Multi-objective global optimization (MOGO): Algorithm and case study in gradient elution chromatography

Biotechnological separation processes are routinely designed and optimized using parallel high-throughput experiments and/or serial experiments. Well-characterized processes can further be optimized using mechanistic models. In all these cases - serial/parallel experiments and modeling - iterative strategies are customarily applied for planning novel experiments/simulations based on the previously acquired knowledge. Process optimization is typically complicated by conflicting design targets, such as productivity and yield. We address these issues by introducing a novel algorithm that combines recently developed approaches for utilizing statistical regression models in multi-objective optimization. The proposed algorithm is demonstrated by simultaneous optimization of elution gradient and pooling strategy for chromatographic separation of a three-component system with respect to purity, yield, and processing time. Gaussian Process Regression Models (GPM) are used for estimating functional relationships between design variables (gradient, pooling) and performance indicators (purity, yield, time). The Pareto front is iteratively approximated by planning new experiments such as to maximize the Expected Hypervolume Improvement (EHVI) as determined from the GPM by Markov Chain Monte Carlo (MCMC) sampling. A comprehensive Monte-Carlo study with in-silico data illustrates efficiency, effectiveness and robustness of the presented Multi-Objective Global Optimization (MOGO) algorithm in determining best compromises between conflicting objectives with comparably very low experimental effort.