# Memetic Chains for Improving the Local Wireless Sensor Networks Localization in Urban Scenarios +
## 5 Memetic Algorithm Chains for the Node Location Problem
### General Concept of the Local Search Chains  
The MA-Chains were presented in [52] in order to develop an algorithm that could be scalable and especially designed for large-scale global optimization. The novelty is the introduction of the intensity involved in the LS using parameters that evaluate the strategies used in each area of the space of solutions. The concept of \"_chains_\" comes from the number of LS iterations information that the algorithm can combine to improve an individual of the population. It uses an adaptive step, \(\rho\), to perform a movement to a better point by weighting the success being achieved in this direction in previous steps of the LS applied to the individual. The improvement of the individual and the information obtained in previous LS iterations is stored for its application in the next LS call. Therefore, the storage needs the definition of a memory where the LS parameters evolution is stored such as the number of successes or failures, the parameter bias, and the step. In this way, all individuals not involved in any of the GA operators can continue its improvement with this a priori information. Thus, the algorithm establishes a criterion for choosing individuals, favors those showing more promising skills in the local search area, refines disadvantaged areas and does not penalize exploration (i.e., it tries the avoidance of a premature convergence into a local maximum). In this paper, we are proposing an adaptation of the MA-SW-Chains to the discrete discontinuous optimization of the NLP. Thus, we introduce some changes in the base algorithm (i.e., MA-SW-Chains) for achieving practical results in this problem through a novel algorithm called MA-Variable Neighborhood Descent-Chains (MA-VND-Chains):  
* The introduction of the VND LS in the MA-VND-Chains instead of the SW LS of the MA-SW-Chains for exploring a discrete neighborhood around the individual of the GA selected for the LS. * The utilization of different knowledge for the selection of the individuals of the LS in the MA-VND-Chains through a different definition of the LS Intensity based not only on the improvement of past LS iterations (i.e., MA-SW-Chains) but also in the information of the size of the neighborhood analyzed around each of the nodes of the NLP and diversity criteria through the number of LS iterations applied previously to the individual selected which is critical to address discontinuous optimization as we previously showed in [44]. * MA-SW-Chains presents a steady-state GA which is not optimal for the NLP since an extensive exploration of the space of solutions is required for achieving practical results. Therefore, we introduce a generational GA in the MA-VND-Chains with high elitism values for preserving the knowledge of the LS Chains on the elitist individuals but guaranteeing a broad exploration of the space of solutions. * MA-SW-Chains introduces a variable parameter for quantifying the movement of the exploration of the neighborhood region of a solution (\(\rho\)) which allows the definition of the distance of exploration of the LS for an individual based on an expected value of improvement in the neighborhood considering previous evaluations. Consequently, only potential solutions distanced \(\rho\) from the individual of the LS are explored. Since the NLP requires the addressing of a discrete discontinuous optimization, the methodology of the MA-SW-Chains is invalid since instabilities in the definition of the \(\rho\) can appear during the optimization due to changes in the LOS/NLOS paths of the positioning signal between target and nodes. For this reason, the MA-VND-Chains considers a variable neighborhood size around each node in which all the potential discrete solutions around every node are analyzed avoiding the discontinuities in the fitness evaluations. In this sense, the consideration of a promising region for the improvement of the location of each node is considered through an increasing value of the number of points analyzed around the node location.