# Evolutionary Optimization of Spiking Neural P Systems for Remaining Useful Life Prediction
## 5 Numerical Results
not provided). The boldface indicates the best value per column. Figure 4: Fitness across generations (mean \(\pm\) std. dev. across 10 independent runs) for SNPS (4) on N-CMAPSS (DS02). The importance of reducing the number of parameters can be highlighted by comparing the test execution time. For all the time measurements, we use the same GPU, and the time related to the initialization of the DL library is neglected. Although the test time is not linearly proportional to the number of trainable parameters, there is a positive correlation; our best SNPS in terms of test RMSE that has 232 parameters, i.e., SNPS (5), spends merely 25 ms to compute RUL predictions of the test samples, while a very simple one hidden layer MLP containing 801 parameters takes almost four times as much. Moreover, SNPS (3), which has only 60 parameters, spends only 7 ms to execute the test. In contrast, the CNN and LSTM, which contain a significantly larger number of parameters compared to our models, require a much longer time to complete the test. Thus, the small amount of parameters in our SN P systems represents the main advantage of the proposed method, since it is clear that reducing the number of parameters can reduce the time needed to predict the RUL. Figure 6 visualizes the trade-offs of the different methods (excluding SVM, for which the number of parameters is not available from [38]) in terms of test RMSE vs. number of parameters. We can observe that the proposed method Pareto dominates the MLP. Among the compared algorithms, the proposed method is clearly the best one in terms of number of trainable parameters. Moreover, compared to the LSTM, the best SNPS architecture we found has an approximately 95% shorter test execution time, with around 95% less parameters, while its test RMSE is only about 15% larger. Figure 5: Best SN P system evolved for the RUL prediction task on CMAPSS (FD001). Table 8 presents the comparative results on the N-CMAPSS dataset of the two deep neural networks taken from [39] and the solutions obtained by our proposed method. It should be noted that compared to the shallow MLP used on the CMAPSS dataset, the number of parameters of the MLP used here is more than two orders of magnitude larger (94,701 vs. 801). On the other hand, the CNN has a comparable number of parameters. We can see that the two deep networks can reach a very low RMSE. However, the CNN shows a better prediction accuracy with a lower number of parameters, although the computation for training this DL architecture is still considerably large [19]. Differently from the results on CMAPSS, the \(s\)-score performance of the proposed method is better than that of MLP, but it cannot reach the performance of the CNN. As illustrated in Figure 7, our SN P systems do not outperform the CNN in terms of RMSE, but they have a clear advantage in terms of number of trainable parameters. Especially the best solution in terms of test RMSE, SNPS (4) illustrated in Figure 8, has 56 parameters, and this remarkably simple structure enables predicting RUL very quickly. In fact, the execution time on the test set reported in Table 8 clearly demonstrates this advantage. On this notably larger dataset, the proposed method only takes less than 20 ms to predict the RUL, while the other methods take more than 1 s.