## 5 The Proposed GMDPSO for Our Protocol
### GMDPSO: Greedy Discrete PSO with Memory
The worst result is that these sharing relay nodes will die quickly because they deplete their energy of forwarding too many packets. This will lead to the expensive routing recover. Therefore, after all of individual optimal routing path branches are built, the corresponding routing tree \(X_{i}\) should be evaluated using fitness function. From the above description of our new GMDPSO algorithm, the proposed algorithm has the following features: (1) with a concise framework; (2) the newly defined particle position and velocity

Figure 5: Multi routing paths share some relay nodes. are direct and easy to decode; and (3) redefined updating rules based on the new operators are easy to realize and will significantly reduce the computational complexity, especially for large-scale WSNs. The Redesigned GMDPSO Seems to be Very Suitable for Solving Routing Problem in MWSNs6. Simulations and Results

In this section, we test our protocol against several well-known protocols: ECPSOAR, IAR, and TTDD, which all can deal with routing problem of multi mobile sinks. The performance is compared in terms of the following metrics: average packet delivery ratio (PDR, measured as the average number of successfully delivered packets versus required packets per round), average end-to-end delay (EED) [29], and average energy consumption ratio (ECR, measured as the average energy consumption from source to sink versus the initial energy per round). All simulations are performed using MATLAB R2012b on Windows 7 with Intel core i5-2520M Dual-Core CPU (2.50 GHz) and 8 G RAM. For ease of description for the comparison results of the above metrics, we define another notation, which is called metric comparative advantage for our new protocol as defined below:

\[ \begin{array}{c}\textit{Metric comparative }\textit{advantage}=\\ \frac{(\textit{Metric of GMDPSO }-\textit{Metric of other protocol})}{\textit{Metric of other protocol}}\times 100\end{array}  \tag{37}\]

For example, PDR comparative advantage to ECSPOAR can be calculated as follow:

\[ \begin{array}{c}\textit{PDR comparative }\textit{advantage to ECSPOAR}=\\ \frac{(\textit{PDR of GMDPSO }-\textit{PDR of ECSPOAR})}{\textit{PDR of ECSPOAR}}\times 100\end{array}  \tag{38}\]

### Simulation Setting

Simulations are performed on the MWSN, which consists of diverse number of homogenous sensor nodes ranging from 50 to 450. Each sensor node is assumed to have initial energy of 120 J and the mobile sink is assumed to have sufficient energy and cannot be fault. To build a level playing field, the characteristics of the networks and communication models are configured as illustrated in [10] and as shown in Table 3. The extra PSO parameters used for ECPSOA are fixed to: particle updating energy consumption \(E_{PU}=80\)\(p\)/ the endocrine selection energy consumption \(E_{ES}=50\)\(p\)/ at per iteration, function dimension \(D=30\), division factory \(k=6\), and maximum iteration \(P_{Gen}=800\). The extra PSO parameters used for GMDPSO are fixed to: \(\omega=0.7968\), c1 = c2 = 1.4926 In addition, the population size of ECPSOA and DPSORR is set to be 60; both of the two algorithms are run for maximum of 800. For the weight sum approach, in our proposed algorithms, we give equal weight to each sub-objective. That to say, we set \(w_{1}=w_{2}=w_{3}=0.33\). \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Value** & **Parameter** & **Value** \\ \hline Area & 5000 \(\times\) 5000 m\({}^{2}\) & Packet size & 1 KB \\ Sensor nodes & 50, 150, 250, 350, 450 & Deliver packets rate & 20 per round \\ Mobile sinks & 5 & Simulation iterations number & 200 \\ Initial energy of nodes & 120 J & \(\alpha_{1}\) & 60 nj/bit \\ communication rang & 600 m & \(\beta_{1}\) & 45 nj/bit \\ sensing rang \(R\) & 300 m & \(\beta_{2}\) & 10 nj/bit \\ Speed of mobile \(v_{sink}\) & 5 m/s, 10 m/s, 20 m/s & \(\gamma_{1}\) & 135 nj/bit \\ \(P_{full}\) & 0.1, 0.2, 0.4 & Channel attenuation \(n\) & 2 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Simulation parameters.