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

Kloeppel, Michael

doi:10.1021/ie102426w

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

2011-03-31

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DOI：10.1021/ie102426w

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Abstract

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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.

Keywords:

MODEL-PREDICTIVE CONTROL

BATCH PROCESSES

SYSTEMS

ALGORITHM

EQUATIONS

LOOP

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