# Optimization of Submodularity and BBO-Based Routing Protocol for Wireless Sensor Deployment
## 4 Experimental Verification
### Results and Analyses  
(1) Comparison of communication cost and the number of sensors  
Table 2 is a set of experimental data of the simulation. Tables 2 and 3 compare the greedy algorithm, the pSPIEL algorithm, and the IHACA algorithm, respectively. The algorithm proposed in this paper not only meets the same deployment requirements but also achieves the best results, that is, the lowest communication cost and the number of sensors. With the same amount of mutual information and compared with the greedy algorithm, the pSPIEL algorithm, and the IHACA algorithm, the communication cost of the IHACA-COpSPIEL algorithm is also the lowest. When mutual information is 0.16, sensor deployment has a high-cost performance, and the communication cost of the IHACA-COpSPIEL algorithm is 38.42% lower than that of the greedy algorithm, 24.19% lower than that of the pSPIEL algorithm, and 8.31% lower than that of the IHACA algorithm. The sensor deployments of the four algorithms are shown in Figure 1, where the blue dots indicate the possibly-deployed points and the red squares indicate the selected points for deployment. The \(r\) value of the pSPIEL algorithm is randomly selected and the number of clusters is also random. Thus the number of clusters affects the selection of nodes and it is difficult to obtain the optimal number of clusters. Therefore the communication cost is high. The IHACA-COpSPIEL algorithm adds a chaotic operator, which can traverse the local parameter \(r\) value to obtain the number of clusters under different \(r\) values. The deployed nodes are selected within the optimal number of clusters. The heuristic function concerns the distance between the next node and the adjacent cluster head to minimize the communication distance between sensors. The first node of the solution set of the COpSPIEL algorithm is used as the first node of the IHACA. The node with maximum mutual information is selected as the deployment point. This can reduce the number of sensors and reduce the total communication cost, so it has better performance than any other algorithm. The objective function of sensor deployment is submodular. When mutual information was 0.14 and the number of sensors was small, or when mutual information was 0.20 and the number of sensors was large, a sensor is added each time and the communication cost was the lowest compared with the greedy algorithm, the pSPIEL algorithm, and the IHACA algorithm. The more the amount of mutual information increases as the number of sensors increases, the better the sensor deployment effect. When the number of sensors is small, the increment of submodular benefit is large by adding a new sensor each time. As the number of sensors increases, the increment of submodular benefit starts to decrease whenever a new sensor is added. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Mutual Information**} & \multicolumn{4}{c}{**Communication Cost**} \\ \cline{2-5}  & **Greedy** & **pSPIEL** & **IHACA** & **IHACA-COpSPIEL** \\ \hline
0.14 & 49.22 & 36.01 & 39.7 & 35.42 \\
0.15 & 59.47 & 50.4 & 45.16 & 40.06 \\
0.16 & 71.83 & 58.34 & 48.24 & 44.23 \\
0.17 & 74.31 & 62.44 & 60.36 & 53.26 \\
0.18 & 78.48 & 70.43 & 67.75 & 64.11 \\
0.19 & 80.82 & 78.28 & 78.41 & 75.22 \\
0.20 & 98.57 & 95.21 & 97.76 & 89.05 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparison of communication cost for the four algorithms. Figure 2 shows that under the mutual information of 0.14-0.20, the ratio of the IHACA-COpSPIEL algorithm is higher than that of the greedy algorithm, the pSPIEL algorithm, and the IHACA algorithm. Therefore, IHACA-CpSPIEL achieves the best cost-benefit ratio.