## 6 Proposed Approach
### Multi-Objective Area Coverage Optimization Based on IAPSO
It can be observed from the figures that the IAPSO-MOACO outperformances the SA and RD in most of time because the proposed IAPSO can effectively avoid local optima and reduce the redundancy ratio. As the round of data transmission increases, the redundancy ratio gradually decrease with the number of alive nodes gradually decreases. However, the IAPSO-MOACO still has better optimization performance when the round is no more than 700. It also can be seen that the IAPSO-MOACO can still guarantee lower redundancy ratio in comparison with other approaches with the size of the network changes. #### 7.2.3 Comparison of Number of Alive Nodes

In this experiment we run the approaches for comparing the number of alive nodes by varying number of sensor nodes from 100 to 200 and number of cluster heads from 6 to 12. The number of alive nodes in each round will directly reflect whether the optimization approach can effectively guarantee energy consumption balance. The comparison results of IAPSO-CHSO with LEACH, LEACH-C and PSO-C are shown in Figure 6a-c. It can be observed from the three figures that the IAPSO-CHSO can guarantee higher number of alive nodes because the approach not only considers the residual energy of cluster head candidates but also consider the energy consumption balance of them in a round. In contrast, LEACH and LEACH-C do not consider the residual energy when selecting cluster head. The proper cluster head selction optimization model makes the energy consumption evenly distribute on each node which has higher residual energy. The PSO-C consider the residual energy of cluster head, but cannot guarantee the energy consumption balance of cluster heads. As the size of the network increases, the IAPSO-CHSO still has better performance

Figure 5: Comparison in terms of redundancy ratio with 100 to 200 nodes. (**a**) 100 nodes with 6 cluster heads; (**b**) 150 nodes with 9 cluster heads; (**c**) 200 nodes with 12 cluster heads. Figure 6: Comparison in terms of number of alive nodes with 100 to 200 nodes. (**a**) 100 nodes with 6 cluster heads; (**b**) 150 nodes with 9 cluster heads; (**c**) 200 nodes with 12 cluster heads. in comparison with other approaches, and 70% sensor nodes was alive during the early 700 rounds under different circumstances. #### 7.2.4 Comparison of Number of Data Packets Received by BS

In this experiment, we run the approaches for comparing the number of data packets received by BS with varying number of sensor nodes from 100 to 200 and cluster head from 6 to 12. The number of data packets received by BS is directly affected by the number of alive nodes. The data packets received by the base station with different number of initial sensor nodes are shown in Figure 7a-c. It can be observed from the three figures that the IAPSO-CHSO has advantage over LEACH, LEACH-C and PSO-C in terms of data packets received by BS. The reason is that our proposed approach can guarantee higher number of alive nodes by achieving energy consumption balance. The IAPSO-CHSO has much higher number of packets receipt in comparison with existing approaches after the round is over 500. As the round of data transmission increases, the IAPSO-CHSO approach accomplish the cluster head selection by using proper energy efficiency fitness function. It also can be noted from the figures that the performance of IAPSO-CHSO approach is still better than existing ones with the size of the network increases. To sum up, the simulation results show that our proposed approach can effectively achieve high coverage ratio, low redundancy ratio and energy consumption balance. For area coverage optimization, we can guarantee higher coverage ratio and lower redundancy ratio compared to SA and RD. For energy consumption optimization, we can guarantee energy consumption balance compared to LEACH, LEACH-C and PSO-C.

## 8 Conclusions

In this paper, we proposed an area coverage and energy consumption optimization problem based on IAPSO for DSN.