# An Effective Scheduling Algorithm for Coverage Control in Underwater Acoustic Sensor Network
## 4 Performance Evaluations
### Convergence of the ESACC  
To prove the fast convergence characteristics of ESACC, under the same condition, we assessed the computational time and fitness of ESACC in UASNs of different sizes and compared it with the results of genetic algorithm (GA) [30]. We randomly deployed 64 events in 3D monitoring waters with a length, width and height of 100 m. The number of nodes deployed ranged between 50 and 500. No matter the number of sensor nodes deployed, the node's perceived radius was 30 m. Every experiment was repeated 30 times. Figure 5: Network reconfiguration mechanism flow chart. In general, due to the evolutionary constraints of GA, it requires more generations to generate optimal solutions. However, with the use of additional local search schemes, ESACC is able to generate optimal solutions in fewer generations. Assume that both ESACC and GA use the same criteria to prevent evolution, and when the fitness of the best chromosome is above a predetermined threshold, the evolutionary process is terminated. Based on our previous experimental studies to determine fitness thresholds for different network sizes, we found that, based on experimental results, ESACC is highly adaptable around the second generation. Moreover, we also recorded the timestamp and fitness of the GA. Then, we compared the calculation time of ESACC with the calculation time of GA under different fitness values. The statistic results of experiments are as follows in Table 1.  
It is worth noting that the computing platform is Intel (R) Core (TM) i7-3770 CPU @ 3.40 GHz, 8 GB memory. Table 1 plainly shows that the ESACC could offer an optimum schedule for nodes that is much better compared to that of GA. We could see that, with the same fitness, ESACC takes lower computing time to generate solutions with far better fitness compared to that in GA. As the network grows in size, the advantages of ESACC become more apparent. This is because the SCP becomes more complex as the number of nodes and events deployed increases. When it comes to network with 450 nodes, the computing time for the ESACC at a fitness value of 0.86 is 12.10 s, 81.6% faster than GA. In all other cases, the proposed ESACC is also able to achieve higher fitness and use less time. In summary, because the nodes deployed in the UASNs become more dense, the convergence and fitness generated by the ESACC is better than that in GA.  
Next, we tested the impact of changes in the number of nodes and sensing radius \(r_{s}\) on ESACC performance. Figures 6 and 7 show the effect of the sensing radius \(r_{s}\) from 20 m to 70 m and the number of nodes from 50 to 500 on ESACC performance (fitness value and minimum number of node subsets) when nodes are randomly distributed in the 3D water environment monitoring area. It can be seen in Figure 6 that, as the sensing radius \(r_{s}\) or the number of nodes increases, the fitness value increases, which is mainly because, as the sensing radius \(r_{s}\) or the number of nodes increases, the union of the sensing ranges of nodes in the network increases. As a result, the network coverage is also increased. From another perspective, the number of redundant nodes in the network also increases, and the number of nodes that need to sleep will become more and more, which will reduce the node utilization. This shows that the fitness function proposed in this paper can effectively evaluate network performance. Figure 7 depicts the change trend of the number of nodes in the minimum set of nodes as the number of nodes changes and the sensing radius \(r_{s}\) of the nodes changes. It is easy to be seen that, as the sensing radius \(r_{s}\) or the number of nodes increases, the number of nodes in the minimum set of nodes decreases. This is mainly because, as the sensing radius \(r_{s}\) or the number of nodes increases, the number of redundant nodes in the network increases, and the number of nodes that need to sleep also increases.