## 4 Numerical Results
### Performance of Proposed Schemes  
Figure 5 focuses on the method of applying thresholds on EDA, which is described in section 3.4. We ran an EDA with parameters \(\left(M,I_{m,k}^{max},w_{1},w_{2},\delta\right)\) = (1, 10 \(mW\), 0.5, 0.5, 5) for threshold values = {0.3, 0.7, 0.9}. Note that setting \(\gamma\)= 1 is equivalent to not applying the threshold at all. Setting the threshold closer to 1 means that the algorithm generates the population from an almost identical distribution in each iteration; that is, the algorithm does not take advantage of the natural selection. An interesting issue is what values of the threshold facilitates the computation. From Figure 5, we can observe that the performance of EDA is poor at \(\gamma\) = 0.9 and 0.7. We can interpret this as, at the threshold values of \(\gamma\) = 0.9 and 0.7, which are close to 1.0, the algorithm does not evolve significantly. Figure 6 presents the effect of selection probability, \(\rho_{s}\), on the performance of EDA. The parameters are \(\left(M,I_{m,k}^{max},w_{1},w_{2},\delta\right)\) = (1, 10\(mW\), 0.5, 0.5, 5). From Figure 6, we can observe that the performance of EDA is better if selection probability, \(\rho_{s}\), is not close to either 0 or 1. There will be no evolution if selection probability, \(\rho_{s}\), is close to 1, the EDA will behave like a random algorithm. On the other hand, if selection probability, \(\rho_{s}\), is close to 0, the algorithm does not evolve significantly, because it is more likely that EDA will get stuck in the local optimum.  
Figure 4: Power and sum-capacity trade-off with \(\left(M,K,L,I_{m\cdot k}^{max}\right)=\left(1,10,20,1W\right)\).  
Figure 5: Effect of threshold parameter on EDA. The parameters are \(\left(L,K,M,I_{m,k}^{max},w_{1},w_{2}\right)=\left(10,10,1,1W,0.5,0.5\right)\).  
Figures 7 and 8 present the fitness _vs._ iterations plot for different numbers of relays and users. The fitness function was defined in Equation (7). The parameters are \(\left(M,I_{m,k}^{max},w_{1},w_{2},\delta\right)\) = (1, 10\(mW\), 0.1, 0.9, 5) and (1, 10\(mW\), 0.5, 0.5, 5), respectively. The value of threshold \(\gamma\) is set to 0.3. From the results, we can observe that the performance of MEDA is better than EDA and GA. This is because a simple EDA and GA can get stuck in the local optimum after a few iterations. We can also note that fitness values with less relays is better than fitness values with more relays. This is because the assignment takes more iterations for a large number of relays.  
Figures 9, 10 and 11 present the impact of SUs, relays and PUs on the performance of the green sensor network. The parameters are \(\left(K,L,M,I_{m,k}^{max}\right)\) = (\(\{5,10,20\},10,1\),10\(mW\)), (20, \(\{10.20,40\}\),1,10\(mW\)) and (10,10,\(\{1,2,3\}\),10\(mW\)), respectively. In all simulations, \((,w_{1},w_{2},\delta)\) are set to (0.5,0.5, 5). We observe that for a fixed number of secondary users, the fitness of the objective function will always be better with a lesser number of relays. This is because the assignment takes more iterations for a large number of relays. In the simulation results, we also observe that the objective function is better at a low number of PUs. This is because the relay assignment needs to satisfy more interference constraints as the number of PUs increases.  
Figure 6: Effect of selection probability \(\rho_{s}\) on EDA. The parameters are \(\left(L,K,M,I_{m,k}^{max},w_{1},w_{2}\right)=(10,10,1,1W,0.5,0.5)\).  
Figure 7: Iterations _vs._ Fitness plot with \((w_{1},w_{2})=(0.5,0.5)\).  
Figure 8: Iterations _vs_. Fitness plot with \((w_{1},w_{2})=(0.1,0.9)\).  
Figure 10: Iterations _vs_. Fitness plot with \((w_{1},w_{2})=(0.5,0.5)\).  
Figure 9: Iterations _vs_. Fitness plot with \((w_{1},w_{2})=(0.5,0.5)\).