# Difference-Based Mutation Operation for Neuroevolution of Augmented Topologies +
## 3 Results
The first hidden layer contained 100 neurons, and the second hidden layer had 50 neurons. The training was performed for 25 epochs with a batch size of 100. The presented setup is a typical usage scenario for neural networks. In addition to the NN, the Decision Trees (DT) training implemented in sklearn library [32] were used, as well as Random Forest (RF) training, K nearest neighbors classifier (K-NN) and Support Vector Machine for classification (SVM). For these algorithms, the standard training parameters were used for all cases, as this represents a typical usage scenario. Table 7 contains the comparison on the test set, and Table 8 provides the results of Mann-Whitney statistical test, comparing NEAT-DBM with other approaches. The modified NEAT with DBM was able to get the best test set accuracy for Australian credit, German credit, and ranked second for the Page-blocks and third for the Twonormt datasets. However, it appeared to be worse than all other methods for the Segment dataset, \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Dataset** & **HEFCA** & **NN (Keras)** & **DT** & **RF** & **K-NN** & **SVM** \\ \hline Australian credit & 0.8537 & 0.8552 & 0.8202 & 0.8724 & 0.8579 & 0.8507 & **0.8824** \\ German credit & 0.7280 & 0.7530 & 0.6930 & 0.7610 & 0.6960 & 0.7590 & **0.7660** \\ Segment & 0.9100 & 0.9476 & 0.9619 & **0.9801** & 0.9472 & 0.8662 & 0.8087 \\ Phoneme & 0.8260 & 0.7957 & 0.8760 & **0.9197** & 0.8862 & 0.8442 & 0.7950 \\ Page-blocks & 0.9406 & 0.9616 & 0.9613 & **0.9741** & 0.9550 & 0.9055 & 0.9631 \\ Twonorm & 0.9043 & 0.9792 & 0.8455 & 0.9736 & 0.9728 & **0.9803** & 0.9751 \\ Ring & 0.9237 & 0.8262 & 0.8782 & 0.9500 & 0.6888 & **0.9781** & 0.9011 \\ Magic & 0.8415 & 0.8274 & 0.8157 & **0.8790** & 0.8072 & 0.8198 & 0.8369 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: NEAT compared to alternative approaches, test set. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Dataset** & **HEFCA** & **NN (Keras)** & **DT** & **RF** & **K-NN** & **SVM** \\ \hline Australian credit & 0, \(Z=0.91\) & 0, \(Z=0.98\) & **1, \(Z=2.27\)** & 0, \(Z=0.08\) & 0, \(Z=0.76\) & 0, \(Z=1.44\) \\ German credit & **1, \(Z=2.56\)** & 0, \(Z=0.57\) & **1, \(Z=2.81\)** & 0, \(Z=0.04\) & **1, \(Z=3.07\)** & 0, \(Z=0.53\) \\ Segmentand has similar performance to the NN trained in Keras on the Phoneme dataset, where the rule or tree-based approaches have achieved much better results. This shows that NEAT has certain potential when solving some problems, however, its performance is similar to a feed-forward neural net due to approach similarity. The statistical test in Table 8 shows that NEAT is capable of significantly outperforming decision tree, K-NN, HEFCA, SVM and conventional neural net on several datasets, although when compared to the random forest, it usually shows worse results. The reason for that could be that the RF is an ensemble-based classifier, while all others are single classifiers. Combining several neural nets designed by NEAT-DBM into an ensemble is one of the ways to improve generalization ability. Figure 5 shows an example of solution trained by NEAT-DBM for the Phoneme dataset. Figure 5 shows that NEAT-DBM is capable of designing relatively compact models with few connections, thus making it possible to solve the classification problems with minimum computational requirements. For the second set of experiments, the control problem was considered, in particular the stabilizing of the Rotary Inverted Pendulum (RIP). Due to the complexity of this problem and its properties, such as nonlinearity, non-minimum phase and instability, it is often considered as a test problem in the control community. If an algorithm is capable of solving this problem, it should be able to solve many others, such as control of a space booster rocket, automatic aircraft landing system, stabilization of a cabin in a ship, etc. [33]. This was the main reason why this problem was considered in this study. There are several known problems which include pendulum stabilization.