  Bayesian optimization (BO) is a popular approach for sample-efficient
optimization of black-box objective functions. While BO has been successfully
applied to a wide range of scientific applications, traditional approaches to
single-objective BO only seek to find a single best solution. This can be a
significant limitation in situations where solutions may later turn out to be
intractable. For example, a designed molecule may turn out to violate
constraints that can only be reasonably evaluated after the optimization
process has concluded. To address this issue, we propose Rank-Ordered Bayesian
Optimization with Trust-regions (ROBOT) which aims to find a portfolio of
high-performing solutions that are diverse according to a user-specified
diversity metric. We evaluate ROBOT on several real-world applications and show
that it can discover large sets of high-performing diverse solutions while
requiring few additional function evaluations compared to finding a single best
solution.
