(463c) Multidimensional Design Space Identification and Analysis Via Multi-Parametric Programming

The design space is characterized by good candidate condition sets, within which the process is guaranteed to meet the target specifications [1, 2]. In recent years, this approach has been increasingly adopted by the biopharmaceutical industry as part of the Quality by Design initiative, which aims to facilitate the development of more robust processes [3]. Various methodologies have been proposed to identify and define design spaces [4-6]. However, challenges related to computationally expensive models, dimensionality and definition of the design space boundaries may hinder the formulation and solution of problems that combine design with operating variables and process disturbances. To this end, we propose a novel methodology that harnesses multi-parametric programming for the identification of high-dimensional design spaces via optimal operational policies [7].

The exact solution of a multi-parametric programming problem is defined as piecewise affine functions across different critical regions [8], whereby the critical regions arise from the optimality conditions and combination of active and inactive constraints. In this work, we propose the formulation of an integrated design and operation problem that considers all design inputs as parameters (θ) of the mp-problem formulation. On the other hand, the feasibility and performance constraints are formulated as usual. This formulation projects the critical regions onto the design input space. Therefore, the boundaries of the critical regions define the boundaries of the design space itself. Explicit multi-parametric solutions for non-linear problems remains a big challenge in the current landscape of process systems engineering. To this end, we propose to incorporate ReLU (rectified linear unit) artificial neural networks (ANNs) to capture the behavior of the process and reformulate as multi-parametric mixed-integer linear programming problems (mp-MILPs) for which the explicit solutions exist [9].

In this work, we focus on the design space identification of a protein A chromatography process for monoclonal antibody capture. The process is modelled in partial differential and algebraic equations and has been experimentally validated by Steinebach, et al. [10]. Due to the non-linearity of the system, we utilize ReLU ANNs to capture the behavior of the system and reformulate the problem as mp-MILP. Two case studies are considered in this work. First, a design space identification study in three-dimension (3D) is carried out and validation with previous work [6]. Then, a higher dimensional problem with more design inputs is considered which is the advantage that the proposed novel framework has.

We demonstrate how the proposed framework can be utilized for the identification of design space for both low and higher dimensional problems. The advantage of this formulation of the design space is the formation of the multi-parametric map. This enables the rapid evaluation of any combination of design inputs, quantifying acceptable ranges, and key performance indicator distributions in high dimensions.

Acknowledgements:
Funding from the UK Engineering & Physical Sciences Research Council (EPSRC) for the i-PREDICT: Integrated adaPtive pRocEss DesIgn and ConTrol (Grant reference: EP/W035006/1) is gratefully acknowledged.

References

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