Abstract: Bayesian optimisation and active learning methods typically target problems where data is severely limited and must be obtained through costly sequential processes. This talk explores scalable solutions for the feasible set estimation problem, addressing the challenges of increasing data size, parallelisation through large batch strategies, and simultaneously considering multiple outputs. Inspired by Thompson sampling algorithms, we present practical and high-performance solutions that effectively handle these challenges. By leveraging feasible sets, we demonstrate their potential as an attractive and robust alternative to optimisation in solving complex design problems.