## 5 Results  
In this section, we present the results of HGS considering the following parameter vectors:  
* Base parameter values for the HGS metaheuristic (as defined in [5]). * Parameter values predicted by KNN with \(K\in\{1,3,5,7,9,11\}\). * Parameter values predicted by the artificial neural network. * Parameter values samples from a random distribution. The set of base parameter values (A) is constant for all instances as specified in the literature. We evaluate six different values for KNN. \(K=1\) borrows the parameters from the instance's most similar neighbor, while \(K=3\) through \(K=11\) takes the nearest neighbors and averages their parameter vectors. Interestingly, even when the predicted values are restricted to a specific set (for the tuning discretization required by ParamILS), the prediction of KNN allows the use of new values coming from the averages of the corresponding \(k\) neighbors' values. Here, a complementary behavior between the discretization during the tuning process and the in-detail analysis of the prediction step can help reduce the tuning effort without losing the ability to select intermediate values for the parameters. We also consider a set of random parameter values (D) to test the metaheuristic's sensitivity to parameter selection. Parameter values were randomly sampled for each instance, using a uniform distribution that covered the discrete parameter space used for parameter prediction. The following results consider the testing set of instances. For each instance-vector pair, we perform ten independent executions of HGS, to reduce the effect of the stochasticity on the results. For each parameter vector, the metaheuristic was executed considering 10, 30, and 60 s.  
Table 4 shows the results of evaluating the predicted parameter configurations on HGS. We show the average quality value obtained in each tuning scenario tested for each method (Base, KNN, Neural Network, and Random) and the subgroups of instances (C1, C2, R1, R2, RC1, and RC2). The last three columns summarize the method's performance on the set of Homberger problem instances. Bold values show the best performance per instance subgroup, and an asterisk indicates the worst values per set. The results show that the algorithm that suggested the parameter configurations that produce the best performance in HGS for a higher number of subgroups was KNN with \(K=7\) for the 10 s execution time. These results were obtained in the C1 and C2 subgroups. For the 30 s time budget, KNN with \(K=1\) performs best in two subgroups (C1 and \(RC1\)). On the other hand, KNN with \(K=5\) was the algorithm that suggested the best parameter configurations for 60 s of time budget. Considering the algorithms related to the lowest quality performance of HGS, for 10 s, the base configuration and KNN5 produce the worst results in two subgroups (C1 and \(RC1\), and \(C2\) and \(R1\), respectively). For 30 and 60 s, the random configuration produces the worst performance in five subgroups. After analyzing the average of all the quality values, KNN1 has the best average quality value for 10 s, and KNN11 has the worst. Similar behavior occurs in the 30 s time budget, where KNN1 has the best average quality value, and KNN7 has the worst. The base configuration reaches the best average quality value for the 60 s time budget, and KNN1 obtains the worst one. Regarding the performance of ANN, it is interesting to observe that the predicted parameter values are not the poorest or best suggested for any subgroup of instances. However, compared to the Base parameter set, with 10, 30, and 60 s of execution of HGS, the ANN suggested better configurations in five out of six subgroups of instances. Compared to KNN approaches, the ANN does not obtain better configurations on average. This situation is due to the low number of features obtained from the instances provided to the ANN to generalize and suggest configurations to unseen instances.