## 5 Experiments
### Experimental Results
#### 5.2.2 Benchmark Models  
The same experiments presented in the previous subsection were repeated for the 42 benchmark models, and the same metrics were used to analyze the results. Thus, the next three figures present the distances, time to the first solution, and the number of solutions. Different from the previous graphs, the results are presented via paired boxplots. All our experiments are paired experiments, i.e., for given experimental conditions (e.g., a decision model, a starting alternative, and a desired outcome), a pair of experiments was performed, one set of experiments with the proposed method and another set of experiments with the baseline. We use the term \"set of experiments\" because each experiment was repeated 10 times to minimize the influence of the randomized steps on the experimental results. The lines connect the experimental runs that had the same experimental conditions (same model and same starting alternative). The blue line shows that our method was better for those specific experimental conditions. The red line shows that the baseline was better for those specific experimental conditions. The corresponding set of alternatives is compared using: the number of attribute changes required to reach the generated alternatives (Figure 11); the time to obtain the first appropriate alternative, Figure 12; and the number of generated alternatives (Figure 13). Figure 11 presents the distance between the final solution and the starting alternative. From the results, it can be seen that in all of these experiments, BAG-DSM found solutions with equal or shorter distances compared to the solutions found by the baseline. The difference is larger for the more complex models (depth 4 and depth 5). Figure 10: Boxplots for the time (shorter is better) required to find the first optimal alternative by BAG-DSM vs. baseline for the Landmark model. Figure 12 presents the time (in seconds) required to find a first solution. The blue horizontal line represents the experimental runs where BAG-DSM found the first solution faster than the baseline. Red horizontal lines represent the experimental runs where the baseline method was faster. From the results, it can be seen that for the more complex models (depth 4 and depth 5), BAG-DSM was much faster by finding the first solutions in the first few seconds, while the baseline method required more than 100 s in some of the cases. The only experiments in which the baseline performed better than BAG-DSM were those for the models with depth 3. However, the difference is smaller than 3 s.  
The observations have been statistically confirmed with statistical tests. BAG-DSM significantly dominates the baseline across all models (\(p\)-value very close to 0), as well  
Figure 11: Paired boxplots for the distances (shorter is better) between the current alternative and the optimal alternative found by BAG-DSM (Bayesian) vs. baseline for decision support models with a depth of 3, 4, and 5. The horizontal lines connect two experimental runs with the same experimental setup. Figure 12: Paired boxplots for the time (shorter is better) required to find the first optimal alternative by BAG-DSM vs. baseline for decision support models with a depth of 3, 4, and 5. The horizontal lines connect two experimental runs with the same experimental setup. The red lines represent the experimental setups in which the baseline performed better. Figure 13: Paired boxplots for the size of the solution set (bigger is better) generated by BAG-DSM vs. baseline for decision support models with a depth of 3, 4, and 5. The horizontal lines connect two experimental runs with the same experimental setup. The red horizontal lines represent the experimental setups in which the baseline performed better. as with respect to individual model types (e.g., models with normal, skewed, or uniform distribution or various depths). However, BAG-DSM has a less significant dominance in the problems with uniform distribution of attributes' weights compared to the other two (Supplementary Materials--Section S2.1.1).