(542f) Towards Exact Designs in Optimal Experiment Campaigns

Model-based design of experiments for parameter precision is essential to accelerating the development of nonlinear mechanistic models¹; however, due to the nonconvex nature of the problem, standard local criteria are sensitive to initial parameter values^1,2,3. Additionally, the computational burden introduced when designing campaigns of parallel experiments is typically too high. Effort-based methods^4,5 overcome the above drawbacks by discretising the experimental space into a set of experiment candidates and determining the fraction of the total number of experiments (the “effort”) associated with each candidate, with the objective of selecting the experiments that will generate the highest information content. Effort relaxation leads to a convex formulation⁴ that can readily be solved using existing nonlinear programming codes. However, as the efforts are treated as continuous variables, the solution obtained needs to be modified to derive integer numbers of experiments of each type. Such a posteriori adjustments can lead to large suboptimality, especially for campaigns with a limited number of experiments.

In this article, a discrete-effort approach to the exact design of experiment campaigns comprising a finite number of experiments is presented. The experimental design space is discretised using Sobol sampling⁶ and efforts are treated as integer optimisation variables, leading to pure integer programs with a convex objective function and linear constraints. Integer programming techniques for solving the exact design problem are assessed, with a view on understanding which problems may be tractable, both in terms of number of design variables and number of experiment samples. The proposed approach is implemented within the gPROMS modelling platform⁷ to rely on existing optimisation solvers. Case studies are conducted for a range of experiment design problems.

References:

(1) Franceschini, G., and S. Macchietto (2008), “Model-based design of experiments for parameter precision: State of the art”, Chemical Engineering Science, 63 (19), pp. 4846-4872.

(2) Asprey, S. P., S. Macchietto, and C. C. Pantelides (2000), “Robust optimal designs for dynamic experiments”, IFAC Proceedings Volumes, 33 (10), pp. 845-850.

(3) Asprey, S. P., and S. Macchietto (2002), “Designing robust optimal dynamic experiments”, Journal of Process Control, 12 (4), pp. 545-556.

(4) Kusumo, K. P., K. Kuriyan, S. García-Muñoz, N. Shah, and B. Chachuat (2021), “Continuous-effort approach to model-based experimental designs”, presented at the 31st European Symposium on Computer Aided Process Engineering, Istanbul, Turkey.

(5) Kusumo, K. P., K. Kuriyan, S. Vaidyaraman, S. García-Muñoz, N. Shah, and B. Chachuat (2022), “Risk mitigation in model-based experiment design: A continuous-effort approach to optimal campaigns”, Computers & Chemical Engineering, 159, pp. 107680-107693.

(6) Sobol, I. M. (1967), “On the distribution of points in a cube and the approximate evaluation of integrals”, USSR Computational Mathematics and Mathematical Physics, 7 (4), pp. 86-112.

(7) Siemens Process Systems Engineering Limited, gPROMS, www.psenterprise.com/products/gproms, 1997-2022.