Stochastic coordinate-exchange optimal designs with complex constraints

The paper provides a method to construct the exact optimal experimental designs for both physical and computer experiments with any regular or irregularly constrained design space. We modify the original greedy coordinate-exchange algorithm into the stochastic version by adding the random selection of the “bad” coordinates that can be exchanged for “better” values to improve the optimal design criterion. More importantly, we adapt it to accommodate the non-convex or disconnected constrained design space. We implement the stochastic coordinate-exchange (SCE) algorithm for D- and linear- (A- and I-) optimal designs for physical experiments, and ϕp-optimal space-filling designs for computer experiments.