# Memetic Chains for Improving the Local Wireless Sensor Networks Localization in Urban Scenarios +
## 1 Introduction
However, the CRB is a discontinuous function due to the steps generated in the evaluated function among contiguous solutions (i.e., sensor distributions of the space of solutions which minimally differ in a unique spatial coordinate) considering LOS/NLOS propagations of the positioning signal. This discontinuity appears through the difference of the LOS/NLOS path loss exponents which produces notable differences in the signal quality if it faces or saves an obstacle in its propagation. These limitations characterize the NLP in localization as a discontinuous non-derivable combinatorial optimization problem. In addition, the huge dimensions of the space of solutions due to the necessity of considering a high number of possible sensor distributions for reaching acceptable results for the LPS applications and the high number of decision variables of the algorithm (i.e., the spatial coordinates of each sensor) in large-scale LPS applications also makes the NLP to be considerably challenging. Therefore, we first proposed a GA [35] for the NLP in LOS environments and we later improved our algorithm through an intelligent employment of the genetic operators during the diversification and intensification phases of the optimization [49]. The dimensions of the space of solutions of the NLP and the consideration of the NLOS paths in the fitness function generating discontinuities in the quality evaluations suggested the introduction of MA (i.e., hybridizations of GA with Local Search (LS) procedures) in both outdoor [44] and urban environments [28]. This memetic strategy for the NLP proved to be promising for analyzing the space of solutions of the NLP which presents numerous local optima complicating the optimization process. Figure 1 shows part of the differences between the GA and MA previously introduced and introduces the new algorithm designed for the NLP in this paper. Consequently, based on these previous results, in this paper, we introduce a novel MA for the NLP with the consideration of some memory within the LS iterations through the consideration of LS chains [50]. The introduction of these LS chains was proposed in [51] later showing the best results in the competition devoted to Large Scale Global Optimization of the IEEE Congress on Evolutionary Computation (CEC'10) for continuous large-scale optimization problems [52]. However, the characteristics of the NLP with their inherent discontinuities in the fitness evaluations promotes the adaptation of the MA-Solis Wets-Chains (MA-SW-Chains) algorithm introduced in [52] for the discontinuous optimization of the NLP. We adapt this algorithm in this paper through the consideration of a different LS strategy (i.e., Variable Neighborhood Descent (VND [53]) versus the classical Solis Wets algorithm [54] of the MA-SW-Chains algorithm) and the consideration of the movement of the sensor nodes during the LS process for the definition of an intelligent strategy for analyzing the neighborhood of the NLP potential solutions which also differs from our previous strategies implemented in [28; 44]. The introduction of the memory chains must also be adapted in this paper to the particularities of the NLP obtaining finally improved results in the solution presented with regards to the previous methodologies proposed for the NLP. The remainder of the paper is organized as follows: In Section 2 we define the combinatorial NLP together with an analysis of its complexity and state-of-art approaches to this problem, in Section 3 we introduce the scenario of simulations, we present the CRB model for evaluating the fitness of the node distributions analyzed in Section 4, we propose the adaptation of the MA-SW-Chains for the NLP; in Section 5, we show the results obtained through this novel methodology in Section 6 and we conclude the paper in Section 7.