Enhanced expected hypervolume improvement criterion for parallel multi-objective optimization

To reduce optimization time spent on real-world expensive multi-objective optimization problems (MOPs), a relatively large number of points added in each cycle is an effective way to push the Pareto front approximation to the optimal Pareto front as more time-consuming experiments can be performed in a parallel manner. In this study, an enhanced multi-point infill criterion, namely, nearest-neighbor Euclidean distance-based pseudo-expected hypervolume improvement (PEHVInne), is proposed to enhance the efficiency of the convergence during the process of point infills, particularly when a relatively large number of point infills are added. This criterion is calculated by multiplying the traditional expected hypervolume improvement (EHVI) criterion by the nearest-neighbor Euclidean distance-based pseudo-expected improvement matrix (PEIMnne) criterion. Therefore, the effective information of an evaluation point with a huge potential for improvement, and the crowding distances between this point and the nearest-neighbor Pareto front points around it can be considered simultaneously. The proposed criterion was compared with the EHVI and Euclidean distance-based pseudo-expected improvement matrix (PEIMe) criteria for multi-objective benchmarks. The results show that the proposed criterion enhances the efficiency and convergence of the EHVI criterion for most benchmarks. Moreover, the PEHVInne can either converge better than the PEIMe with the same efficiency or converge to a close-level Pareto front with higher efficiency as more points in each cycle can be selected to add. Therefore, the PEHVInne is more suitable as a highly efficient criterion for seeking an acceptable-quality Pareto front with less time in multi-objective optimization (MOO). In addition, the influence of the optimizer on the proposed criterion was investigated. The results indicate that the PEHVInne has some internal robustness even if the convergence level of the optimizer significantly influences its performance, which can help to set up an optimizer.