Mathematical Problems in Engineering

Volume 2016, Article ID 7918581, 12 pages

http://dx.doi.org/10.1155/2016/7918581

## Optimization of the Distribution and Localization of Wireless Sensor Networks Based on Differential Evolution Approach

^{1}Department of Electrical and Computer Engineering, Tecnológico de Monterrey, Eugenio Garza Sada No. 2501 Sur, Monterrey, NL, Mexico^{2}School of Engineering and Sciences, Tecnológico de Monterrey, Eugenio Garza Sada No. 2501 Sur, Monterrey, NL, Mexico

Received 9 November 2015; Accepted 7 February 2016

Academic Editor: Hou-Sheng Su

Copyright © 2016 Armando Céspedes-Mota et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Location information for wireless sensor nodes is needed in most of the routing protocols for distributed sensor networks to determine the distance between two particular nodes in order to estimate the energy consumption. Differential evolution obtains a suboptimal solution based on three features included in the objective function: area, energy, and redundancy. The use of obstacles is considered to check how these barriers affect the behavior of the whole solution. The obstacles are considered like new restrictions aside of the typical restrictions of area boundaries and the overlap minimization. At each generation, the best element is tested to check whether the node distribution is able to create a minimum spanning tree and then to arrange the nodes using the smallest distance from the initial position to the suboptimal end position based on the Hungarian algorithm. This work presents results for different scenarios delimited by walls and testing whether it is possible to obtain a suboptimal solution with inner obstacles. Also, a case with an area delimited by a star shape is presented showing that the algorithm is able to fill the whole area, even if such area is delimited for the peaks of the star.

#### 1. Introduction

It is well-known that location is a fundamental problem in wireless sensor networks (WSN) and it is essential based on either the distance or the connectivity among the nodes in the wireless sensor network. It is necessary to truthfully localize the sensors to determine the value of different parameters such as temperature and geographic coordinates of a given location, detect the occurrence of events, classify a detected object, and track an object. Sensors usually have low energy consumption, network self-organization, collaborative signal processing, and querying abilities. In consequence, it is crucial that the required data be disseminated and localized to the proper end users [1, 2].

A WSN is comprised of a large number of sensor nodes, which are densely positioned into a given area. Basically, they are a set of almost-static nodes and the nodes are not connected to each other. Their distribution inside a given area with minimum energy connectivity is an NP-complete problem [3–6].

For applications like automatic location, tracking, and guidance, the well-known global positioning system (GPS) is a space-based navigation system that provides location any time and is widely used. One way to acquire location information of sensor nodes is to equip each sensor with a GPS, but, in practice, in sensor networks with a large number of sensor nodes, only a limited portion of sensors are equipped with a GPS called* anchors* in the literature [7, 8]. An example of location-based protocol is presented by [9], it maintains a minimum energy communication network for wireless networks using low power GPS, and also it helps to calculate a minimum-power topology for mobile and stationary nodes by the use of a sink or concentrator node. Moreover, topology optimization finds the best network topology under certain constraints assuming that nodes must maintain communication to at least one neighbor [10].

Localization algorithms usually assume that sensors are distributed in regular areas without cavities or obstacles, but outdoor deployment of wireless sensor networks is very different. To solve this problem a reliable anchor-based localization technique is proposed by [7] in which the localization error due to the irregular deployment areas is reduced. Locating sensors in irregular areas is also analyzed by [8]; the problem is formulated as a constrained least-penalty problem. The effects of* anchors* density, range error, and communication range on localization performances are analyzed. Nonconvex deployment areas such as C-shaped and S-shaped topologies are used. Moreover, in [11] the authors focused on the area coverage problem in a nonconvex region, as the region of interest limited by the existence of obstacles, administrative boundaries, or geographical conditions. The authors apply the discrete particle swarm optimization (PSO) algorithm with the use of a grid system to discretize the region of interest.

WSN deployment consists in determining the positions for sensor nodes in order to obtain the desire coverage, localization, connectivity, and energy efficiency. Available PSO solutions for the deployment problem are analyzed centrally on a base station to determine positions of the sensor nodes, the mobile nodes, or base stations as described in [12–14]. A node localization approach using PSO is described in [15–17].

On the other hand, flocking is the event or singularity in which a large number of agents (sensors) with limited environmental information and simple rules are organized into a coordinated motion and are widely used in many control areas including mobile sensor networks. Flocking of multiagents with virtual leader is presented in [18], in which the sensors in a network can be moved by using the improved algorithm. However, coordinated control of multiagent systems with leaders points to making all agents reach a coordinated motion with leaders. The case with multiple leaders is named containment control, in which every control input of agents is subject to saturation owing to its upper and lower limits in multiagent systems. This case is cleverly described in [19], focused on switching networks. The containment control with periodically intermittent communication and input saturation is deeply analyzed by [20] in which the authors design both state feedback and output feedback containment control protocols with intermittent input saturation via low gain feedback. This technique achieves a practical semiglobal containment of such agents on fixed networks.

There are some existing results in the literature that analyze the wireless sensors distribution in the three-dimensional space such as in [21–23]. These scenarios analyze the distribution of the sensor networks under certain conditions that are not considered in this research work. The three-dimensional sensor distribution is out of the scope of this research paper but is considered as a future work. For instance, to extend this research paper to the three-dimensional case, it is necessary to consider new objective functions, new scenarios with regular and irregular areas, and new upper and lower bounds; also, instead of computing the coverage area, it will be necessary to compute the involved volume and this requires more computational time to obtain results with low granularity.

In this research work, to optimize the distribution and location of sensor nodes, the Differential Evolution Algorithm (DEA) is applied. This technique has been successfully applied on different problems due to its simplicity of use [24–26]. Its taxonomy is in the category of bioinspired techniques. For each cycle denoted as generation, DEA uses a set of potential random solutions in a given search space, called individuals. In this research paper, an individual contains the information of the coordinates of the sensor nodes and their communication radii values. For each individual in the population, a descendant is generated from three parents. One parent, called the main parent, is disturbed by the vector of differences of the other two parents. In the case of the descendant having a better performance according to the objective function, it substitutes the individual, else the original individual is retained and is passed on to the next generation of the algorithm and the descendant is eliminated. This process is repeated till it attains the stop condition. The readers are referred to [24] for a complete theoretical analysis of the DE algorithm.

Early work to solve the node distribution optimizing area and energy based on Differential Evolution Algorithm is presented in authors of [27]. But they only consider a typical square area without obstacles and the work lacks information about the energy consumption and the mobility of the sensor nodes; also, the localization of sensors is not analyzed. Extended cases for irregular areas are shown by [28], in which the interference rate is included and how much nodes are turned on at same time. In [29], the problem is divided in uniformity (node spreading) and connectivity (node clustering) regarding the area; the energy is analyzed by dividing the problem in operational consumed energy and data-exchange consumed energy.

Differential evolutions with heuristic algorithms for nonconvex optimization on sensor network localization are analyzed in [30]; here, the connections and disconnections constraints are considered by the authors. Also, the connectivity-based localization problem is analyzed as an optimization problem with both convex and nonconvex constraints. In [31], the minimization equation of WSN localization error problem and an approach of differential evolution for minimization of localization error in WSN are studied considering that sensor node localization is the ability of an individual node to determine the location information. There are also surveys related to localization in wireless sensor network described in [32, 33].

Compared to the previous listed works, here, the contributions are focused on building and establishing communication links even in the presence of obstacles or very restricted boundaries. DEA is used to optimize the distribution and as a consequence the location of the sensor nodes to minimize the overlap by using an extra function as shown by [28]. The main difference with [28] is that the overlap considered as the interference is also managed in terms of restrictions to minimize the overlap very quickly. It also applies for [29]. Besides, an extra parameter called random- is used in the mutation operator to avoid the stagnation of DEA as suggested in [25].

In this research work, the results are presented for two area boundaries: inner star and a typical square room. But, instead of having an empty square room, the room includes subdivisions called walls, which will act as obstacles regarding the signal propagation, showing the optimization of the fitness function formed by the area coverage rate, the energy consumption, and an additional parameter that is related to the overlap among the nodes: the redundancy. For the used configurations, the initial node positions are randomly assigned. For the inner star, a minimum spanning tree (MST) is used at the end of each generation to check the connectivity of the nodes. For the scenarios with obstacles, such verification is performed for each individual of the population. At the end of each generation, the Hungarian algorithm [34] is used to find the shortest distance from their initial to the final location. In all scenarios here presented, the algorithm determines the initial and the final location of the sensor nodes. Each sensor node is located with respect to any of each other following the branches of the minimum spanning tree. The distance between nodes is also calculated by adding the respective distances of the branches among them.

The rest of this paper is organized as follows. Section 2 describes the methodology. Section 3 presents the DEA and minimum spanning tree algorithms for wireless sensor networks distribution and location. Section 4 summarizes the pseudocode applied on DEA. Section 5 presents the numerical results and a discussion. Finally, Section 6 presents some conclusions.

#### 2. Description of the Method

##### 2.1. Sensor Coverage Model

There is a particular interest in the sensor distribution and location where communication with neighboring nodes is more energy efficient. Also, a particular interest in the sensor distribution and location on irregular areas is considered. The main purpose of the sensor coverage model is to obtain a balance among the maximum effective coverage area, the minimum communication sensor energy, and reducing overlap.

The node set on the target area is given byand here is the cardinality of .

The coverage range of a node is defined as a circle centered at its coordinates with sensing radius . coordinates define the position of sensor nodes and the subindex is the sensor node index. A grid point is covered by a sensor node if and only if its distance to the center of the circle is not larger than the sensing radius .

A random variable is defined in order to describe the event that the sensor node covers a given point . Then, the probability of event , given by , is equal to the coverage probability . This probability is a binary valued function which is expressed aswhere a point is covered by a sensor node if and only if its distance to the center is less than or equal to the sensing radius . It is obvious that a point must be evaluated against all the nodes in the network; thusand here represents the number of times that the coordinate is covered by the node set.

However, to find the proper covered area by the set of nodes, the function is calculated to check if the coordinate is covered at least once or if it is not covered at all ;

The covered area is calculated as

Equation (5) is applied in our simulation by sweeping all points of the target area . For different area configurations, this area is replaced by the bounded area of interest. Now, is expressed as

##### 2.2. Redundant Area

The uncovered nonnormalized area is computed as

The redundant area is computed aswhich verify if a coordinate is covered by more than one node. As a result,where is the area covered by the nodes, is the redundant area, and is the area not covered by the nodes. Now, is defined as

The function is equivalent to the one given by [28].

##### 2.3. Energy Consumption

There exist several models for wireless networks efficient energy consumption; for example, see [6, 35, 36], among others. In this paper, the total energy consumption in maintaining the network connectivity is given byand here is the node sensing parameter in milliwatts per square meter (mW/m^{2}) and is the sensor radius of in meters (m), and since our communication medium is the air [37]. In this research work (mW/m^{2}) is used. Now, is expressed asNevertheless, to normalize , it is needed to use a constant which considers the maximum value that may obtain. Then, the possible maximum value is used in its inverse form asand here is the maximum sensor radius in meters (m).

##### 2.4. Wall Behavior Analysis

To simplify the analysis of the obstacles, it has adopted on-off criterion to compute the area coverage in the same way that a channel is modelled with the well-known binary symmetric channel model [38], by omitting existing effects such as signal propagation through barriers or obstacles. A similar approach is used in [28]. Figure 1 shows how the MST should be formed. Additionally, it also shows how the area can be treated and computed if a wall crosses the area coverage of a given node. It can see that is used to connect and to prevent the wall. That means a link should not cross a wall. About the computed area coverage, dark areas in and are not computed because they are not located aside from the center of the area coverage; that is, they are located at the other side of the wall. Such restriction is considered to compute the area coverage in order to give feedback on this research work.