This work presents a methodology for the optimization of chemical processes using genetic algorithm and kriging metamodels. The methodology is appropriate when the use of computationally expensive and complex processes first principle models is required (e.g. modular process simulators as ASPEN). Such models face many obstacles when used in optimization using Derivative Based Optimizers (DBO), because of the inaccurate estimation of the derivatives; moreover DBO could be easily trapped in local ...

This work presents a methodology for the optimization of chemical processes using genetic algorithm and kriging metamodels. The methodology is appropriate when the use of computationally expensive and complex processes first principle models is required (e.g. modular process simulators as ASPEN). Such models face many obstacles when used in optimization using Derivative Based Optimizers (DBO), because of the inaccurate estimation of the derivatives; moreover DBO could be easily trapped in local optima [1]. Genetic Algorithms (GAs) are stochastic search procedures that mimic the biological evolution process. They do not require the derivatives estimation and so avoid the associated difficulties [2]. However, GAs require a huge number of evaluations of the fitness function so, their use to solve the complex real size problems which usually appear in industry would lead to unaffordable computational time and cost [1],[2].
Many works have proposed the use of accurate computationally inexpensive surrogate models instead of
complex original models to reduce the computational cost of evaluating the fitness function and constraints [2]. Kriging surrogate models present outperforming characteristics, as high prediction accuracy and an ability to estimate a prediction variance (prediction uncertainty), which extends the kriging capabilities when compared with other metamodel types, and enables the use and development of new powerful optimization tools [1].
In this work, the use of GAs to continuously improve the metamodels accuracy during the optimization step
allows to better exploit the potentials of the kriging estimated variance, taking into account the metamodels
uncertainties as well as the predictions.
In the first stage of the proposed algorithm, a set or a matrix ([X]n×k) of n input combinations of the k
optimization/design variables X are evaluated (simulated) using the complex original process model, in order to obtain the output responses [Y]n (the objective and constraints); then, these data matrices ([X]n×k ; [Y]n) are used to fit the kriging metamodels (one kriging metamodel for each of the objective and the constraints). The second stage corresponds to the optimization itself: in each iteration, the GA explores the metamodels through a specified number of generations (Ng), and evaluates the metamodels predictions (fitness and constraints values) and variances which represent the uncertainty about the predictions. Once the specified number of generations has been reached, two individuals are selected from the last generation: the individual with best fitness value, and the individual with highest prediction variance. The original complex process model is evaluated at these two points to obtain accurate response values; then, these two new data are added to the original set of training points, and the metamodels are refitted to enhance the metamodels accuracy. Ng takes small values at the early iterations, as the uncertainty in the metamodels are expected to be relatively high, so the GA is just used to explore the whole search domain to identify the areas with high uncertainty in order to add points at these areas to enhance the metamodels. As the algorithm proceeds, Ng gradually increases, since the confidence in the
metamodel results also increases; consequently, the GA is allowed to deeply explore the metamodels with less uncertainty. Results of the application of this procedure to different mathematical examples and to chemical process operation optimization case study show the benefits, both in terms of computational effort and, even more important, results reliability obtained through the proposed methodology.