## 6 Experiments and Evaluation  
We use Matlab to perform the simulation experiments of MOCADMA in which the sink is placed at the center of the target area. In fact, the sink may be deployed at any place in the area, but the energy consumption will be distributed over the field evenly if the position of the sink approximates the geometric center of the target area [15]. An energy consumption model [15,16,25] is used in the simulation experiments. In the energy consumption mode, the transmission energy \(E_{xx}\) for transmitting \(K\) bits of information between two sensor nodes is calculated by Equation (18); the consumed energy \(E_{xx}\) for receiving \(K\) bits of information by one sensor node is calculated by Equation (19); when the clustered routing algorithm is applied to the WSNs, the energy consumption of one cluster head [16] is calculated by Equation (20):  
\[E_{xx}=K\times E_{ac}+\varepsilon_{bs}\times K\times\mathrm{d}^{2} \tag{18}\]  
\[E_{xx}=K\times E_{ac} \tag{19}\]  
\[E_{CH}=(\frac{n}{C}-1)\times K\times E_{ac}+K\times E_{ac}+\frac{n}{C}\times K \times E_{DA}+\varepsilon_{amp}\times K\times\mathrm{d}^{4}_{nosink} \tag{20}\]  
where \(n\) is the number of sensor nodes, \(C\) is the number of clusters, \(d_{nosink}\) is the distance between the cluster head and the sink, \(E_{ac}\) is the energy consumed by the electronics in the transmitter or receiver, \(\varepsilon_{bs}\) is the energy consumption of the signal power amplifier per square meter, \(E_{DA}\) is the energy consumption of processing one-unit bit data, and \(\varepsilon_{amp}\) is the energy consumption of transmitting one-unit bit data to the sink node. To evaluate the performances of MOCADMA, simulation results are compared to those of CoCMA [15], MA [18] and iMA [19] using the same parameters shown in Table 1, and all the results are from the experiments repeated 30 times. For MOCADMA, the \(M\times N\) virtual cells dividing the target area at the initial stage bridge the problem space of WSNs and the solution space of chromosomes. In the simulation experiments, we consider 400 sensor nodes with no sensing error (\(\tau_{e}=0\)) and 64 points of interest randomly and uniformly deployed in a 100 m \(\times\) 100 m target area. Figure 1 shows the average sensing coverage degree (SCD) _versus_ different dividing of virtual cells and indicates that the average SCD has the maximum value at \(N=6\) when \(M=6\), \(N=8\) when \(M=8\), \(N=12\) when \(M=12\), and \(N=13\) when \(M=14\). As Figure 2 shows, we can get the best dividing of virtual cells having maximum average SCD if \(M=N\). In the fitness function of MOCADMA, \(\alpha\) and \(\beta\) ( \(\beta=1-\alpha\) ) are the node utilization weighting coefficient and the energy balance weighting coefficient, respectively. In the next simulation experiments, we assume that \(N=8\), \(M=8\), or \(N=10\), \(M=10\), or \(N=13\), \(M=14\). Figures 3 and 4 depict \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Network size: n & \(\leq 400\) \\ Number of points of interest & 64 \\ Crossover probability: pcross & 0.6 \\ Mutation probability: pmutation & 0.1 \\ Maximum iterations & \(\leq 8000\) \\ Communication radius & 20 m\(-80\) m \\ Packet length: \(K\) & 300 bit \\ Number of clusters: \(C\) & \(\leq 40\) \\ Node initial energy: \(E_{0}\) & 10 J \\ Maximum ideal sensing radius: r\({}_{i}\) & 15 m \\ Sensing error value: r\({}_{e}\) & \(\leq\)1 m \\ \(\lambda\) & 1 \\ \(E_{disc}\) & 50 nJ/bit \\ \(\varepsilon_{{}_{B}}\) & 100 pJ/bit/m\({}^{2}\) \\ \(E_{{}_{DA}}\) & 5 nJ/bit \\ \(\varepsilon_{amp}\) & 0.0013 pJ/bit/m\({}^{4}\) \\ \(\delta_{i}\) & 1 \\ \(\delta_{2}\) & 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameters used in simulations  
Figure 1: Average SCD _versus_ different dividing of virtual cells. the network lifetime (rounds) _versus_ different values of \(\alpha\) when \(r_{e}=0\) and \(r_{e}=1\), respectively, and we can see that the network has a maximum lifetime (rounds) when \(\alpha=0.4\) (\(\beta=0.6\)).