finite elements is used for the numerical integration, through which sensitivities of the chance constraints can be computed as well. The proposed approach is applied to the optimization of two process engineering problems under various uncertainties.