Using Sparse-Grid Methods To Improve Computation Efficiency in Solving Dynamic Nonlinear Chance-Constrained Optimization Problems

• Published in: Industrial & engineering chemistry research 2011-05, Vol.50 (9), p.5693-5704
• Main Authors: Klöppel, Michael, Geletu, Abebe, Hoffmann, Armin, Li, Pu
• Format: Article
• Language: English
• Subjects: Process Design and Control
• ISSN: 0888-5885; 1520-5045
• DOI: 10.1021/ie102426w

Chance-constrained programming is known as a suitable approach to optimization under uncertainty. However, a serious difficulty is the requirement of evaluating the probability of holding inequality constraints through the numerical computation of multidimensional integrals. If a nonlinear system with many uncertain variables is considered, the computational load will be prohibitive when using a full-grid integration method. Thus our aim is to investigate a method to decrease the computation expense in solving nonlinear chance-constrained optimization problems with many uncertain variables. In particular, we consider dynamic nonlinear process optimization under uncertainty, which will be transferred into a nonlinear chance-constrained optimization problem by a discretization scheme. To solve this problem, we propose to use sparse-grid methods for the evaluation of the objective function, the probability of constraint satisfaction, and their gradients. These components are implemented in a nonlinear programming framework. A dynamic mixing process is taken to illustrate its computation efficiency. It can be shown that the computation time will be significantly reduced using the sparse-grid method, in comparison to using full-grid methods.