# Data Transmission in Wireless Sensor Networks Based on Ant Colony Optimization Technique
## 3 Results
Figure 29 uses the whale optimization algorithm (WOA), with the horizontal axis representing the number of iterations and range, and the vertical axis representing the mean squared error and range. As the number of iterations increases, the mean squared error gradually decreases and the accuracy gradually improves. Figure 7 shows that the number of iterations for the mean squared error significantly decreases, while the change in the mean squared error is minimal. The data generated based on the whale optimization algorithm (WOA) are input into a backpropagation (BP) neural network to predict the wireless SN. In Figure 30, red represents the BP prediction error, green represents the WOA-BP prediction error, the vertical axis represents the range of prediction error values, and the horizontal axis represents the sample size and value range. From the graph, it can be seen that the red BP has the highest prediction error value, while the green WOA-BP has a smaller prediction error. \begin{table}
\begin{tabular}{p{113.8 pt} p{113.8 pt} p{113.8 pt}} \hline \hline
**Serial Number** & \ \begin{tabular}{} \end{tabular}  & \begin{tabular}{} \end{tabular}  \\ \hline
1 & 4 & 0.032 \\ \hline
2 & 5 & 0.024 \\ \hline
3 & 6 & 0.026 \\ \hline
4 & 7 & 0.027 \\ \hline
5 & 8 & 0.032 \\ \hline
6 & 9 & 0.022 \\ \hline
7 & 10 & 0.032 \\ \hline
8 & 11 & 0. In Figure 31, * stands for multiplication, the circle in Figure 31 represents the real data, the dashed line represents the real regression curve, and the blue line represents the fitted curve after BP training. R is the regression correlation coefficient, representing the correlation between the predicted output and the target output. The closer the R value is to 1, the closer the relationship between the prediction and the output data, and the higher the accuracy. The smaller the value, the poorer the proximity and accuracy between the predicted and output data. R = 0.90877 in Figure 32.  
In the WOA-BP regression plot, \(R=0.96009\), indicating that the accuracy of the WOA-BP algorithm is higher than that of the BP algorithm. After 1000 cycles, the BP prediction accuracy is 81.3735%, and the WOA-BP prediction accuracy is 90.2353%. Therefore, this improved whale algorithm enhances the node search capability, accelerates the global search speed, and optimizes network performance by increasing the node coverage in wireless sensor networks. This also solves the major problems that disrupt the overall efficiency of wireless sensor networks, such as low energy efficiency and a shortened network lifespan. In addition, we adopted the ACOD to establish the optimal movement trajectory for the moving convergence point, intelligently considering the distance between CHs. The enhancement in the distance heuristic factor generated thereby avoids local optima, accelerates convergence speed, improves network performance over time, and reduces the latency of Sink data retrieval. Figure 30: Comparison of BP prediction error and WOA-BP prediction error. Figure 29: Using whale optimization algorithm (WOA) to reduce mean squared error. Finally, in order to effectively compare and evaluate the performance level of our proposed model and existing multi-objective evolutionary algorithms (MOEAs), we adopted two evaluation metrics, namely the hyper volume (HV) metric and the Epsilon (\(\epsilon\)) metric. The HV index evaluates the convergence and diversity of the obtained solutions, while the Epsilon index measures the minimum transformation factor required to ensure non-dominance. In both cases, our proposed model exhibits superior performance, highlighting its potential in optimizing wireless sensor networks.