  Space-filling designs are important in computer experiments, which are
critical for building a cheap surrogate model that adequately approximates an
expensive computer code. Many design construction techniques in the existing
literature are only applicable for rectangular bounded space, but in real world
applications, the input space can often be non-rectangular because of
constraints on the input variables. One solution to generate designs in a
constrained space is to first generate uniformly distributed samples in the
feasible region, and then use them as the candidate set to construct the
designs. Sequentially Constrained Monte Carlo (SCMC) is the state-of-the-art
technique for candidate generation, but it still requires large number of
constraint evaluations, which is problematic especially when the constraints
are expensive to evaluate. Thus, to reduce constraint evaluations and improve
efficiency, we propose the Constrained Minimum Energy Design (CoMinED) that
utilizes recent advances in deterministic sampling methods. Extensive
simulation results on 15 benchmark problems with dimensions ranging from 2 to
13 are provided for demonstrating the improved performance of CoMinED over the
existing methods.
