## 5 Performance Evaluation
### Experimental Setup
\begin{table}
\begin{tabular}{l l} \hline
**Properties** & **Values** \\ \hline Initial node energy & 0.5 J \\ Electronics energy, \(E_{elec}\) & 50 nJ/bit \\ Consumption loss for \(d^{2}\), \(\varepsilon_{fs}\) & 10 pl/bit/m\({}^{2}\) \\ Consumption loss for \(d^{4}\), \(\varepsilon_{amp}\) & 0.0013 pJ/bit/m\({}^{4}\) \\ Data aggregation energy & 50 nJ/bit/signal \\ Packet size, \(l\) & 400 bit \\ The optimal communication radius, \(r_{s}\) & 40 m \\ The threshold distance, \(d_{0}\) & 75 m \\ The minimum residual node energy, \(\hat{\epsilon}\) & 5 uJ \\ The initial probability \(p\) of being a CH & 0.05 \\ The maximum number of iterations in HEED & 12 \\ The population size in GASONeC & 30 \\ The generation size in GASONeC & 30 \\ The crossover probability in GASONeC & 0.8 \\ The mutation probability in GASONeC & 0.006 \\ Duty cycle \(\gamma\) in DCFR & 10\% \\ Duration of a data period \(T_{r}\) in DCFR & 10 s \\ Energy consumption rate for idle listening \(E_{iidle}\) in DCFR & 0.88 mJ/s \\ \hline \end{tabular}
\end{table} 
Table 1: The algorithms’ setting parameters. Figure 3: Averages of sensor nodes’ energy consumption for one transmission round in the dynamic hierarchical protocol based on combinatorial optimization (DHCO) algorithm. Wireless Sensor Network Longevity versus the Width of the Sensing Field and the Number of Sensor Nodes  
The number of sensor nodes and the width of the sensing field are critical factors influencing the energy consumption of sensor nodes and the WSN longevity. For diverse widths of the sensing fields and various numbers of sensor nodes, we carried out several simulation experiments, whose results are exhibited vividly by Figures 5 and 6, respectively. Figure 4: Percentage of live sensor nodes with sensor nodes of a random distribution for various algorithms in the deployment scenario of a 100 m \(\times\) 100 m square region and the coordinate (50, 50) of the BS: (**a**) 100 sensor nodes of a random distribution, and (**b**) 200 sensor nodes of a random distribution. Figure 5: Comparison of transmission rounds with different dead sensor nodes for various algorithms in the deployment scenarios of 100 sensor nodes of a random distribution and the coordinate (50, 50) of the BS: (**a**) at the 40% dead-sensor-nodes level for different widths of the sensing field, and (**b**) at the 80% dead-sensor-nodes level for different widths of the sensing field. In the deployment scenario of 100 randomly distributed sensor nodes and the BS located at the coordinate (50, 50), transmission rounds decreased with the increasing width of the sensing field, according to Figure 5a, showing 40% dead sensor nodes, and Figure 5b, showing 80% dead sensor nodes, which resulted from the increase of the transmission distance between the sensor nodes. Simultaneously, according to Figure 6a, showing 40% dead sensor nodes, and Figure 6b, showing 80% dead sensor nodes, transmission rounds also decreased with the increasing number of sensor nodes in the deployment scenario, where the region was a 100 m \(\times\) 100 m square and the BS was located at the coordinate (50, 50). Although the effect of the reduction resulting from the increasing number of sensor nodes was not significant, the decreasing trend still existed. In WSNs, because the increase in the number of sensor nodes brings about a much greater amount of information gathered, this will produce a decline in transmission rounds. The experimental results are apparent and can be supported perfectly by Equation (4). Thus, the figures (including Figures 5 and 6) indicate that, regardless of various numbers of sensor nodes or diverse widths of the sensing field in WSNs, the DHCO algorithm always performs more transmission rounds in comparison with state-of-the-art WSN routing algorithms such as LEACH, HEED, GASONeC, and DCFR. Therefore, the DHCO algorithm has a better effectiveness and scalability than these WSN routing algorithms.