(138g) A Surrogate-Based Multi-Objective Optimization with Adaptive Sampling for Advanced Pharmaceutical Manufacturing

Incentivized by increasing market competition, pressure to maximize profit while maintaining product quality, and initiatives from regulatory entities to develop agile, flexible, and robust manufacturing lines, pharmaceutical manufacturing processes are shifting from batch to continuous operations^1-3. With extensive research efforts, progress has been made in modeling solid-based continuous manufacturing processes^3,4. Based on the developed models, mathematical optimization can be conducted to identify the best operating conditions to achieve different objectives, such as minimizing cost and energy consumption while maintaining product quality. The optimization results from in silico simulations can guide the experimental team in searching for optimal conditions, saving valuable time in the process development⁵. Some optimization case studies in continuous pharmaceutical manufacturing include the optimization of a crystallization process^6-9, a continuous direct compaction process³, and an end-to-end system consisting of upstream crystallization of active pharmaceutical ingredients and downstream tableting process^7,10.

As simulations become more complex to include more accurate representation of process dynamics, the computational complexity also increases¹¹. Thus it can be inefficient to solve the optimization problems with traditional optimization approaches and may lead to suboptimal solutions within limited time¹¹. To address such difficulty for computationally intense models, surrogate-based optimization strategies have been proposed as a promising alternative. A surrogate model is built to approximate complicated models, and it is iteratively updated with using an adaptive sampling strategy that searches for new promising points based on specific infill criteria. The workflow is repeated until a user-defined stopping criterion is met, and the final surrogate model with low approximation error is used to identify the near-optimal solution^12-17. Previous work has applied this approach to the continuous direct compaction process by using a weighted expected improvement (EI) function as an infill criterion to guide the search for new sample points toward feasible regions with low objective values^11,18. A modified EI on the objective follows this step to search for global optimum within the identified feasible region¹¹. Although the work demonstrates high accuracy in obtaining both feasible region boundary and the optimum, it is only applied to single-objective problems.

In this work, an updated framework of surrogate-based, feasibility-driven, multi-objective optimization with adaptive sampling is proposed to consider multiple objectives. Each objective function in the multi-objective problem is approximated using a surrogate. The constraints are grouped into a feasibility function based on maximum constraint violation and substituted with another surrogate model. For the infill criteria, both the centroid method and the expected hypervolume improvement (EHVI) method are implemented. The centroid method computes EI based on the first moment of the joint probability density function of the objectives. The EHVI method seeks Pareto solutions based on the difference of hypervolumes between the current and the next sample set. Following the identification of the Pareto front, a goal programming approach is implemented to provide guidance on the best solution. To demonstrate the effectiveness of the proposed framework, an example benchmark problem, and a case study of continuous pharmaceutical manufacturing process via the wet granulation route are presented. Sampling requirement, computational time, and solution accuracy resulting from the framework are compared against the optimization results obtained using surrogates without the adaptive sampling strategy. The framework is shown to have better performance in obtaining more accurate results with smaller sampling requirements. The proposed approach can thus become an integrated part of the Pharma 4.0 framework and effectively used by industry to investigate multiple competing objectives under quality constraints, allowing for a better decision-making strategy.

References

1. Ierapetritou M, Muzzio F, Reklaitis G. Perspectives on the continuous manufacturing of powder-based pharmaceutical processes. AIChE Journal. 2016;62(6):1846-1862.

2. O'Connor TF, Yu LX, Lee SL. Emerging technology: A key enabler for modernizing pharmaceutical manufacturing and advancing product quality. Int J Pharm. 2016;509(1-2):492-498.

3. Wang Z, Escotet-Espinoza MS, Ierapetritou M. Process analysis and optimization of continuous pharmaceutical manufacturing using flowsheet models. Comput Chem Eng. 2017;107:77-91.

4. Metta N, Ghijs M, Schäfer E, et al. Dynamic flowsheet model development and sensitivity analysis of a continuous pharmaceutical tablet manufacturing process using the wet granulation route. Processes. 2019;7(4):234.

5. Rogers AJ, Inamdar C, Ierapetritou MG. An Integrated Approach to Simulation of Pharmaceutical Processes for Solid Drug Manufacture. Industrial & Engineering Chemistry Research. 2014;53(13):5128-5147.

6. Sen M, Rogers A, Singh R, et al. Flowsheet optimization of an integrated continuous purification-processing pharmaceutical manufacturing operation. Chemical Engineering Science. 2013;102:56-66.

7. Patrascu M, Barton PI. Optimal Dynamic Continuous Manufacturing of Pharmaceuticals with Recycle. Industrial & Engineering Chemistry Research. 2019;58(30):13423-13436.

8. Su Q, Benyahia B, Nagy ZK, Rielly CD. Mathematical Modeling, Design, and Optimization of a Multisegment Multiaddition Plug-Flow Crystallizer for Antisolvent Crystallizations. Organic Process Research & Development. 2015;19(12):1859-1870.

9. Zhao Y, Kamaraju VK, Hou G, Power G, Donnellan P, Glennon B. Kinetic identification and experimental validation of continuous plug flow crystallisation. Chemical Engineering Science. 2015;133(Complete):106-115.

10. Patrascu M, Barton PI. Optimal campaigns in end-to-end continuous pharmaceuticals manufacturing. Part 2: Dynamic optimization. Chemical Engineering and Processing - Process Intensification. 2018;125:124-132.

11. Wang Z, Escotet-Espinoza MS, Singh R, Ierapetritou M. Surrogate-based Optimization for Pharmaceutical Manufacturing Processes. In: Espuña A, Graells M, Puigjaner L, eds. Computer Aided Chemical Engineering. Vol 40. Elsevier; 2017:2797-2802.

12. Jones DR, Schonlau M, Welch WJ. Efficient Global Optimization of Expensive Black-Box Functions. Journal of Global Optimization. 1998;13(4):455-492.

13. Bhosekar A, Ierapetritou M. Advances in surrogate based modeling, feasibility analysis, and optimization: A review. Comput Chem Eng. 2018;108:250-267.

14. Boukouvala F, Ierapetritou MG. Derivative‐free optimization for expensive constrained problems using a novel expected improvement objective function. AIChE Journal. 2014;60(7):2462-2474.

15. Wang Z, Ierapetritou M. Constrained optimization of black-box stochastic systems using a novel feasibility enhanced Kriging-based method. Comput Chem Eng. 2018;118:210-223.

16. Wang Z, Ierapetritou M. Surrogate-based feasibility analysis for black-box stochastic simulations with heteroscedastic noise. Journal of Global Optimization. 2018.

17. Boukouvala F, Ierapetritou M. Surrogate-Based Optimization of Expensive Flowsheet Modeling for Continuous Pharmaceutical Manufacturing. Journal of Pharmaceutical Innovation. 2013;8(2):131-145.

18. Metta N, Ramachandran R, Ierapetritou M. A novel adaptive sampling based methodology for feasible region identification of compute intensive models using artificial neural network. AIChE Journal. 2020;67(2).