# Memetic Chains for Improving the Local Wireless Sensor Networks Localization in Urban Scenarios +
## 7 Conclusions  
Local Positioning Systems (LPS) have attracted considerable research interest during the last few years. They rely on the deployment of sensor networks that particularly adapt to the environment characteristics where they are deployed. This adaptation allows the mitigation of the system uncertainties in harsh environments where the application of Global Navigation Satellite Systems (GNSS) is not recommended for high-demanded accuracy applications such as autonomous navigation, low-level flights, surveillance or indoor localization. Among LPS, those based on time measurements are the most extended in the literature due to their trade-off among reliability, cost, robustness, accuracy, and easy-to-implement hardware architectures. In this paper, we analyze the Time Difference of Arrival (TDOA) architecture for its application in LPS harsh environments. However, regardless the architecture used, LPS require an optimization of the sensor distribution in space in order to achieve competitive results. This supposes the solution of the Node Location Problem (NLP) which has been assigned as NP-Hard. Therefore, the employment of metaheuristics for this problem has been widespread in the literature. In this paper, we first introduce Local Search (LS) chains for optimizing the LS procedure of a Memetic Algorithm (MA) for the NLP. This enables the reduction of the algorithm complexity and a more intelligent exploration of the huge space of solutions of the localization NLP. For this purpose, we perform an adaptation of the so-called MA-SW-Chains algorithm for the NLP. This implies the transformation of this continuous global optimization methodology to discrete discontinuous optimization. This supposes the application of the Variable Neighborhood Descent (VND) LS instead of the Solis Wets LS of the MA-SW-Chains and the selection of the individuals of the LS based on diversity and elitist criteria for analyzing potential unfavored regions of the space of solutions in the evolutionary optimization of the NLP. In addition, the new algorithm introduced in this paper, MA-VND-Chains, utilizes a pseudo-function in the LS for reducing the complexity of the fitness evaluation based on the slight variations in the clock and geometric uncertainties of the NLP inside a bounded region analyzed (i.e., neighborhood). This entails the definition of a pseudo-function that exclusively considers the LOS/NLOS paths of the positioning signal among target and architecture sensors in the neighborhood LS. Consequently, the acceleration of the LS calculations enables incremental values of the LS depth and LS frequency for attaining improved results in the NLP. The consideration of the memory chains through the MA-VND-Chains algorithm in this paper enables the introduction of the setting of the hyperparameters of the LS based on previous iterations of an individual. This allows both an enhanced search in the neighborhoods and the adequate selection of the best candidates to apply the LS considering a parameter called intensity which is analyzed based on the improvement of the fitness of an individual in previous LS iterations, the analysis of the neighboring solutions examined in the last LS iteration and the frequency of selection of the individual for LS conserving the diversity as an important factor to determine the LS candidates. This novel methodology applied in an LPS urban scenario outperforms our previous optimization algorithms proposed for the NLP by 17% with regards to GA and by 11% with regards to MA in terms of accuracy of the TDOA architecture. This improvement shows the validity of this technique for the NLP optimization and presents the MA-VND-Chains methodology as an interesting algorithm for discrete discontinuous optimization thus fulfilling the main objectives of this paper. Conceptualization, P.V. and J.D.-G.; Formal analysis, H.P. ; Investigation, P.V. and J.D.-G., Methodology, P.V. and R.F.-G.; Project administration, H.P. ; Resources, J.D.-G. and R.F.-G.; Software, P.V. ; Supervision, J.D.-G. and H.P.