## 3 The Relay Experiment and Parameters Analysis
### The Relay Lifetime Prediction Based on the IFWA Optimizing GNN Model  
The six variates \(a,\ b_{1},\ b_{2},\ b_{3},\ b_{4},\ b_{5}\) compose a whole firework and five seed fireworks are randomly generated. The number of each next generation seed fireworks is 5; the maximum number of sparks generated by each seed fireworks explosion is 50; the minimum is 10; the coefficient \(u\) of the explosion sparks number \(S_{i}\) is 160; the coefficient \(R_{c}\) of the explosion radius \(R_{i}\) is 0.5; the number of iteration is 600; and the sparks generated by Gaussian mutation is 5.  
Ten sparks with better fitness are selected from the sparks generated from the initial fireworks explosion, Gaussian mutation sparks, and the original sparks. The mean value and standard deviation of each dimension variate are calculated. The two-dimensional variates with the smallest standard deviation are chosen to deeply local search. Taking the first explosion for example, the standard deviation and the mean value of each dimension variate of the ten sparks are calculated. Therefore, the local search of \(b_{2}\) and \(b_{3}\) whose standard deviation are smaller should be strengthened in next explosion. The radius of variate \(b_{2}\) with the range [0.3780, 0.4530] and variate \(b_{3}\) with the range [0.4161, 0.4675] should be limited in next explosion. The standard deviation and mean value of each dimension variates are shown in Table 9.  
The one spark with best fitness and four other sparks selected randomly are regarded as the original fireworks of the next explosion. After the explosion is completed, the standard deviation and mean value of the ten best fitness sparks are calculated. Then, the two-dimensional variates and the scope of explosion are reconfirmed. The process is repeated until the termination condition is satisfied. There is certain randomness of the optimization results due to the randomness of the initial coefficient selection and the uncertainty of the explosion. The traditional FWA optimization model and the IFWA optimization model were run ten times. The relative errors between prediction value and the actual  
Figure 7: The relationship curve between error and evolution time.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Dimension Variate** & **a** & **b1** & **b2** & **b3** & **b4** & **b5** \\ \hline Standard deviation & 0.0610 & 0.0826 & 0.0378 & 0.0257 & 0.0718 & 0.0695 \\ Mean value & 0.4889 & 0.3674 & 0.4158 & 0.4418 & 0.4824 & 0.3645 \\ \hline \hline \end{tabular}
\end{table}
Table 9: The standard deviation and mean value of each dimension variates.  
value are shown in Table 10. The relative error of the IFWA is smaller compared with the traditional FWA and the calculation result is more stable.  
The improved fireworks algorithm (IFWA) optimization model and fireworks algorithm (FWA) optimization model were run five times. Ten sets of fitness iteration curves were obtained. The curve comparison is shown in Figure 8.  
Figure 8 shows that the convergence rate of the grey neural network model--improved fireworks algorithm (IFWA-GNN) model is faster than the traditional grey neural network model--fireworks algorithm (FWA-GNN) model. The improved fireworks algorithm (IFWA) fitness is lower than that of fireworks algorithm (FWA), which proves that the error of the IFWA is smaller and the fitness is better. The best results of the IFWA optimizing model and the traditional FWA optimizing model are compared. The average relative error of traditional FWA optimization model is \(\overline{\epsilon}_{1}=2.31\%\), while that of the IFWA optimization model is \(\overline{\epsilon  
Figure 9 presents the increase in the number of samples and the times of trains compared with the traditional FWA. The error between the lifetime prediction value and the actual lifetime value obtained by IFWA-GNN model is smaller and closer to the actual lifetime value.