A multi-point mechanism of expected hypervolume improvement for parallel multi-objective Bayesian global optimization

The technique of parallelization is a trend in the field of Bayesian global optimization (BGO) and is important for real-world applications because it can make full use of CPUs and speed up the execution times. This paper proposes a multi-point mechanism of the expected hypervolume improvement (EHVI) for multi-objective BGO (MOBGO) by the utilization of the truncated EHVI (TEHVI). The basic idea is to divide the objective space into several sub-objective spaces and then search for the optimal solutions in each sub-objective space by using the TEHVI as the infill criterion. We studied the performance of the proposed algorithm and performed comparisons with Kriging believer technique (KB) on five scientific benchmarks and a real-world application problem (i.e., a low-fidelity multi-objective airfoil optimization design). The stochastic experimental results show that the proposed algorithm performs better than the KB with respect to the hypervolume indicator, indicating that the proposed method provides an efficient parallelization technique for MOBGO.