## 3 Results and Discussion
### Performance of the Three Hybrid Classifiers
These results were obtained after conducting numerous independent computer experiments. In Table 6, the first column corresponds to the name of the hybrid algorithm; the second column corresponds to the value of the parameter _alpha_ that was used in the fitness function of the GA, according to Equation (2); the third column presents the classification accuracy (_acc_) that was achieved by the fittest individual of the last generation of the GA; the fourth column presents the size \(S\) of the training set, in the number of cases, for the corresponding fittest individual; the fifth column presents the number of cases in the training set that should proceed to biopsy; and, finally, the sixth column presents the number of cases in the training set that should not proceed to biopsy. According to the findings presented in Table 6, the GAKK and GACLUST hybrid algorithms seem to achieve almost the same performance with respect to the size \(S\) of the training set. In addition, it is noteworthy that, according to Table 6, the GACLUST algorithm outperformed the GAKMEANS algorithm in terms of the size \(S\) of the training set, which is essential to achieve 100% classification accuracy on the test set. Namely, the GACLUST algorithm utilized 16.37% of the dataset to form the optimal training set, whereas the GAKMEANS algorithm utilized 33.64% of the dataset to achieve maximum classification performance. A final comment that can be made regarding the findings presented in Table 6 is that, especially in the cases of the GAKNN and the GACLUST algorithms, the pressure that the _alpha_ factor exerts on the construction of the training set is clearer. Figure 9: Evolution of the training set size \(S\) and classification accuracy on the test set for the GACLUST hybrid algorithm. Finally, Table 7 summarizes the obtained results for two groups of computer experiments. In the first group of experiments, the dataset of \(N=660\) cases that was used in all the aforementioned results (from now on referred to as set 1) was split into three subsets, namely, the training, the validation, and the test subsets, with the validation and the test subsets of equal size. This follows a widely used practice in machine learning for dataset splitting. In these experiments, the hybrid algorithms were trained with the use of the training set, and during the training procedure, the data of the validation set, as well as the data of the test set, were kept unseen. After the completion of the training procedure, the trained hybrid algorithms were evaluated with the use of the validation set and the test set. The classification accuracy achieved with the use of dataset 1 is presented in the third column of Table 7, regarding four independent computer experiments for each one of the hybrid algorithms. In the second group of experiments, the trained algorithms were evaluated with the use of a second, independently generated dataset (set 2), which consisted of 100 cases. The surrogate data in dataset 2 were generated by the same means that the surrogate dataset 1 was generated. The data in set 2 were kept unseen by the algorithms during the training procedure with the use of the data in set 1. The classification accuracy achieved on the second dataset (set 2) is presented in the fourth column of Table 7. According to Table 7, the hybrid algorithms retained their high classification performance in the first group of experiments, where dataset 1 was split in three subsets (namely, the training subset, the validation subset, and the test subset) since no significant difference was observed with respect to the corresponding results shown in Table 6, where dataset 1 was split into only two subsets (training subset and test subset). Regarding the additional evaluation of the performance of the hybrid algorithms on a second independent dataset (set 2), the algorithms proved robust and were not overfitted.