# Memetic Chains for Improving the Local Wireless Sensor Networks Localization in Urban Scenarios +
## 6 Results
The fitness function tries to maximize the coverage points of the scenario, which benefits sensor locations that are in the center of the scenario for reaching more possible target locations. Due to the exploratory nature of the GA, most of the TLE space is covered with good accuracy. The MA maintains the characteristics of the GA, so it does not increase the  
Figure 5: RMSE obtained in the TLE by the best individual reached by the MA-VND-Chains. \begin{table}
\begin{tabular}{c c c} \hline \hline  & **Parameter** & **Magnitude** \\ \hline Population & Individuals & 80 \\  & Elitism & 13\% \\ \hline \multirow{3}{*}{Operators} & Selection & Tournament 2 \\  & Crossover & Single-point \\  & Mutation & 3\% \\ \hline \multirow{3}{*}{LS} & Depth & 5 \\  & Individuals & 15\% \\  & Algorithm & VND \\ \hline \multirow{2}{*}{Intensity} & Threshold & 1 \\  & \(\rho\) & \(\geq\)0.25 m \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Values used by the Genetic Algorithm (GA), Memetic Algorithm (MA) and MA-Variable Neighborhood Descent-Chains (MA-VND-Chains) [49]. number of affected areas but minimizes their size through the reduction of the NLOS links of the architecture. The MA-VND-Chains achieves even more accurate results than the MA due to the better exploratory technique of the neighborhoods described in this paper. In addition, the attainment of more promising individuals earlier in the optimization process in the MA-VND-Chains algorithm also contributes for reducing the NLOS paths of the positioning signal in the TLE ray-tracing algorithm introduced in [48] thus supposing a major reduction in the time complexity of the optimization since the initial evolutionary steps. This allows the achievement of better results for the MA-VND-Chains algorithm even employing less time in the optimization than in our previous MA. Therefore, these illustrations confirm that the optimization achieved by the MA-VND-Chains allows for a more accurate adjustment of the sensor distribution. Table 4 shows the percentage of points of the scenario that attain a specific RMSE bound. As it can be seen in the table, the introduction of more knowledge of the problem, produces a reduction in the number of points with large errors in accuracy. Hence, the results obtained above verify that the proposed technique reduces the areas of lower coverage. The MA-VND-Chains has more points with less error and fewer points with more error, benefiting the accuracy of target positioning. In addition, the results show that it is the technique that has the most points close to the average, improving the overall robustness and the coverage efficiency of the TDOA architecture. Table 5 shows the progressive reduction of the RMSE of the TDOA architecture in the scenario of simulations presented in Section 3 for each of the methodologies proposed (i.e., GA, MA, and MA-VND-Chains). The elitism applied in the metaheuristic methods described guarantees that in each interaction the individual obtained is never worse than the previous one and is closer to the global best distribution. Figure 5 shows the convergence of the MA-VND-Chains methodology that has been investigated and implemented in this article. Figure 7 displays \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Interval for RMSE Value (m)** & **GA (\%)** & **MA (\%)** & **MA-VND-Chains (\%)** \\ \hline Less than 2.5 & 35.64 & 26.76 & **47.79** \\ Less than 5 & 76.43 & 84.96 & **89.26** \\ More than 5 & 23.57 & 15.04 & **10.74** \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The percentage of points of the TLE for the proposed techniques with different error bounds. Figure 6: Error obtained in the TLE by the previous techniques implemented: (**a**) RMSE obtained by the GA (**b**) RMSE obtained by the MA. the executions of the VND-Chains LS introduced in this paper in red and the speed at which the algorithm converges for the final best solution. This is observed in the improvement margin that each iteration undergoes. The method is run using a 9-node distribution.