## 5 Results
The quality of predicted parameters depends on the runtime limit, as seen in Figure 9. For a 10-second time limit, KNN with one neighbor provides the best result, with a 4% improvement over the base set. For a 30 s time limit, both KNN1, KNN9, and KNN11 provide similarly good results, though the difference between said parameter sets and the  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Parameter Set** & **Instances** & **10 [s]** & **30 [s]** & **60 [s]** & **Avg. 10 [s]** & **Avg. 30 [s]** & **Avg. 60 [s]** \\ \hline \multirow{4}{*}{Base} & C1 & 14,934 * & 14,686 & 14,608 & \multirow{4}{*}{10,514} & \multirow{4}{*}{15,366} & \multirow{4}{*}{**14,920**} \\  
base set is nearly negligible. Finally, with a 60 s time limit, the base parameter set provides the best results, with all predicted parameter set evaluations landing within 2% of each other. When considering the three-time limits together, KNN1 provides the best average results (See Figure 10). Figure 11 shows the loss curves for the training and validation sets during the training process of the neural network that uses the data concerning all the problem instances. A typical learning rate can be observed in these curves. Starting with a high loss value, the process converges to low loss levels for both training and validation data sets. Figure 10: Bar plot of the performance of HGS using the suggested parameter configurations. The average results over the three running times scenarios are presented. Figure 9: Bar plot of the performance of HGS using the suggested parameter configurations. The average results obtained in ten runs over all the running times scenarios are presented per parameter set. Blue bars show results for 10 s, orange bars for 30 s, and green bars for 60 s.  
The main issue concerning predicting a metaheuristic's optimal parameter configuration for a given instance is the stochastic nature of the tuning algorithm and the metaheuristic itself. When constructing a model to map an instance's features to its optimal parameter vector, we must consider that an instance deterministically produces a feature vector but may produce different parameter vectors depending on the execution of the tuning method and the metaheuristic algorithm. A significant disadvantage of our proposal is that it requires an extended period for parameter tuning to build the training data. As a tuning algorithm must run the metaheuristic thousands of times to obtain a result, increasing the metaheuristic's execution time produces a multiplicative growth in parameter tuning time. Given the size of our improvement, computation time would likely be better spent increasing HGS's run time. It is important to note that the Base parameters used for comparison here were sourced from a per instance-based tuning process whose time was not reported, and tuned the algorithm for run times ranging from 4 to 40 min. The true efficiency of machine learning models is realized when we have overwhelmingly large amounts of training data at our disposal. In the theoretical scenario of having a widely spanning set of instances, the potential for parameter prediction through machine learning models could be a game-changer in tackling intractable problems. This is particularly beneficial if quick and suitable solutions are required.