## 5 Computational Experiments, Results, and Discussion
### Tuning MOSS Parameters
In the additional tuning experiments, there was no limit on the number of iterations, and the computational time was restricted to 120 s. The values of \(TGD(\mathcal{D})\) and \(\mathcal{H}(\mathcal{D})\) were recorded at the end of the initialization phase and every 30 s afterward. The selected levels in the additional tuning experiments focused on the values of 15, 20, 25, 30, 35, and 40 for \(RefSetSize\) and the values of 40, 50, 80, 100, 150, and 200 for \(n_{maxitr}^{TS}\). Lower values for both parameters were excluded, as their results in the former tuning experiments showed deficient performance. Using the same set of small-sized instances with six values for \(|\mathcal{P}|\), and conducting 30 independent runs for each treatment combination, revealed a total of \(30\times 6\times 6^{2}=6480\) independent runs that were conducted in random order. Figure 8 summarizes the average computational performance for the second MOSS-tuning experiments throughout the improvement phase. It is evident that the quality of the solutions at the end of the initialization phase increased with the increase in both \(RefSetSize\) and \(n_{maxitr}^{TS}\). However, this characteristic was quickly reversed, as the developed MOSS, after 30 s, produced better results with low values for both parameters. This continued as time proceeded. For the average \(\mathcal{H}(\mathcal{D})\), the effect of \(n_{maxitr}^{TS}\) is evident in Figure 8b, while the effect of \(RefSetSize\) is apparently lower, as shown in Figure 8a. The same behavior can be noticed for the average \(TGD(\mathcal{D})\), as shown in Figure 8c,d. These results suggest that low values for \(RefSetSize\) at 15 or 20 and low values of \(n_{maxitr}^{TS}\) at 40 or 50 can produce good-quality solutions in short computational times. Figure 7: Main effect plots from the first MOSS-tuning experiments. (**a**) Main effect plots for \(\mathcal{H}(\mathcal{D})\). (**b**) Main effect plots for the computational time. In addition to the conclusions about the preferred levels of the MOSS parameters, there was an important phenomenon involving the \(TGD(\mathcal{D})\) measure that is worth mentioning here. Figure 8c,d show that, unlike \(\mathcal{H}(\mathcal{D})\), which is monotone non-increasing with respect to the computational time, the value of \(TGD(\mathcal{D})\) can increase despite the improvement in the solutions in set \(\mathcal{D}\). This increase is apparent in Figure 8c,d after 90 s of computational time. The reason behind this phenomenon is that the evaluation of the performance measures is based only on the found set of non-dominated solutions at any given time. If better non-dominated solutions are found, other solutions that were non-dominated in a previous iteration and become now dominated are removed from set \(\mathcal{D}\), and therefore, they are no longer used in evaluating the performance measures. When the \(TGD(\mathcal{D})\) is evaluated, there could be a non-dominated solution that is close to one of the optimal Pareto front solutions in a previous iteration, which is then dominated by another solution that is far from that Pareto optimal solution. This phenomenon indicates that the gravitational distance measures do not have the consistency of the hypervolume-based measures.