Similar to synthetic benchmark experiments, we compare both approaches based on 3 metrics, omitting dimensional contour plots:
  1. Optimisation trajectory in objective space for 100 iterations x 8 points per batch
  2. Probability density function in objective space for 24 iterations x 8 points per batch
  3. Comparison of batch size for log hypervolume difference  
Figure 7 further supports our conclusions drawn from results reported in Figure 4. As seen in Figure 7 b) and d), qNEHVI is highly sample efficient, with points at or near the PF within the first 20 iterations or so, indicated by the darker points lying on the red line.  However, qNEHVI shows a large random distribution of non-optimal points away from PF across the entire optimisation as seen by both dark and bright points, which we attribute to the stochastic QMC sampling.  U-NSGA-III performs a gradual evolution of points towards the PF as seen in Figure 7 a) and c), as well as maintaining a large pool of near-optimal solutions. This is reflected by the lower HV scores for U-NSGA-III compared to those of qNEHVI.