(673d) Multi-Objective Bayesian Optimisation for Sustainable Reactions Development

Optimising chemical reactions to discover the best conditions is important at multiple stages of reaction development, from lab-scale condition screening to large-scale manufacturing. Often multiple objectives need to be considered alongside yield optimisation, for example, achieving high yield with high selectivity, considering economic and sustainability aspects at the same time, or optimizing yield and throughput simultaneously for scale-up. Finding such optimal solutions usually requires searching in a large design space for a set of Pareto solutions rather than one solution, which tends to be tedious and time-consuming. In this study, we focus on optimising two chemical reactions in flow with multiple objectives using Bayesian optimisation, to consider space-time-yield and sustainability factor at the same time.

Amide bond formation is one of the most prevalent reactions in pharmaceutical industry, among which the Schotten-Baumann reaction with a long history is useful as a potential green amide formation approach. However, the use of water in the reaction system often causes undesired hydrolysis and can generate a multiphase system. This makes the reaction space complex and challenging to find the optimal conditions. In the first case study, a Schotten-Baumann reaction was studied in continuous flow and was optimised with two objectives using a Bayesian optimisation algorithm based on the q-Noisy Expected Hypervolume Improvement (qNEHVI)^[1]. The algorithm guided the experiment design over a range of mixed variables, i.e. electrophiles, equivalents, solvents, and flow rates, and was able to identify the Pareto front of optimal solutions efficiently. Based on the optimisation results, reaction under flow and batch conditions were compared; undesired hydrolysis was suppressed successfully using the flow conditions. Finally, the relationship between solvent and flow rate was discussed to gain more insights into this reaction.

In the second case study, we focus on robust applications where large noises are unavoidable. This is useful when dealing with unstable reagents and for large-scale manufacturing processes. To cope with large noises, a multi-objective Bayesian optimisation algorithm based on Euclidian expected quantile improvement (MO-E-EQI^[2]) was adopted to consider heteroscedastic noises. First, an in silico benchmarking was conducted to evaluate algorithm performances. MO-E-EQI was compared to two state-of-the-art multi-objective Bayesian algorithms and showed the best performance for a noise level up to 20%. Then MO-E-EQI was implemented in a real case to optimize an esterification reaction in flow with four continuous variables: flow rates, equivalents, catalyst loadings, temperatures. The algorithm efficiently identified a clear trade-off under noises between space-time yield and E-factor.

In conclusion, the study demonstrates multi-objective reaction optimisation using Bayesian algorithms for two complex systems: multi-phase reaction system and noisy system. A set of Pareto front solutions can be found efficiently guided by Bayesian approach, which shows a promising way to allow multiple factors to be considered at early-stage reaction development.