^{*}

Reproduction is permitted for noncommercial purposes.

The limited energy supply of wireless sensor networks poses a great challenge for the deployment of wireless sensor nodes. In this paper, we focus on energy-efficient coverage with distributed particle swarm optimization and simulated annealing. First, the energy-efficient coverage problem is formulated with sensing coverage and energy consumption models. We consider the network composed of stationary and mobile nodes. Second, coverage and energy metrics are presented to evaluate the coverage rate and energy consumption of a wireless sensor network, where a grid exclusion algorithm extracts the coverage state and Dijkstra's algorithm calculates the lowest cost path for communication. Then, a hybrid algorithm optimizes the energy consumption, in which particle swarm optimization and simulated annealing are combined to find the optimal deployment solution in a distributed manner. Simulated annealing is performed on multiple wireless sensor nodes, results of which are employed to correct the local and global best solution of particle swarm optimization. Simulations of wireless sensor node deployment verify that coverage performance can be guaranteed, energy consumption of communication is conserved after deployment optimization and the optimization performance is boosted by the distributed algorithm. Moreover, it is demonstrated that energy efficiency of wireless sensor networks is enhanced by the proposed optimization algorithm in target tracking applications.

Wireless sensor networks (WSNs) can implement various complicated tasks in the sensing field via a large number of smart wireless sensor nodes which have sensing, storage, processing and communication capabilities. All the wireless sensor nodes work collaboratively to leverage their individual efforts for the entire application. Since battery-powered wireless sensor nodes are greatly constrained with regards to energy supply, energy efficiency becomes a critical problem in WSNs. As an essential requirement, sensing coverage has been investigated in a few literature reports [

Due to the above-mentioned requirements of deployment in WSNs, we propose distributed particle swarm optimization and simulated annealing (DPSOSA) for energy-efficient coverage. This method takes the energy consumption of target tracking into account to optimize the energy efficiency of WSN coverage with distributed computing. Sensing coverage and energy consumption models for WSNs are introduced first. The purpose of optimization is to find the best deployment of mobile wireless sensor nodes so that the sensing coverage requirement is satisfied and communication energy consumption can be minimized. Then the grid exclusion algorithm is exploited to calculate the coverage rate of specific network deployment, which has minimized computational cost and scalable granularity. We adopt Dijkstra's algorithm to search the lowest cost paths for data collection, which will be regarded as packet transmission paths in target tracking applications. The sensing coverage rate and total energy consumption of data collection are defined as coverage and energy metrics, respectively. The DPSOSA algorithm is then employed to optimize the communication energy consumption under a given sensing coverage requirement. It is executed over a number of nodes, in which the particle swarm optimization (PSO) procedure is aided by the optimization results of simulated annealing (SA) for the global optimal solution. In DPSOSA, a number of particles are given a better view to search for better solutions in their vicinity, by which the PSO procedure can be corrected. Meanwhile, as multiple particles need to be optimized, the optimization task is assigned among wireless sensor nodes to boost up the computational capability. With simulations of deployment optimization and target tracking, the energy efficiency of the proposed distributed optimization algorithm is verified.

The rest of this paper is organized as follows: section 2 formulates the energy-efficient coverage problem with stationary and mobile wireless sensor nodes in WSNs, where the sensing coverage and energy consumption models are presented. In Section 3, two important metrics, coverage and energy, are defined for network deployment evaluation according to the fundamental model, where the grid exclusion and Dijkstra' algorithm are introduced. Then Section 4 presents the DPSOSA algorithm for energy-efficient coverage in WSNs. In Section 5, we simulate the deployment optimization algorithm for target tracking application and analyze energy-efficiency of WSNs. We conclude the paper in Section 6.

We assume a WSN composed of two types of wireless sensor nodes: stationary and mobile nodes. In the sensing field, the stationary nodes are deployed randomly, while the mobile ones can adjust their positions adaptively against the environment. With the mobile nodes located at their proper positions, WSN can implement target tracking applications. As shown in

Each wireless sensor node integrates three radar sensors with the same sensing radius _{i}_{i}_{target}_{target}_{0} is a constant which denotes the strength of emission signal, _{target}_{,}_{i}

According to the sensitivity and reliability of sensor, we can define a threshold of received signal strength _{th}_{0} is the reliability of sensor when the received signal strength exceeds _{th}_{0}<1. Thus, wireless sensor node _{a}_{i}_{i}_{a}

Considering the inherent redundancy of WSNs, we discuss the

During target tracking, wireless sensor nodes have the functions of data acquisition, processing and reporting. The related sensing, computation and communication operations will lead to energy depletion. Out of all the energy consumption sources in WSNs, wireless communication is the largest portion. Thereby, it is the main one taken into account here. As radio signal attenuation in the air is related with the propagation distance, we adopt the free space propagation model [_{p}_{s}_{i}_{,}_{j}_{i}_{i}_{j}_{j}

Accordingly, a model of wireless communication is assumed to analyze energy consumption of communication. Here, the power consumption of data transmission between wireless sensor node _{d}_{1}_{2}

To achieve reliable detection and energy conservation in target tracking application, WSNs should apply an energy-efficient coverage scheme. Coverage and energy performance is concerned in potential mobile node deployment. For specified detection reliability, sensing area needs to be covered by certain number of wireless sensor nodes. The area which can satisfy this reliability requirement in the whole sensing field can reflect the coverage performance. On the other hand, data packet transmission from wireless sensor nodes to the sink node results in energy consumption. An energy-efficient communication framework can be established by the lowest cost paths. This framework indicates the lowest energy consumption level which can be provided by different deployment of WSNs.

It is assumed that there are _{i}_{i}

Typically, certain detection reliability ^{req}_{0} at the same time, can be calculated as:

The area which is covered by ^{req}

As discussed in Section 2.1, each wireless sensor node covers a plate area with radius _{a}

Divide the square sensing field into

Simplify the grids into points, then each grid can be denoted by its centre point. The coordinates of points are:

Initialize the coverage state matrix {cov(

Set the number of reliable detection point _{r}

Check the detection reliability point by point.

^{g}^{g} = L^{g}^{g}^{g}^{g}^{req}

Check the detection reliability excluding the reliable detection point.

_{r}^{g}_{j}_{j}_{i}_{i}_{j}_{j}^{req}

Instead of calculating the coverage state of all wireless sensor nodes at one time, the coverage state matrix of stationary nodes is first extracted in the grid exclusion algorithm. Excluding the reliable area, the coverage state of mobile nodes is then calculated on the remaining area. In this way, only Step 3 of the algorithm needs to be implemented repeatedly when a different deployment of mobile nodes is evaluated, thereby computational costs could be reduced. Moreover, only the recorded information of unreliable detection area is necessary for multiple wireless sensor nodes in distributed optimization algorithms, such as DPSOSA, to be covered in Section 4, so that the distributed optimization structure can be simplified and its communication costs will be low. Notice that granularity of computation is scalable by easily adjusting the division parameter

During target tracking in WSNs, wireless sensor nodes spend significant energy reporting their observations. With the model presented in Section 2.2, we analyze the energy consumption of wireless communication.

According to

Here, Dijkstra's algorithm is introduced to solve this lowest path problem, which can accomplish breadth-first path search between one single destination vertex and all the other vertexes on the connected graph [

For any given WSN deployment, the sink node is regarded as the destination vertex and denoted by _{0}_{1},_{2},…,_{n}_{+}_{m}_{i}_{j}

Then the pseudo-code for the lowest cost path search is outlined in Algorithm 2.

Adopt variable _{i}_{i}_{0}

The set of vertexes which have found the lowest cost paths is denoted by

_{0}_{i}_{i}_{i}_{0}_{i}_{0}_{j}_{j}

After iteration, _{i}_{i}_{0}

Thus, the lowest cost paths from all wireless sensor nodes to sink node are available, which form an energy-efficient communication framework. This framework reflects the lowest energy consumption level which can be provide by the given network deployment. Since each wireless sensor node has the opportunity to detect a target and report its data, we can evaluate the energy consumption by the total cost of all the reporting paths. Therefore, the energy metric

When WSNs are initially organized, proper deployment of mobile nodes is desirable to achieve energy-efficient coverage. Also, the environment may cause changes in WSNs, such as the appearance of node failures. Therefore, position adjusting of mobile nodes is necessary for resource re-allocation. With the proposed coverage and energy metrics, deployment optimization should be implemented to provide adaptability for WSNs in these cases. Then, the optimization results are broadcasted over the network so that WSNs can be self-organized.

Following the previous assumption, there are _{0}, namely the optimized coverage metric, is demanded under the detection reliability requirement. Thus, the objective of optimization is to decrease the energy consumption level of WSNs in target tracking applications under the condition that the required coverage metric is satisfied.

Kennedy

PSO has a strong ability for finding the most optimal result. However, it has a disadvantage in local minima. Thus, simulated annealing [

We propose distributed particle swarm optimization and simulated annealing here. SA is applied on the global best position of PSO. Then the vicinity of the global best position is searched to obtain a local optimal result. Thereby, the procedure of PSO is corrected by the result. In the same way, the best position achieved by individual particle can be corrected by SA. Since SA maintains only one solution, this extended optimization tasks can be assigned simply to a number of wireless sensor nodes utilizing the distributed computing capacity of WSNs. The pseudo-code for DPSOSA is outlined in Algorithm 3.

The sink node performs main part of the algorithm.

The population of particles is set as

_{i}_{i}_{i}_{i}_{i}_{i}_{i}_{i}_{0} is a constant which denotes the upper bound of energy metric, while _{0} is the demanded coverage ratio.

_{1}={^{1}_{j}} and Γ_{2}={^{2}_{j}} are two separate random sequences, where _{1} and _{2} are acceleration constants, representing the weight of acceleration terms that pull each particle toward the local best position and global best position and

The sink node sorts _{i}_{i}^{s}

The sink node transmits each particle to the related node. Then sink node and these nodes perform parallel SA optimization.

_{j}_{j}_{j}_{0} in [1, 2^{−}^{df}^{/}^{(}^{γT}^{)} >

In PSOSA, the sink node performs

In this section, we will analyze the efficiency of DPSOSA algorithm with simulation experiments. The simulation environment will be specified. Then the simulation and comparison of algorithms will be given. Finally, the network simulations will be present for target tracking application.

The fundamental parameters of WSN are presented in

In the energy consumption model, we set _{1} = 50_{2} = 100^{2}

In the DPSOSA algorithm, the particle number _{1}=_{2}=1, and the PSO iteration number

Target tracking application of the optimized WSN will be simulated on a modeling platform, Opnet Modeler, which is developed for communication network and distribution system. It is assumed that the sampling period of WSN is 0.5 s. Without loss of generality, a mobile target moves randomly in the sensing area for 120 s. Wireless channel model is bpsk, the free space propagation model is utilized and data rate is 1 Mbps.

With the stated simulation environment, the DPSOSA algorithm can be adopted to achieve energy-efficient coverage. First, we should define the coverage requirement, which is given by two parameters, detection reliability ^{req}_{0}. Considering the initial coverage state, we discuss two kind of coverage requirement to analyze the performance of algorithm against different conditions: (1) ^{req}_{0} = 95%; (2) ^{req}_{0} = 95%. The required covering node numbers ^{req}

Second, the constant _{0} which denotes the upper bound of energy metric should be specified for the fitness calculation. Here, we search the lowest cost paths of the station nodes without any mobile node. Assume the related path cost is {^{s}_{i}_{0} is defined as:
_{0} is 7.26 × 10^{−5}^{5}.

Then, we implement DPSOSA to optimize the deployment of WSN with a different computing node number

To obtain ideal optimization results, the computing node number is fixed as 9 in the following discussion. Then, ^{req}_{0} = 95%, it is more difficult to achieve the coverage requirement that ^{req}_{0} = 95%. Therefore, the former coverage requirement is satisfied at the beginning, while the latter one is satisfied after 8 iterations in the optimization procedure, which is shown in

Furthermore, we will compare the performance of DPSOSA and general PSO algorithms. Here, only the coverage requirement that ^{req}_{0} = 95% is considered. The same scenario and fitness function is employed in PSO. In

According to the optimization results of PSO and DPSOSA, we can obtain optimized deployment and communication paths of WSN as shown in ^{−5}^{−5}

Finally, scenarios of WSN are set up according to

From the experiments, the efficiency of multiple computing nodes is verified and it is shown that DPSOSA can applied under different coverage requirements. Then, the improved energy efficiency of DPSOSA is demonstrated by algorithm simulations and target tracking application compared with general PSO.

Focusing on the energy-efficient coverage problem of WSNs, this paper has proposed distributed particle swarm optimization and simulated annealing to optimize the network deployment. In a network composed of stationary and mobile wireless sensor nodes, the proper placement of mobile nodes is discussed, considering sensing coverage and energy consumption. Then, the coverage metric is defined utilizing a grid exclusion algorithm, while the energy metric is calculated by Dijkstra's algorithm, which provides the optimal communication paths for data reporting. Particle swarm optimization and simulated annealing are combined to find the global optimal solution, where the fitness function is designed to minimize the energy metric guaranteeing specified coverage ratio. Besides, computation capability of multiple wireless sensor nodes is adopted to enhance the optimization capacity. Experimental results represent that significant energy conservation can be achieved by the proposed optimization algorithm compared to general PSO, and energy efficiency of WSN is boosted up in target tracking application. This paper presents an evaluation method for energy-efficiency of coverage problem in WSNs. The application-oriented property is realized by target tracking. Still, further investigation should be made on adaptive routing schemes and scalable network topologic.

This paper is supported by the National Grand Fundamental Research 973 Program of China under Grant No.2006CB303000 and the National Natural Science Foundation of China (No.60673176; No.60373014; No.50175056).

In the target tracking application of WSNs, the mobile target moves through the sensing field and wireless sensor nodes around it will report their data to the sink node in a multi-hop manner.

Initial deployment and coverage state of WSN: (a) Placement of sink node and stationary nodes; (b) Coverage state of stationary nodes in the sensing field.

Detection reliability as a function of covering node number.

Optimization results of DPSOSA utilizing different computing node numbers under two kinds of coverage requirement: (a) ^{req}=_{0} = 95%; (b) ^{req}_{0} = 95%.

Convergence curves of the metrics under two kinds of coverage requirement during DPSOSA: (a) Coverage metric; (b) Energy metric.

Convergence curves of the metrics during DPSOSA and PSO under the coverage requirement that ^{req}_{0} = 95%: (a) Coverage metric; (b) Energy metric.

Optimized WSN deployment and communication paths adopting two algorithms: (a) PSO; (b) DPSOSA.

Energy consumption comparison of WSNs optimized by PSO and DPSOSA in target tracking application

Fundamental parameters of WSN.

Sensing field dimension |
240 |

Stationary node number |
108 |

Mobile node number |
20 |

Sink node coordinates | (120,120) |

Sensing radius _{a} |
30m |

Sensor reliability _{0} |
0.6 |

The initial coverage metric of k-coverage area.

1 | 2 | 3 | 4 | 5 | 6 | |
---|---|---|---|---|---|---|

98.00 | 91.45 | 83.17 | 70.80 | 54.03 | 37.25 |