# On the Use of Learnheuristics in Vehicle Routing Optimization Problems with Dynamic Inputs
## 6 Analysis of the Results  
The columns of gaps in Table 1 show the relative differences between the best solutions obtained with the static and dynamic approaches. The positive gaps between SRC and DRC proves the importance of considering the intrinsic dynamism of the system. Indeed, the maximum gap reaches a value of 23.58%, while the average gap is around 12.02%. All the gaps are strictly positive, thus the static approach does not outperform the dynamic one in any instance. Regarding the gaps between DFC and DRC, the amount is lower: the greater gap in terms of absolute values is 0.26%, and the mean is 0.00%. This is due to the fast learning of the linear regression model, which can be explained due to the fact that the BB model is linear and has a relatively small error term. Finally, there are positive and negative gaps between SFC and DRC, but SFC is, on average, 1.25% lower than DRC. Thus, when the dynamism is not considered, the forecast of real costs tends to be optimistic, misleading the planner. It is worth remarking that, while SFC and SRC are similar in some instances, the routes of those solutions are different. The planner may be deceived into thinking that ignoring dynamism leads to a solution with a similar performance to that of the optimal solution; however, once those routes are completed, SRC is greater than SFC.  
Figure 2 represents graphically the gaps considering the different instance sets. Regarding the gaps between DFC and DRC (first raw of boxplots), we observe that the groups of instances have different distributions of gaps, but they tend to be relatively small. The distributions are relatively symmetric, except for sets A (negative skew) and F (no variability at all). There are no outliers. We focus now on the gaps between SRC and DRC. They range between almost 0% and 25%. The boxplots per group of instances share some similarities with the previous ones: symmetry except for sets A (positive skew) and F (no variability at all), there are no outliers, and the variability (either total range and interquartile range) depends on the set (higher for set E and lower for set M, for example). Finally, the last row displays the boxplot of the gaps between SFC and DR. They range between \(-10\%\) and \(5\%\), approximately. There are only two outliers, and the variability is also group-dependent: for sets B and E is higher than for F. There is also symmetry in this case. Since there is not any pair of sets with a similar distribution of gaps, it is difficult to link the main differences of the sets (described in Section 5.1) to the boxplots.  
Figure 3 aggregates the gaps by sets, and displays them using a unique scale, thus allowing a direct comparison. The gaps range between \(-10\%\) and \(25\%\), approximately. The boxplot for the gaps between DFC and DRC is a single line. Regarding the gaps between SFC and DRC, the boxplot represents a symmetric distribution with a negative outlier and a slightly negative median. Finally, the boxplot for the gaps between SRC and DRC shows a higher variability but is also symmetric. The first and third quartiles are close to \(10\%\) and \(15\%\), respectively.  
Figure 3: Multiple boxplots comparing the gaps of the different costs relative to the DRC with a uniformly distributed error term \(\epsilon\in[-10^{-3},10^{-3}]\).