fig4

Figure 4. Optimization trajectory in objective space for a single run of 100 iterations × 8 points per batch. (A and B) ZDT1; (C and D) ZDT2; (E and F) ZDT3; (G and H) MW7. The red line represents the true PF, while MW7 being a constrained problem has an additional blue line to show the unconstrained PF. The color of each experiment refers to the number of iterations. All problems clearly show a more gradual evolution of results as the number of iterations progresses in U-NSGA-III, whereas qNEHVI rapidly approaches PF and then fails to converge further. HV: hypervolume; MOBO: multi-objective Bayesian optimization; MOEA: multi-objective evolutionary algorithms; qNEHVI: q-Noisy Expected Hypervolume Improvement; U-NSGA-III: Unified Non-dominated Sorting Genetic Algorithm III.