fig8

Figure 8. Probability density maps in objective space for 10 runs of 24 iterations × 8 points per batch. (A and B) Thin film; (C and D) concrete slump. The evaluated data points are plotted with a Gaussian kernel density estimate using SciPy to illustrate the distribution of points across objective space, with a color bar to represent the numerical value of probability density. Results are averaged over 10 runs, taking a smaller evaluation budget of 24 iterations × 8 points = 192. The results here reinforce the finding that qNEHVI has a more random distribution of points, but still outperforms U-NSGA-III for a low evaluation budget. HV: hypervolume; MOBO: multi-objective Bayesian optimization; MOEA: multi-objective evolutionary algorithms; U-NSGA-III: Unified Non-dominated Sorting Genetic Algorithm III.