## 5 The Proposed GMDPSO for Our Protocol
### GMDPSO: Greedy Discrete PSO with Memory
This is because our protocol adopts the GMDPSO algorithm, whose better performance in reaching the global optimum allows it to build the optimal routing tree with shorter transmission distance. Furthermore, its faster convergence feature make it can build the optimal routing tree more quickly. Moreover, by using our neighbor table, the routing information is stored in each node to improve the speed of route establishment. All these advantages of GMDPSO can help to decrease the end-to-end delay. It is worthy to note that, as illustrated in Figure 8d, the average EED comparative advantage (i.e., Equation (17)) decreases as the number of sensor nodes increases, this is because our greedy search rule spends more time to select the best relay nodes from larger scale nodes to build the optimal routing tree. Nevertheless, the fast response \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{2-11}  & \(\mathbf{P_{fault}}\)**-01** & \(\mathbf{P_{fault}}\)**-02** & \(\mathbf{P_{fault}}\)**-04** & \(\mathbf{P_{fault}}\)**-01** & \(\mathbf{P_{fault}}\)**-02** & \(\mathbf{P_{fault}}\)**-04** & \(\mathbf{P_{fault}}\)**-01** & \(\mathbf{P_{fault}}\)**-02** & \(\mathbf{P_{fault}}\)**-04** \\ \hline GMDPSO & 0.924 & 0.852 & 0.821 & 0.843 & 0.781 & 0.721 & 0.794 & 0.728 & 0.694 \\ ECPSOAR & 0.896 & 0.814 & 0.771 & 0.803 & 0.721 & 0.634 & 0.736 & 0.643 & 0.571 \\ IAR & 0.829 & 0.773 & 0.679 & 0.737 & 0.626 & 0.595 & 0.633 & 0.571 & 0.456 \\ TTDD & 0.755 & 0.6890 & 0.698 & 0.670 & 0.643 & 0.551 & 0.620 & 0.567 & 0.486 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Average packet delivery ratio (PDR) with respect to different \(P_{fault}\). Figure 7: Average packet delivery ratio with respect to different node failure probabilities. (**a**) When the node failure probability is 0.01; (**b**) When the node failure probability is 0.02; (**c**) When the node failure probability is 0.04; (**d**) Average PDR comparative advantage. of routing recovery and less communication control overhead by our unicast flooding mechanism also make our protocol end-to-end delay lower than the other protocols. Secondly, the end-to-end delay increases with the increase of the node failure probability by comparing Figure 8a-c, as the less stable topology causes more route recovery operation, which consumes more time for the protocols to maintain the network and prolong the delay. However, our protocol can still achieve the optimal delay; this is because we have designed the quick routing recovery mechanism for failure relay nodes. Thirdly, similar to average PDR, it can be observed from Figure 8a-c and Table 5 that our protocol achieves best average EED with respect to different sensor nodes and different \(P_{fault}\), which means that our protocol can find a better solution than others. That to say, our protocol keeps better robustness of EED, this is because that the GMDPSO adopted in our protocol can also build the global optimum routing tree in different network size, however, others maybe build different suboptimal routing solutions for different network sizes, which increase the volatility of delay. Moreover, once the existing routing path is broken due to failure nodes, an alternative optimal path can be quickly established for the source node in our protocol. In addition, the other failure nodes (i.e., not the relay nodes) never be selected as the relay nodes due to our fitness function. #### 6.2.4 Energy Consumption

Although mobile sink protocol can alleviate hotspots implicitly by changing the possible high energy consumption zones around the sinks as the sinks move. However, these operations may cause the overall energy consumption in the network to increase. Now, we compare the average ECR of these protocols, which is used to measure the influence of node failure probability and mobile sink speed to the network.