Space-filling Design Generators via Particle Swarm Optimization with GPU Acceleration

Abstract

Space-filling design is popular used in computer experiments. In this work, we study two types of space-filling designs, the Latin hypercube designs based on the fp criterion and the uniform designs based on central composite discrepancy for irregular regions. The challenges for generating these two space-filling designs are (i) the huge number of feasible points and (ii) irregular sensitivity of the objective function values in terms of the nearby feasible points. Here we transfer these two space-filling design problems as discrete optimization problems with respect to different criteria. Discrete versions of particle swarm optimization (PSO) algorithms are proposed to overcome the challenges. Moreover, we use graphic processing unit (GPU) to accelerate the search processes. Finally numerical results are used to demonstrate the performances of the proposed search methods. ?Joint with Weichung Wang, Dai-Ni Hsieh, Yen-Wen Shu (NTU) and Ying Hung (Rutgers University)