Minimax and Minimax Projection Designs Using Clustering
提出一种结合粒子群优化和聚类的新混合算法，用于生成凸有界设计空间上的极小极大设计，计算时间随维度线性增长，并引入极小极大投影设计以提升投影子空间上的性能。
Minimax designs provide a uniform coverage of a design space X⊆Rp by minimizing the maximum distance from any point in this space to its nearest design point. Although minimax designs have many useful applications, for example, for optimal sensor allocation or as space-filling designs for computer experiments, there has been little work in developing algorithms for generating these designs, due to its computational complexity. In this article, a new hybrid algorithm combining particle swarm optimization and clustering is proposed for generating minimax designs on any convex and bounded design space. The computation time of this algorithm scales linearly in dimension 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 spaces. 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 X compared to existing designs. An efficient implementation of these algorithms can be found in the R package minimaxdesign. Supplementary material for this article is available online.