Mathematical Problems in Engineering

Volume 2015, Article ID 214905, 8 pages

http://dx.doi.org/10.1155/2015/214905

## The Wireless Sensor Networks Base Layout and Density Optimization Oriented towards Traffic Information Collection

^{1}College of Information Science and Technology, Chengdu University, Chengdu 610106, China^{2}Key Laboratory of Pattern Recognition and Intelligent Information Processing, Institutions of Higher Education of Sichuan Province, Chengdu 610106, China^{3}Faculty of Computer Science, Chengdu Normal University, Chengdu 611130, China^{4}School of Traffic and Transportation, Beijing Jiaotong University, Beijing 100044, China^{5}Unocal East China Sea, Co. Ltd., Chengdu 610012, China

Received 26 November 2014; Accepted 29 March 2015

Academic Editor: Roman Lewandowski

Copyright © 2015 Musong Gu 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

Wireless sensor networks (WSN) are applied in Intelligent Transport System for data collection. For the low redundancy rate of the wireless sensor networks nodes of traffic information collection, the senor nodes should be deployed reasonably for the WSN nodes to work effectively, and, thus, the base network structure and the density optimization of the sensor network are one of the main problems of WSN application. This paper establishes the wireless sensor networks design optimization model oriented to the traffic information collection, solving the design optimization model with the chemical reaction optimization (CRO) algorithm. The experimental results show that CRO algorithm outperforms the traditional particle swarm optimization (PSO) in solving the wireless sensor network design optimization oriented to the traffic information collection, capable of optimizing the wireless sensor network deployment of traffic information collection to contribute to the great improvement of the comprehensive value of the network performance. The reasonable design of the wireless sensor network nodes has great significance for the information collection, post-maintenance-and-extension, and cost saving of a monitoring system.

#### 1. Introduction

The wireless sensor network is a brand new information collection and processing technology. Compared with the various technologies of the present traffic monitoring system, the wireless sensor network boasts the advantage of being unrestricted by the environment, self-organizing, and distribution. And, thus, WSN is now tentatively applied in the intelligent traffic system [1] for data collection. With the low redundancy rate of the sensor nodes in the traffic monitoring system [2], reasonable deployment of the sensor nodes should be made to enable WSN to function more effectively, and, thus, the base network structure composition and density optimization [3, 4] are one of the main problems of WSN application.

Most of the researches on WSN both domestic and overseas are conducted in the monitoring area where nodes are spilled randomly and multiple optimization methods are employed for nodes distribution such as virtual force oriented particle swarm strategy [5], genetic algorithms [6], and simulated annealing algorithm [7]. In [8], an approximate algorithm is applied to solve the sensor distribution integral linear planning problem for the purpose of the lowest cost based on the satisfaction of coverage. Literature [9] applies Particle Swarm Algorithm to study the coverage of the wireless sensor networks.

Although the existing research results have provided the optimization method of the sensor network node deployment, they take no account of the impact on the perception coverage by the intercommunication among sensors. In the paper, according to the requirement of the traffic information collection for the sensor, the comprehensive evaluation function of coverage and connectivity of the wireless sensor network nodes is used; for the reasonable deployment of the sensor network nodes, the multiple constrained optimization mathematical model is established, which is converted into the single constrained optimization problem by means of the geometric weighting method, solving the problem by means of the chemical reaction optimization (CRO) [10–13].

#### 2. Problem Description

WSN consists of management grids, sink nodes, and wireless sensor nodes. The management nodes are set in the regional control room or cabinet; the sink nodes are set around roadside traffic signal controller and cabinet; the wireless sensor nodes are buried on road surface or roadside. The traffic information collected by the wireless sensor nodes is transmitted hop by hop to the sink nodes along other sensor nodes. The sink nodes integrate the data of the wireless sensor nodes to obtain the data of the region or a small area, communicating with the management nodes through the Ethernet. The management nodes receive the data transmitted by the sink nodes to make an integration and comprehensive application of a large-scale regional data.

For the characteristics of the traffic information acquisition system and the wireless sensor networks, the following provisions are made for studying the problem:(1)The starting point and the ending point of the simulation road section are known; there are wireless sensor nodes, sink nodes, and one management node.(2)The number of sensor nodes set on the road is relevant to the length of the road and the distance of the sensor communication; depending on the traffic information collection need and the experience of experts, the position of sink nodes is determined around the signal or in the cabinet.

#### 3. Wireless Sensor Networks Coverage Problem

In building the wireless sensor networks, the network coverage is one of the standard problems of the wireless sensor networks, which is concerning how to deploy the sensor network nodes to reach the biggest network coverage with as few network nodes as possible while guaranteeing the quality of service to some degree. Priority should be given to the node coverage rate and the regional coverage rate in the optimization of network coverage of the wireless sensor.

The node coverage rate: we assume that the monitored two-dimensional area is distributed into meter by figure, where the number of sensor nodes with the same parameter launched is , the coordinate of every node is known, the perception radius is , and the communication radius is . To ensure the connectivity of the network, the communication radius is usually bigger than the sensor radius . Meanwhile, the communication effect may be influenced by the wireless disturbance if the communication radius is too big. According to experimental results, it achieves the best communication effect when equals . is applied to indicate the circle with the node coordinate as the center and the monitored radius as . We assume the pixel coordinate is ; then the distance between the target pixel and the sensor node is . The case of the pixel being covered by the sensor nodes is defined as ; then the probability of the case occurring is the same as that of the pixel being covered by the sensor node ; considering the monitored environment and the noise interruption [14], the measuring model of the sensor node shows the probability distribution with certain characteristics in actual application, which is

In the formula, is the reliability parameter of the sensor node measurement, , , , and are the measuring parameters relevant to the characteristics of sensor nodes, and and are the input parameters:

Communication model: to analyze the network performance, we adopt probability model as the communication model of the wireless sensor node , reflecting the communication quality between nodes in actual network environment:

In the formula, is the communication strength between the sensor nodes and . is effective communication range, is the communication range value of signal attenuation, and we set = 50 m and = 100 m. is the physical parameter of the sensor nodes, indicating the degree of attenuation of the communication strength as the distance increases; we set .

#### 4. Optimization Model of Wireless Sensor Networks Deployment of Traffic Information Collection

Evaluation function: the position vector of all sensor nodes in the wireless sensor network is indicated as the -dimensional vector, in which is the vector of the sensor node coordinate.

*(a) Coverage Redundancy*. Take the mean value of the probability of all the nodes being detected on the road, indicating the coverage performance of the sensor networks. In order to improve the target measurement probability, multiple sensor nodes are needed to measure the target. The joint probability is as follows:

*(b) Regional Coverage Rate*. There is meter in the monitored region . The node set and the measuring probability are used to measure whether every pixel is covered. In the paper, the regional coverage rate of the node set is defined as the ratio of the coverage area of the node set to the total area of the monitored area , which is

*Step 1. *Formula (1)~formula (2) are used to calculate the coverage rate of one pixel over each sensor node.

*Step 2. *Formula (4) is used to calculate the joint coverage rate of the pixel over each sensor node.

*Step 3. *Repeat procedures of Steps 1 and 2 to calculate the joint coverage rate of each pixel over each sensor node.

*Step 4. *Formula (5) is used to calculate the regional coverage rate of the region.

*(c) The Number of Neighboring Nodes of the Network*. Take the mean value of the number of neighboring nodes of all sensor nodes, indicating the connectivity of the network. The concept of the neighboring node is that if = 1, then the sensor node and the sensor node are the neighboring nodes of each other. We set that there are neighboring nodes for the node ; the number of the neighboring nodes of the network is

*(d) The Communication Strength of Network*. Take the mean value of the communication strength of all wireless sensor nodes, indicating the network communication performance. Depending on the communication model, the communication strength of the node is (which is the communication strength of the wireless sensor network)

*(e) The Number of Islands*. The entire network can be divided into unconnected regions, indicating the connectivity of the network. The concept of the joint node is that if , then the sensor node and the sensor node are the joint nodes of each other. The -dimensional adjacency matrix is written, in which

According to the rules above, is converted to , where is referred to as the connection matrix, the characteristic of which is, in the row vector with module value 1, the working nodes corresponding to the row of nonzero factor are connected; the working nodes corresponding to the different row vector with the module value 1 are not connected. Therefore, the rank() connecting the matrix indicates the number of the connection areas in the separate regions formed by the nodes, which is the number of islands.

*(f) The Minimum Cost Model*. is the sensor node, is the cost of every sensor node, and is the number of the sensor nodes:

##### 4.1. Constrained Optimization Problem

The solution to multiple target planning is the main research area of multiple target planning problem. For the characteristics of the multiple target planning itself, seeking the solution to the multiple target planning is also seeking the noninferior solution. The main solution methods are evaluation function method, constraint method, interaction, voting analytic hierarchy process, power function method, fuzzy method, maximum entropy, and human intelligence method. Moreover, there are also some improved hereditary algorithms, particle swarm optimization and other human intelligence algorithms.

The key of the wireless sensor network deployment optimization is, through optimizing the position of the sensor nodes, the coverage and connectivity performance of the network comprised of nodes can reach the optimal state and meet the requirement of both the coverage of the road network and the connectivity of the network. And, thus, the wireless sensor network deployment optimization oriented towards the traffic information collection is a constrained optimization problem:

But formula (10) does not reflect the cost of the sensor network building; formula (9) should be introduced to our final model. Meanwhile, through comparison, the geometric weighting method can make a better result.

The first step is to uniform the dimension and standardize the target functions (). Solve the maximum value and the minimum value of the target functions, standardizing the target function by means of the function .

The second step is to give a group of weight coefficients corresponding to the target function based on different significance of the target function; in the formula, () and . The linear weighting method is to give a group of nonnegative number () corresponding to the target for different significance of the target function; then the linear combination is made of and to obtain the following evaluation function:

The multiple target solution problem is converted to be

is the constraint set of the multiobject function, which ensures that the solution of the objective function is a noninferior solution of the multiobject programming.

Specifically, when (), the evaluation function is

This is the arithmetic mean made of . Similar to the arithmetic mean, the geometric mean is made of , obtaining

Generally, when () are not all equivalent, the evaluation function is taken:

Then the multiple target solution problem is converted to be

The unconstrained optimization problem equivalent to the constrained optimization problem above is

In the formula, is the constrained condition determined by the requirement of the road network coverage and the network connection.

*(a) Coverage Requirement*. The sensor networks coverage level reaches to some certain value. In the formula, is the requirement of the road networks for the coverage level, which should be more than 95%.

*(b) Connectivity Requirement*. The number of the neighboring nodes of any sensor node is larger than 0. The number of the neighboring nodes of any sink node is larger than 0. In the island formed by the networks, the number of islands not including the sink node is 0.

The problem can be classified as the optimization problem. As the problem model is complex, thus we can employ a new intelligent optimization algorithm, the chemical reaction optimization algorithm, to solve it.

#### 5. Chemical Reaction Optimization Algorithm

The chemical reaction optimization algorithm simulates the chemical molecules’ change and migration which prompt the molecules to move towards the optimal node in the solution space. A chemical reaction occurs in a vessel containing a certain number of molecules. Every molecule has one molecule solution structure, dynamic energy, and potential energy. The chemical reaction optimization uses the potential energy to simulate the value of optimization function: , where is the optimization function and is the molecule solution structure. These reaction modes include the following: nondestructive on-wall collision, decomposition reaction, nondestructive molecule collision, and combination reaction. These basic reaction modes all have different algorithms of changing the molecule solution structure.

##### 5.1. Algorithm Design

In the nondestructive on-wall collision, one molecule strikes the vessel wall. We can make small perturbation by randomly changing the position of any two of the binary strings, changing the existing solution to ; for example, consider the following.

*(a) On-Wall Ineffective Collision*. This operator only changes the solution structure of one molecule when the nondestructive on-wall collision occurs. Therefore, in the algorithm, the existing molecule should be the input, outputting a new molecule . The main design purpose of the operator is to make a small-scale exploration on the potential energy surface, and thus it should change the molecule solution structure in a small scale:

*(b) Decomposition*. A molecule is decomposed into two new molecules and ; the new molecules have a big difference from the original molecule. In order to achieve this, we adopt the following method. Consider the -bit of as . If it equals 1, then its value is copied to the same position of and the rest bits of are set at random. Meanwhile, the value of is copied to the same position of and the rest bits of are set at random. With this method, and will have clear difference. This mechanism will make CRO algorithm jump out of the local minimum value; for example, consider the following.

This operator applies the existing two molecules to produce two new molecules and . This operator can help the molecule jump out of the regional minimum value. In the chemical reaction optimization, we divide into two parts, and , and then complement randomly the missing part of the molecules to produce two new molecule solution structures:

*(c) Intermolecular Ineffective Collision*. In the intermolecular ineffective collision, the two molecules and strike each other. We add perturbation to the two molecules simultaneously to obtain the new molecules and . In order to achieve this, we employ the same method for and as that in the nondestructive on-wall collision. For example, consider the following.

This operator randomly changes the two existing and to produce new molecules and when the nondestructive molecules collide with each other. This operator randomly combines and exchanges the existing molecules, so different parts of the potential optimum can possibly be changed into the same molecule solution structure. In the chemical reaction optimization, the operator involves two steps. Step one: the comparison is made of the two molecule solution structures for selecting one commonly owned node. Step two: the four parts with the node as the boundary will be crossed and exchanged to produce a new molecule solution structure:

*(d) Synthesis*. We produce the existing two molecules and into a new molecule . In order to differentiate from and , we make a XOR of and to produce the new molecule . For example, this operator combines two existing molecules and to produce a new molecule . In the chemical reaction optimization, the operator is rather similar to the nondestructive collision operator. Differently, after choosing the commonly owned node in step one, the four parts will pair with each other two by two to calculate the occupation rate of the total resources. The new molecule solution structure is the structure occupying the minimum rate of the total resources:

Figure 1 illustrates the flowchart of CRO algorithm; the main procedures of the algorithm are described as follows.