Minimax designs using clustering

Minimax designs provide a uniform coverage of a design space $\mathcal{X} \subseteq \mathbb{R}^p$ by minimizing the maximum distance from any point in this space to its nearest design point. Although minimax designs have many useful applications, e.g., for optimal sensor allocation or as space-filling designs for computer experiments, there has been little work in developing algorithms for generating these designs. In this paper, a new clustering-based method is presented for computing minimax designs on any convex and bounded design region. The computation time of this algorithm scales linearly in dimensionality $p$, meaning our method can generate minimax designs efficiently for high-dimensional regions. Simulation studies and a real-world example show that the proposed algorithm provides improved minimax performance over existing methods on a variety of design regions. Finally, we introduce a new type of experimental design called a minimax projection design, and show that this proposed design provides better minimax performance on projected subspaces of $\mathcal{X}$ compared to existing designs.