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

Abstract

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 is important to recognize the role of other surrogate-based approaches in conventional chemistry optimization problems. This is particularly relevant for chemical problems involving mixed-variable design space with mixed-variable physical constraints, where conventional BO approaches struggle 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 medium-sized mixed-variable problems (up to around 100 variables after encoding) subject to known linear constraints. We demonstrate the effectiveness of this approach in optimizing experimental planning through three case studies. 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, with emphasis on problems subject to known discrete/mixed-variable linear constraints.