Simulation Results and Analysis

In Fig. 4.5, the X-axis represents the number of the sensor nodes n, while the Y-axis represents the evaluated factors,i.e., the size of the constructed CDS|B|,CDS p-norm |B|p,

Allocation Scheme p-norm |A|p, the fitness score f, network lifetime T, and the average

remaining energy E over the whole network respectively.

Fig. 4.5(a) shows the number of dominators |B| of the constructed CDSs by using LBCDS-GA and MIS. From Fig. 4.5(a), we can see that, with the increase of the number of the sensor nodes n, |B| almost keeps stable for the MIS scheme. This is because MIS aims to find a minimum-sized CDS and the area covered by the deployed sensors does not change. On the other hand, for LBCDS-GA, |B| increases when n increses. This is because the objective of LBCDS-GA is to balance energy consumption on each dominator. If more nodes are chosen as dominators, the energy consumption can be distributed to more components. More importantly, the more dominators, the more possibilities to create diversity of dominatee allocation schemes. Therefore, the load-balanced objective can be achieved.

Fig. 4.5(b) shows theCDS p-norm|B|pvalues of the constructed CDSs by using LBCDS- GA and MIS. With the increase ofn, |B|p increases correspondingly for both schemes. This is because when n increases, the area covered by the deployed sensors does not change. Therefore, the density of sensors increases, which means the degree of each dominator in- creases correspondingly. According to Definition 4.2.1, larger degrees of dominators imply larger subitem, thus|B|p of both shemes increase. Moreover, the|B|p of LBCDS-GA is larger than that of MIS. This is because we need more nodes to build an LBCDS (shown in Fig. 4.5(a)). More dominators imply more sum subitems based on Definition 4.2.1, thus, the|B|p of LBCDS-GA is larger.

Fig. 4.5(c) shows the Allocation Scheme p-norm |A|p values of the constructed CDSs by using LBCDS-GA and MIS. As mentioned before, the smaller the |A|p value, the more load-balanced the dominatee allocation scheme A. With the increase of n, |A|p increases quickly for the MIS scheme. This is because, in MIS, dominatees are always allocated to

the dominator with the smallest ID. The results also imply that A of MIS becomes more and more imbalance when n is getting larger. Nevertheless, for LBCDS-GA, |A|p keeps almost the same, which means no matter how large the size of the set B is, LBCDS-GA always can find a load-balanced A. Additionally, with the increase of n, the difference of |A|p values between the two schemes becomes more and more obvious. This indicates LBCDS-GA becomes more and more effective to find an LBCDS in large scale WSNs.

Fig. 4.5(d) shows fitness scores f of the constructed CDSs by using LBCDS-GA and MIS. As mentioned before, the higher the fitness score is, the better quality the solution has. From Fig. 4.5(d), we can see that, with the increase of n,f does not change too much for MIS. However, for LBCDS-GA, f increases quickly. The results imply LBCDS-GA can find a more load-balanced CDS than MIS. This is because the MIS scheme does not consider the load-balance factor when building a CDS and allocating dominatees to dominators. Additionally, it is apparent that LBCDS-GA has more benefits when n becomes large.

Fig. 4.5(e) shows network lifetime of the two schemes. From Fig. 4.5(e), we know that the network lifetime decreases for both schemes with n increasing, since the WSN becomes denser and denser. Additionally, we can see LBCDS-GA prolongs network lifetime by 65% on average compared with MIS. In some extreme cases, such as n = 1000, network lifetime is extended by 100% compared with MIS. The result demonstrates that constructing an LBCDS and load-balancedly allocating dominatees to dominators can improve network lifetime significantly.

Fig. 4.5(f) shows the average remaining energy E over the whole network of the two schemes. With the increase ofn,E increases for both schemes. As the WSN becomes denser and denser, a lot of redundant sensors exist in the WSN. From Fig. 4.5(f), we know that LBCDS-GA has less remaining energy than MIS. This is because LBCDS-GA considers the load-balance factor when building a CDS and allocating dominatees to dominators. Thus, the lifetime of the whole network is extended, which means the remaining energy of each node is less than MIS. This also indicates that constructing an LBCDS can balance the energy comsumption on each sensor node, making the lifetime of the whole network prolonged

0 200 400 600 800 1000 40 60 80 100 120 140 160 180 200 220 T h e n u m b e r o f d o m i n a t o r s

The number of nodes MIS GA (a) 0 200 400 600 800 1000 0 2 4 6 8 10 12 14 16 18 20 22 24 26 C D S p - n o r m

The number of nodes MIS GA (b) 0 200 400 600 800 1000 0 50 100 150 200 250 300 A ll o ca t i o n p - n o r m

The number of nodes MIS GA (c) 0 200 400 600 800 1000 2 4 6 8 10 12 14 16 18 f i t n e ss sco r e

The number of nodes fMIS GA (d) 0 200 400 600 800 1000 20 40 60 80 100 120 140 160 180 N e t w o r k l i f e t i m e

The number of nodes MIS GA (e) 200 250 300 350 400 450 2000 2500 3000 3500 4000 4500 5000 5500 6000 6500 7000 7500 8000 8500 9000 9500 S D o f R e m a i n i n g E n e r g y

The number of the nodes

LB-A LB-ID MIS-A MIS-ID

(f)

Figure 4.5. Simulation results: (a) fitness score; (b) CDS p-norm; (c) Allocation Scheme

considerably.