Many challenges encountered in chemistry and materials science can be framed as optimization tasks. In fact, due to its ubiquity in all quantitative disciplines, optimization is a fundamental area of applied numerical science. Solving an optimization problem involves the systematic selection of input parameters from an allowed set, with the goal of identifying the parameters that produce the most desirable outcome. The property being optimized is typically referred to as the objective function, or figure of merit. Advances in the field of optimization research have consistently enabled technologies with significant societal impact. For instance, stochastic gradient descent is the key optimization algorithm that enables the training of deep neural networks. Non-linear optimization strategies are also used heavily in molecular modelling, which is indispensable to the fields of computational chemistry, drug design, materials science, and computational biology. A subset of optimization problems of particular interest in the experimental sciences are global, black-box problems, which involve objective functions whose structure is a priori unknown, and must be resolved by sequential (oftentimes noisy) measurement. Prevalent examples include chemical reaction optimization (the maximization of the yield of the desired chemical product given a set of allowed conditions), optimization of properties of advanced materials or functional molecules, such as photovoltaics, nanomaterials, and catalysts, among others. Model-based optimization approaches, such as Bayesian optimization, are proving particularly suited to black-box optimization tasks encountered in experimental sciences. Recently, the com-bination of model-based optimization with automated laboratory equipment has shown potential for the development of fully autonomous research platforms, also referred to as self-driving laboratories or materials acceleration platforms. Although the mentioned experimental science applications are diverse in discipline, they have several characteristics in common. In particular, they typically (i) are black-box problems with no analytical gradient information available, (ii) involve expensive-to-evaluate objectives (with respect to monetary cost, time, or other resources), (iii) consist of several input parameter types (continuous, discrete, and categorical), (iv) involve measurement procedures which are subject to noise, and (v) involve multiple, potentially competing objectives that must be optimized simultaneously.