GPU-Accelerated Infill Criterion for Multi-Objective Efficient Global Optimization Algorithm and Its Applications

In this work, a novel multi-objective efficient global optimization (EGO) algorithm, namely GMOEGO, is presented by proposing an approach of available threads' multi-objective infill criterion. The work applies the outstanding hypervolume-based expected improvement criterion to enhance the Pareto solutions in view of the accuracy and their distribution on the Pareto front, and the values of sophisticated hypervolume improvement (HVI) are technically approximated by counting the Monte Carlo sampling points under the modern GPU (graphics processing unit) architecture. As compared with traditional methods, such as slice-based hypervolume integration, the programing complexity of the present approach is greatly reduced due to such counting-like simple operations. That is, the calculation of the sophisticated HVI, which has proven to be the most time-consuming part with many objectives, can be light in programed implementation. Meanwhile, the time consumption of massive computing associated with such Monte Carlo-based HVI approximation (MCHVI) is greatly alleviated by parallelizing in the GPU. A set of mathematical function cases and a real engineering airfoil shape optimization problem that appeared in the literature are taken to validate the proposed approach. All the results show that, less time-consuming, up to around 13.734 times the speedup is achieved when appropriate Pareto solutions are captured.