On the development of a practical Bayesian optimization algorithm for expensive experiments and simulations with changing environmental conditions

Experiments in engineering are typically conducted in controlled environments where parameters can be set to any desired value. This assumes that the same applies in a real-world setting, which is often incorrect as many experiments are influenced by uncontrollable environmental conditions such as temperature, humidity, and wind speed. When optimizing such experiments, the focus should be on finding optimal values conditionally on these uncontrollable variables. This article extends Bayesian optimization to the optimization of systems in changing environments that include controllable and uncontrollable parameters. The extension fits a global surrogate model over all controllable and environmental variables but optimizes only the controllable parameters conditional on measurements of the uncontrollable variables. The method is validated on two synthetic test functions, and the effects of the noise level, the number of environmental parameters, the parameter fluctuation, the variability of the uncontrollable parameters, and the effective domain size are investigated. ENVBO, the proposed algorithm from this investigation, is applied to a wind farm simulator with eight controllable and one environmental parameter. ENVBO finds solutions for the entire domain of the environmental variable that outperform results from optimization algorithms that only focus on a fixed environmental value in all but one case while using a fraction of their evaluation budget. This makes the proposed approach very sample-efficient and costeffective. An off-the-shelf open-source version of ENVBO is available via the NUBO Python package.