Module-oriented automatic differentiation in chemical process systems optimization

Abstract

It is common that external procedures are incorporated into an equation-oriented model when modeling complex chemical process systems. The so-obtained models are called composite models in this paper. Unlike pure equation-oriented models, composite models include hidden variables that cannot be observed externally by the user. In addition, the ratio of the computing time consumed for Jacobian evaluation to the computing time consumed for optimization in composite modeling framework is higher than that required in equation-oriented modeling framework. However, traditional algorithms are not able to fully exploit the structure of composite model so as to effectively improve the efficiency of optimization. In this paper, a module-oriented automatic differentiation (MAD) approach is presented based on traditional automatic differentiation algorithms. This approach can well exploit the sparsity of the model by partitioning it into a series of sequential modules and choosing the best differentiation algorithm for each module accordingly. Moreover, external Jacobian evaluation codes for specific modules can be easily incorporated into this approach. Numerical results demonstrate its advantage of the procedure in optimization.