Solving for Exact Designs in Optimal Experiment Campaigns under Uncertainty⁎⁎This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 955520 (Digitalgaesation). KPK, CCP and BC gratefully acknowledge funding by Eli Lilly & Company through the Pharmaceutical Systems Engineering Lab (PharmaSEL) and by the Engineering and Physical Sciences Research Council (EPSRC) as part of its Prosperity Partnership Programme under grant EP/T518207/1.

Applying model-based design of experiments to compute maximally-informative campaigns with multiple parallel runs is challenging. Effort-based methods can overcome some of these challenges through discretizing the experimental space into a finite set of candidate experiments, then applying convex optimization techniques to determine the optimal Efforts for each candidate, and finally rounding the Efforts to integer numbers of runs for a target experimental campaign size. For small experiment campaigns in particular, the final rounding can result in large suboptimality. This paper presents an approach to solving the exact design problem, where the Effort variables being optimized are constrained to taking integer values. We consider model parametric uncertainty and formulate risk-inclined, risk-neutral and risk-averse exact design problems as mixed-integer nonlinear programs (MINLPs) with convex participating functions. We demonstrate the tractability of an outer-approximation algorithm to solve such MINLPs to global optimality on a case study involving the exothermic esterification of propionic anhydride with over 1000 experiment candidates and 100 uncertainty scenarios.