## 5 The Proposed GMDPSO for Our Protocol
### GMDPSO: Greedy Discrete PSO with Memory
### Results and Analysis

#### 6.2.1 Performance of GMDPSO

First, we compare the performance of the proposed GMDPSO with ECPSOA, standard PSO [30] and the CPSOA [31]. In order to ensure a fair comparison, we configure these tree algorithms based on the same fitness function in Equation (26) with 450 sensor nodes, all simulation parameters are set to the same value, and the iterated generation for three protocols is fixed to 300. The test result is shown in Figure 6. It can be seen that: GMDPSO outperforms the other PSOAs in term of convergence rate and the minimum fitness value. This is mainly due to the greedy search strategy based on the MWSNs topology, which avoid the blind search of the particle; another reason is that the memory mechanism reduces the repeated and invalid searching. It also can be seen that GMDPSO has the best initial fitness value, which is achieved by our special particle initial mechanism. #### 6.2.2 Packet Delivery Ratio

A routing protocol's reliability depends on PDR to the sink. Here, we run these protocols for comparing average PDR. Figure 7 and Table 4 show the comparison results when the speed of sinks is 5 m/s. Figure 7 shows that our protocol is more reliable and robust. In detail, firstly, average PDR of all protocols are decreasing as the number of nodes increases; however, our protocol still outperforms the others and the advantage (i.e., Equation (17)) is becoming more and more obvious as the number of sensor nodes increase in Figure 7d. Secondly, PDR reduces with the increase of the node failure probability (Figure 7a-c). Still, our protocol can deliver more packets than the other protocols with the same network size. Thirdly, with each same \(P_{fault,t}\), our protocol always keeps the maximum average PDR (Figure 7a-c), which means that our protocol can find a better solution than others respect to different sensor nodes. Meanwhile, Table 4 illustrated that, with each same sensor node, our protocol keeps the maximum average PDR, which means that our protocol can find a better solution than others respect to different \(P_{fault}\). That is to say, no matter with different sensor nodes or different node failure probability, our protocol can find the best path tree among the 4 protocols. Therefore, based on the above two results, we conclude that our protocol is more robust in PDR. Our protocol improved the average PDR noticeably due to the following three reasons: The first reason is, the temporary path (TP) is designed to continue the old data packets transmission when sink moves away the old agent, which can avoid the packets loss before the new optimal routing path coming into services. The second reason is: our protocol can quickly locate the failure node and quickly build an alternative optimal path to recover the broken path link by its fast convergence feature and without any flooding when relay nodes fail, which also can reduce the data packets loss. The third reason is: the proposed GMDPSO can build better alternative routing path than others due to its ability of achieving global optimum, such as shorter total transmission distance and small communication

Figure 6: Compare of convergence. delays, which can enhance the communication reliability and PDR. Moreover, our fitness function minimizes the energy consumption of the relay nodes to reduce the premature death probability of the relay node, which also can reduce the data packets loss due to the broken routing path. #### 6.2.3 End-to-End Delay

Next, we compare the average EED of the proposed protocol on the same experiment environment as Section 6.2.1. Figure 8 and Table 5 show the comparison result. It can be observed from Figure 8 that the proposed protocol has smaller end-to-end delay than the existing protocols. More specifically, firstly, with the increase of the number of nodes, EED of all these protocols is increased. Again, our protocol performs best.