Discrete and mixed-variable experimental design with surrogate-based approach

Experimental design plays an important role in efficiently acquiring informative data for system characterization and deriving robust conclusions under resource limitations. Recent advancements in high-throughput experimentation coupled with machine learning have notably improved experimental procedures. While Bayesian optimization (BO) has undeniably revolutionized the landscape of optimization in experimental design, especially in the chemical domain, it's important to recognize the role of other surrogate-based approaches within conventional chemistry optimization problems. This is particularly relevant because many chemical problems involve mixed-variable design space with physical constraints, making it challenging for conventional BO approaches to obtain feasible samples during the acquisition step while maintaining exploration capability. In this paper, we demonstrate that integrating mixed-integer optimization strategies is one way to address these challenges effectively. Specifically, we propose the utilization of mixed-integer surrogates and acquisition functions--methods that offer inherent compatibility with problems with discrete and mixed-variable design space. This work focuses on Piecewise Affine Surrogate-based optimization (PWAS), a surrogate model capable of handling mixed-variable problems subject to linear constraints. We demonstrate the effectiveness of this approach in optimizing experimental planning through three case studies, each with a different design space size and numerical complexity: i) optimization of reaction conditions for Suzuki–Miyaura cross-coupling (fully categorical), ii) optimization of crossed-barrel design to augment mechanical toughness (mixed-integer), and iii) solvent design for enhanced Menschutkin reaction kinetics (mixed-integer and categorical with linear constraints). By benchmarking PWAS against state-of-the-art optimization algorithms, including genetic algorithms and BO variants, we offer insights into the practical applicability of mixed-integer surrogates.