The development of predictive models is a time consuming, knowledge intensive, iterative process where an approximate model is proposed to explain experimental data, the model parameters that best fit the data are determined and the model is subsequently refined to improve its predictive capabilities. Ascertaining the validity of the proposed model is based upon how thoroughly the parameter search has been conducted in the allowable range. The determination of the optimal model parameters is complicated by the complexity/non-linearity of the model, potentially large number of equations and parameters, poor quality of the data, and lack of tight bounds for the parameter ranges. In this paper, we will critically evaluate a hybrid search procedure that employs a genetic algorithm for identifying promising regions of the solution space followed by the use of an optimizer to search locally in the identified regions. It has been found that this procedure is capable of identifying solutions that are essentially equivalent to the global optimum reported by a state-of-the-art global optimizer but much faster. A 13 parameter model that results in 60 differential-algebraic equations for propane aromatization on a zeolite catalyst is proposed as a more challenging test case to validate this algorithm. This hybrid technique has been able to locate multiple solutions that are nearly as good with respect to the "sum of squares" error criterion, but imply significantly different physical situations.
Bibliographical noteFunding Information:
The authors would like to thank the Indiana 21st Century Research and Technology fund for their support of this research. We also gratefully acknowledge the support of the US Department of Energy, Office of Basic Energy Sciences through the Catalysis Science grant number DE-FG02-03ER15466.
- Genetic algorithm
- Global optimization
- Parameter estimation
- Propane aromatization