# Addressing the Algorithm Selection Problem through an Attention-Based Meta-Learner Approach
## 5 Conclusions and Future Work  
This study proposes using an attention-based neural network as a meta-learner to select a suitable algorithm that best solves a particular VRPTW instance. In our experiments, the proposed AM selector showed a statistically significant advantage over the other five baseline selectors from the literature for choosing the best algorithm for a specific VRPTW instance. Overall, the proposed model proved superior for all the analyzed metrics when selecting a suitable algorithm, i.e., accuracy, precision, recall, and F1-score. Thus, we can conclude that the attention-based meta-learner represents an acceptable alternative for learning problem-algorithm mapping. Moreover, the evidence supports employing more novel neural network architectures as performance mapping mechanisms. We showed that the proposed AM selector performs better when comparing it against the simpler MLP architecture. The improvement \begin{table}
\begin{tabular}{c c} \hline \hline
**Method** & **AM** \\ \hline MLP & \(5.661648\times 10^{-15}\) \\ KNN & \(4.185436\times 10^{-10}\) \\ SR & \(3.547531\times 10^{-17}\) \\ SVM & \(9.443043\times 10^{-7}\) \\ DT & \(9.148237\times 10^{-13}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: \(p\)-values for pair-wise McNemar tests between AM and the other five selectors. concerning the simpler MLP occurs not only in how often it chooses the best algorithm configuration for a specific problem instance but also in its clear advantage in reducing the proportion of false positives when performing a selection. This particular advantage can be observed explicitly in the precision scores for both selectors since, in the case of the MLP, all metrics have roughly the same value, whereas for the AM, the precision score is around two percentage points higher than the remaining metrics and 15.1 percentage points higher than that of the MLP selector, which corresponds to a 20% overall improvement in precision. Such evidence suggests that extracting patterns from the meta-features that characterize problem instances can still be significantly improved. It may be worth researching other architectures to improve the overall process of learning the mappings from problem instances to suitable algorithms. In other words, our model selects the best algorithm out of three options for a given VRPTW instance. Moreover, by significantly outperforming the benchmark models, this method shows that exploring more complex and advanced performance mapping mechanisms appears to have good results that could significantly improve solving a problem instance via the algorithm selection framework. It also shows that neural networks, especially those with more complex architectures, yield better results and are worth studying. An exciting path for future research would be to explore other novel neural network architectures and approaches for the selection process and improve the final problem instance representation. Some possible approaches that would be worth studying could include an adapted MMINet [70], local explanations [71], as well as other non-linear dimension reduction architectures such as EVNET [72]. We could also explore methodologies based on alternative machine learning techniques, such as self-organizing maps, and even explore the use of unsupervised approaches, such as the unsupervised modified graph embedding technique proposed by [PERSON] et al. [73] or mixed methodologies such as the one introduced by [PERSON] et al. [74] combining unsupervised clustering and feature correlation. Furthermore, it would be interesting to explore using a different score function for the attention mechanism, such as employing a parameterized additive score function, which has outperformed multiplicative functions such as the one used in this work [10]. Additionally, employing the attention-based meta-learner for selecting heuristics within an online selection hyper-heuristic seems a potentially good research direction.