## 5 The Proposed GMDPSO for Our Protocol
### GMDPSO: Greedy Discrete PSO with Memory
Simulations are performed on different network sizes with different sink speeds (speed of 5 m/s, 10 m/s and 20 m/s). Here, the node failure probability is set to 0.1. Figure 9 and Table 6 illustrate that the energy consumption of our protocol is the smallest among these protocols, and the comparative advantage (i.e., Equation (17)) becomes larger as the number of sensor nodes increases in Figure 9d. It worth to note that the average ECR of all these protocols increases as the mobile sinks move faster, because the change of the frequent topology results in frequent routing recovery which introduces heavier communication and energy overhead due to flooding operation. In this situation, our protocol can still consume less energy than the other protocols with the same network size. Besides, similar to average PDR, we can also conclude that our protocol achieves better robustness of EED than others from Figure 9a-c and Table 6. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Algorithms**} & \multicolumn{3}{c}{\(150\) **Sensor Nodes**} & \multicolumn{3}{c}{\(350\) **Sensor Nodes**} & \multicolumn{3}{c}{\(450\) **Sensor Nodes**} \\ \cline{2-10}  & \(\mathbf{V_{\textit{Sint}}5}\) & \(\mathbf{V_{\textit{Sint}}10}\) & \(\mathbf{V_{\textit{Sint}}20}\) & \(\mathbf{V_{\textit{Sint}}5}\) & \(\mathbf{V_{\textit{Sint}}10}\) & \(\mathbf{V_{\textit{Sint}}20}\) & \(\mathbf{V_{\textit{Sint}}5}\) & \(\mathbf{V_{\textit{Sint}}10}\) & \(\mathbf{V_{\textit{Sint}}20}\) \\ \hline GMDPSO & 0.264 & 0.302 & 0.352 & 0.382 & 0.482 & 0.549 & 0.416 & 0.539 & 0.618 \\ ECPSO & 0.321 & 0.341 & 0.395 & 0.487 & 0.605 & 0.634 & 0.512 & 0.646 & 0.749 \\ IAR & 0.336 & 0.445 & 0.486 & 0.607 & 0.702 & 0.737 & 0.643 & 0.835 & 0.880 \\ TTDS & 0.405 & 0.512 & 0.560 & 0.618 & 0.815 & 0.869 & 0.728 & 0.929 & 0.941 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Average ECR with respect to different \(V_{\textit{Sint}}\). Figure 9: Average energy consumption ratio (ECR) with respect to different speeds of mobile sinks. (**a**) When the moving speed of sinks is 5 m/s; (**b**) When the moving speed of sinks is 10 m/s; (**c**) When the moving speed of sinks is 20 m/s; (**d**) Average ECR comparative advantage. Our protocol outperforms others in term of ECR. The main reasons are as follows: the improved greedy forwarding mechanism is used ensure each routing branch has the mining energy consumption by selecting the relay node with optimized QoS parameters (energy, delay, energy consumption and so on). In addition, the unicast local flooding mechanism reduces the communication overhead in the network, which can minimize and indirectly reduce energy consumption. In summary, the overall performance of our protocol outperforms LEACH, SEP, ERP and TPSO-CR in terms of the PDR, EED and EDR, while maintaining the best robust. ## 7 Conclusions

In this paper, the routing of MWSNs is formulated as an optimization problem and we employ PSO to design an efficient routing protocol to achieve higher energy efficiency and lower communication delay. However, conventional PSO was originally designed for continuous optimization problems, which limits its application in discrete optimization domains. In addition, conventional PSO suffers from the curse of dimensionality, i.e., its performance deteriorates quickly as the dimensionality of the search space increases exponentially. To address these problems, we design a novel GMDPSO to build the optimal route tree. In GMDPSO, we first deduced a new more suitable fitness function, then redefined the particle position and velocity in a discrete form and subsequently redesigned the particle update rules based on the network topology; consequently a discrete PSO framework was established. When applying the proposed discrete PSO framework to solve the mobile sink route problem, to alleviate prematurity, a greedy local search based method was specially designed for the particle position update rule by improving the greedy forwarding mechanism.