The core methodology significantly reduces the computational burden of knowledge space generation by utilizing GPR surrogate models enhanced through an integrated kernel optimization procedure. This procedure employs a greedy tree search algorithm to select the most suitable composite kernel [2], substantially improving the model’s ability to capture complex, non-linear patterns typical of chemical engineering datasets. As a result, the design space can be accurately approximated using limited data, reducing the overall computational effort required for DSp analysis.
To delineate the feasible region boundaries without relying on convexity assumptions, alpha shape reconstruction is employed. Alpha shapes extend the concept of convex hulls to accommodate non-convex and disconnected geometries, yielding a more accurate depiction of intricate design spaces [3]. The reconstruction is performed using the Python package ‘dside’ developed by Sachio et al. [3], which applies Delaunay Triangulations and a bisection search to identify the largest alpha radius, effectively reconstructing the design space geometry.
The proposed approach was validated through a series of benchmark tests involving constrained, non-convex functions and engineering design problems in spaces ranging from two to seven dimensions. Results confirm that the method reconstructs complex design spaces with high fidelity while requiring significantly fewer computational resources than other surrogate-based approaches. For example, in three-dimensional scenarios, the methodology delivered near-optimal predictive performance using markedly fewer training points [4].
This work advances alpha shape-based design space identification to higher dimensions by addressing computational challenges via surrogate modeling. The proposed framework provides a robust and flexible tool for design space exploration, supporting effective decision-making in chemical process design and optimization. The integration of GPR with kernel optimization and alpha shape reconstruction presents considerable potential for industrial applications requiring fast and reliable design space evaluation.
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
[1] Bhosekar, A., & Ierapetritou, M. (2018). Advances in surrogate based modeling, feasibility analysis, and optimization: A review. Computers & Chemical Engineering, 108, 250–267. https://doi.org/10.1016/j.compchemeng.2017.09.017
[2] Boukouvala, F., & Ierapetritou, M. G. (2012). Feasibility analysis of black-box processes using an adaptive sampling Kriging-based method. Computers & Chemical Engineering, 36, 358–368. https://doi.org/10.1016/j.compchemeng.2011.06.005
[3] Liu, H., Ong, Y.-S., & Cai, J. (2018). A survey of adaptive sampling for global metamodeling in support of simulation-based complex engineering design. Structural and Multidisciplinary Optimization, 57(1), 393–416. https://doi.org/10.1007/s00158-017-1739-8
[4] Geremia, M., Bezzo, F., & Ierapetritou, M. G. (2023). A novel framework for the identification of complex feasible space. Computers & Chemical Engineering, 179, 108427. https://doi.org/10.1016/j.compchemeng.2023.108427
[5] Kudva, A., Tang, W.-T., & Paulson, J. A. (2024). Robust Bayesian optimization for flexibility analysis of expensive simulation-based models with rigorous uncertainty bounds. Computers & Chemical Engineering, 181, 108515. https://doi.org/10.1016/j.compchemeng.2023.108515
[6] Kucherenko, S., Giamalakis, D., Shah, N., & García-Muñoz, S. (2020). Computationally efficient identification of probabilistic design spaces through application of metamodeling and adaptive sampling. Computers & Chemical Engineering, 132, 106608. https://doi.org/10.1016/j.compchemeng.2019.106608