## 4 Performance Evaluation
### Convergence of the CoCMA  
In order to verify the quick-convergence characteristic of the CoCMA, we evaluate the computing time and the fitness of the CoCMA applied to various sizes of the CWSNs. The results will be compared with those of GAs. We consider 64 POIs randomly distributed in a 100 m \(\times\) 100 m monitoring area and the number of deployed nodes varies from 50 to 500. The sensing range of a node is fixed as 17.675 m, regardless of the number of deployed sensor nodes. All sensor nodes are randomly distributed. Each experimental simulation was repeated 30 times. In general, GAs need more generations to generate an optimal solution because of their evolutionary constraints. However, the CoCMA is able to generate the optimal solution within fewer generations as the additional local search scheme is used. We suppose that the CoCMA and GA use the same criterion to stop the evolutionary process. The evolutionary process is terminated when the fitness of the best chromosome is higher than the predetermined threshold. The thresholds of fitness for different network sizes are determined according to our previous experimental studies. We found that the CoCMA has a great leap of fitness around the second generation based on the experimental results. The discrete timestamp and fitness are recorded when one generation finished. Both timestamp and fitness of the GA are also recorded. We utilize a cubic spline interpolation to fit the time-fitness curve for the CoCMA. We then compare the computing time of the CoCMA with that of the GA at different fitness values. The corresponding simulation results are shown in Table 1.  
Note that the higher fitness implies a better energy efficiency schedule for nodes according to the definition of fitness function mentioned above. Table 1 clearly indicates that the CoCMA can provide an optimal schedule for nodes that is better than that of GA. We can see that CoCMA takes lesser computing time to yield solutions with better fitness than that in GA. The advantage of CoCMA becomes more apparent when the network size increases. This is because the SCP becomes more complicated as the numbers of the deployed nodes and POIs increases. In the case of network with 500 nodes, the average computing time for the CoCMA at a fitness value of 0.5 is 34.64 second, a 69.3% shorter than that for the GA. In all other cases, the proposed CoCMA is also capable of reaching higher fitness but using lesser time; the average computing time is several times faster than that of the GA. In summary, the operation performance is both convergence and fitness yielded by the CoCMA is more superior to those of the GA, as the nodes deployed in the CWSN become denser. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**NODE\# 50** & & & & & & & **100** & & \\ \hline fitness & GA & Std. & CoCMA & Std. & fitness & GA & Std. & CoCMA & Std. \\ \hline
0.32 & 3.21 & 11.45 & 0.9 & 0.36 & 0.53 & 2 & 1.7 & 2.14 & 0.09 \\ \hline
0.3 & 0.06 & 0.05 & 0.82 & 0.18 & 0.58 & 0.58 & 0.34 & 2.08 & 0.09 \\ \hline
0.25 & 0.06 & 0.05 & 0.69 & 0.1 & 0.45 & 0.31 & 0.06 & 1.98 & 0.1 \\ \hline
**NODE\# 200** & & & & & & & **300** & & \\ \hline fitness & GA & Std. & CoCMA & Std. & fitness & GA & Std. & CoCMA & Std. \\ \hline
0.59 & 21.21 & 13.31 & 6.23 & 0.14 & 0.55 & 27.34 & 13.37 & 12.99 & 0.41 \\ \hline
0.55 & 6.62 & 3.59 & 6.15 & 0.14 & 0.5 & 6.17 & 1.5 & 12.84 & 0.41 \\ \hline
0.5 & 1.45 & 0.38 & 6.04 & 0.14 & 0.45 & 1.58 & 0.34 & 12.7 & 0.41 \\ \hline \hline
**NODE\# 400** & & & & & & & **500** & & \\ \hline fitness & GA & Std. & CoCMA & Std. & fitness & GA & Std. & CoCMA & Std. \\ \hline
0.52 & 53.49 & 29.81 & 22.43 & 0.49 & 0.5 & 112.8 & 66.8 & 34.64 & 0.78 \\ \hline
0.5 & 24.67 & 8 & 22.36 & 0.49 & 0.45 & 11.64 & 3.74 & 34.41 & 0.79 \\ \hline
0.45 & 4.53 & 1.35 & 22.16 & 0.49 & 0.4 & 2.1 & 0.44 & 34.16 & 0.79 \\ \hline \end{tabular}
\end{table} 
Table 1: Comparison of average computing time (second) for the CoCMA and GA at different fitness values. The number of nodes varies from 50 to 500.