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Multiobjective optimization strategies for linear gradient chromatography

The increase in the scale of preparative chromatographic processes for biopharmaceutical applications now necessitates the development of effective optimization strategies for large-scale processes in a manufacturing setting. The current state of the art for optimization of preparative chromatography has been limited to single objective functions. Further, there is a lack of understanding of when to use a particular objective, and how to combine and/or prioritize mutually competing objectives to achieve a true optimal solution. In this paper, these limitations are addressed by using a physical programming– based multiobjective optimization (MO) strategy. A set of Pareto solutions are first generated for model protein separations for both bi-objective (production rate and yield) and tri-objective (production rate, yield, and product pool concentration) scenarios. These Pareto frontiers are used to visualize the Pareto optimal surface for different components with various purity constraints and provide a qualitative framework to evaluate the optimal solutions. A physical programming– based multiobjective framework is then used for the quantitative evaluation of the optimal solutions for tertiary protein mixtures. This enables the interpretation of results for different sets of hierarchy and priority values assigned to the objective functions and constraints for the chromatographic processes. This novel multiobjective optimization approach computes the tradeoffs between the conflicting design objectives and helps in choosing an operating condition from infinite feasible optimal solutions. The combined quantitative and visualization framework presented in this paper sets the stage for the development of true optimal solutions for complex nonlinear preparative separations. © 2005 American Institute of Chemical Engineers AIChE J, 51: 511–525, 2005