Robust Multi-Objective Global Optimization of Stochastic Processes With a Case Study in Gradient Elution Chromatography

A novel algorithm for robust multi-objective process optimization under stochastic variability of environmental variables is introduced and applied to a case study in gradient elution chromatography. Process variability is accounted for by simultaneously optimizing several scenarios with random but fixed values of the environmental variables. These iterative optimizations are synchronized by planning the same experiments for all scenarios. Experiments are designed by maximizing the cumulative expected hypervolume improvement as predicted by several Gaussian process regression models. A straightforward method is presented for estimating the expected Pareto front and its variability based on the resulting data that maintains traceability of the corresponding process parameters. This information is required for robust process optimization, that is, determination of Pareto optimal processes that fulfil specific minimal criteria with a certain confidence. The presented algorithm can generally be applied to both in silico and wet lab experiments but involves an increased experimental effort as compared to the deterministic case.