Discrete particle swarm optimization for constructing uniform design on irregular regions

Central composite discrepancy (CCD) has been proposed to measure the uniformity of a design over irregular experimental region. However, how CCD-based optimal uniform designs can be efficiently computed remains a challenge. Focusing on this issue, we proposed a particle swarm optimization-based algorithm to efficiently find optimal uniform designs with respect to the CCD criterion. Parallel computation techniques based on state-of-the-art graphic processing unit (GPU) are employed to accelerate the computations. Several two-to five-dimensional benchmark problems are used to illustrate the advantages of the proposed algorithms. By solving a real application in data center thermal management, we further demonstrate that the proposed algorithm can be extended to incorporate the non-collapsing property.