## 5 Experimental Results  
### Performance Evaluation  
Routing is a crucial process to consider in WSNs when dealing with multiple performance metrics, since routing decisions can impact network lifetime, packet delivery rates, and end-to-end packet delays [29]. Different performance metrics can be used for comparing different routing algorithms in WSNs. The main metrics considered in this paper to validate the performance of the proposed algorithm are as follows:  
1. General property, such as communication distance, energy consumption, and hops.
2. Convergence rate, that is, the number of iterations needed to find an approximation to a fixed point.
3. Network lifetime, that is, the duration up to the time when data can no longer be forwarded due to the depletion of energy of the sensor nodes.  
Sensor nodes are assigned at random. Figure 5 shows an instance in which the network range was 1000 \(m^{2}\), and the total number of nodes was 50. Each link between a node and its accessible neighbors was denoted by a dotted line. Figure 5 shows the optimal path obtained by QACMOR, shown as a solid red line. Source nodes were numbered 16, 21, 22, 24, 30, 47, and 50, and the sink node was numbered 1. Notice that the value of \(t_{max}\) should be greater than the number of iterations for the algorithm to converge.  
Three groups of experiments were conducted on a MATLAB simulation platform. Table 2 lists the values of parameters used in this simulation.  
In the first experiment, a comparison of the value of \(F(t)\) in cases in which the number of nodes ranges from 10 to 100 was conducted between two algorithms, that is, BABR and QACMOR. The curve lines in Figure 6 show that the values of \(F(t)\) for the two algorithms are same at the beginning, and descend as the number of nodes increases. Compared with BABR, the curve of QACMOR has a more sluggish downtrend. The reason for this is that QACMOR takes more properties into account, including energy efficiency, load balance, and time delay.  
The aim of the second experiment was to estimate the convergence property by observing the optimal value \(F(t)\) of QACMOR and BABR when the number of iterations grows. As iterations grow, it can be seen in Figure 7 that the value of \(F(t)\) tends to be stable. In addition, we notice that QACMOR begins to converge at nearly 200 iterations, while it takes approximately 350 iterations for BABR. This demonstrates that QACMOR has a faster convergence rate than BABR.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Item** & **Experiment 1** & **Experiment 2** & **Experiment 3** \\ \hline Number of nodes & 10, 20, 30, \(\ldots\), 100 & 50 & 50 \\ Network range & 1000 m\({}^{2}\) & 1000 m\({}^{2}\) & 5000 m\({}^{2}\) \\ Initial energy & / & / & 0.5 J \\ C\({}_{1}\) & 0.5 & 0.5 & 0.5 \\ C\({}_{2}\) & 0.1 & 0.1 & 0.1 \\ C\({}_{3}\) & 0.1 & 0.1 & 0.1 \\ C\({}_{4}\) & 0.1 & 0.1 & 0.1 \\ \(t_{max}\) & 400 & 400 & 400 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Parameter-setting in experiments.  
Figure 5: Optimal path in network topology.  
Figure 6: Value of optimal route vs. number of nodes.  
The third experiment evaluates the network lifetime of QACMOR. The experiment is performed on the condition that the number of dead nodes grows. In Figure 8, the x-axis denotes the number of dead nodes, and the y-axis represents the lifetime of the network. It can be seen that the value of lifetime for QACMOR is consistently higher than the same value for BABR, the gap becomes bigger with increasing dead nodes, and maintains a fixed value after 35 nodes, nearly 900 \(h\).  
The above experimental results indicate that the QACMOR algorithm is capable of use as an efficient and reliable solution for routing, with balanced energy consumption and an improved network lifetime.