Node Task Allocation based on PSO in WSN Multi-target Tracking
Advances in Information Sciences and Service Sciences Volume 2, Number 2, June 2010
Node Task Allocation based on PSO in WSN Multi-target Tracking LIU Mei 1,2 HUANG Dao-ping1 XU Xiao-ling2 1 College of Automation Science and Engineering, South China University of Technology, Guangzhou, Guangdong, 510640, China 2 College of Computer and Electronic Information, Maoming University, Maoming 525000, China [email protected], [email protected] doi: 10.4156/aiss.vol2.issue2.2
Abstract Aiming at the task allocation in multi-target tracking of wireless sensor networks, the discrete particle swarm optimization based on nearest-neighbor is presented to reduce the communication energy consumption between nodes. First, task allocation is initialized with nearest neighbor algorithm. Then the fitness function is compared through change task allocation matrix to achieve task allocation. Simulation results show that task allocation based on particle swarm optimization can effectively reduce communication energy consumption than nearest neighbor optimization in the relatively sparse nodes coverage.
Keywords: Wireless Sensor Network (WSN), Task Allocation, Particle Swarm Optimization 1. Introduction Target tracking is an important application in wireless sensor networks. Task allocation is an important component of target tracking. It brings about challenge of the collaborative task allocation mechanism research due to the unique characteristics of dynamic topology and limited strictly resource in wireless sensor networks. It demands that task allocation mechanism is simple, effective and has a certain robustness, fault tolerance, scalability and dynamic adaptability. Therefore, the appropriate task allocation technology has a significant role in promoting target tracking research. In the existing task allocation research of multi-target tracking, the reference [1] only aims at the situation that tracks a target and the nodes are a special distribution of an equilateral triangle, chooses the nearest three nodes to realize target tracking and positioning, without considering these situations that these randomly distributed nodes and communication energy consumption and other factors. The reference [2] proposes a kind of autonomy node selection method while taking into account positioning accuracy and energy requirements, but does not consider the situation of multi-target tracking and resource conflicts. The reference [3] proposes dynamic alliance to realize collaborative task allocation and solve the resource conflict between a number of dynamic alliances in order to reduce the communication energy between the sensor nodes. Liu Mei[4] improves this algorithm by establishing combination performance index of tracking precision and energy consumption and initializing with the nearest neighbor method in Neurons to achieve the best compromise of system power, precision and real-time. Aiming at reducing the system communication energy consumption in task allocation of WSN, this paper realizes task allocation by particle swarm optimization. The paper shows mainly that: (1) The mathematical model of multi-target tracking node allocation is established, the communication energy consumption under the certain tracking accuracy is considered as the leading indicator of the optimized objective function; (2) The discrete particle swarm optimization is initialized by the nearest neighbor algorithm to obtain the optimal allocation result as quickly as possible.
2. Task allocation description of target tracking In the multi-target tracking, many dynamic tracking clusters are needed to track targets. These nodes allocation uses the minimum energy criterion. Taking into account the positioning accuracy, a dynamic tracking cluster needs at least three sensors to perform a target tracking. It also need that
13
Node Task Allocation based on PSO in WSN Multi-target Tracking LIU Mei, HUANG Dao-ping, XU Xiao-ling considers the sensor capacity constraints, a node only joins a cluster and a cluster only achieves a target tracking. In the overlapping coverage areas of the cluster, different tracking tasks need the same node resource, because a node can only join a cluster, which will produce the phenomenon of node resource competitive conflicts. Shown in Fig. 1, assuming that the two targets of T1 and T2 in the S1 node detection region (dotted circle) at some point, then S1 would need to be resolved whether to join the monitoring alliance and which monitoring alliance. In this case, we must optimize the critical nodes allocation to track targets. sensor node target S6
S5
S7
S9
S8 S4
T1
S10
S1 T2
S11
S3 S2
S12
Figure 1. Competition conflicts in nodes task allocation The node energy consumption consists of the sensing, data processing, communication between nodes. This paper utilizes the radio communication model. E Tx /E Rx denotes the energy consumption of the node transmit/receive information respectively, the node energy consumption of transmits by kbit data through distance d that comprises transmission circuit power consumption and power amplifier consumption, through the formula descript (1):
k × Eelec + k × ε amp × d 2 , d < d 0 ETx (k ,d ) = ETx elec (k ) + ETx amp (k,d ) = ′ × d 4 , d ≥ d0 k × Eelec + k × ε amp
(1)
The node energy consumption of transmitting kbit data can describe as the formula (2): (2) ERx (k )= ETx elec (k )= k × Eelec Where E Tx_elec describe as the energy consumption of the node transmit circuit, E Tx_amp describe as the energy consumption of the node amplifier circuit, E Rx_elec describe as the energy consumption of the node receiving circuit, E elec describe as receiving/sending circuit receives/sends every bit of energy consumption, ε amp and ε’ amp describe as energy consumption of the node amplifying circuit transmits every bits of signal in per unit area, d 0 is a threshold distance. The communication between nodes has a dominant position in energy consumption, so the algorithm only consider the communication energy consumption ignoring other energy consumption; the radio communication model is used in this paper, a distributed tracking fusion architecture is used, the total energy consumption is expressed as formula (3):
= E
∑ ∑
n∈Ωc k ≠ n , k∈Ωc
[lnε amp d nk4 + lnε ele ]
(3)
Where Ω c is a dynamic alliance composed by nodes; ε amp is needed energy of each bit in power amplifier；ε ele is needed energy of each bit in filters and other electronic devices; l n is the total quantity of data that transferred from the node n; d nk is the distance between the target n and the chosen node k. This shows that the total energy E depends primarily on d nk , the communication energy consumption minimum can be equivalent to the sum of d nk minimum. Suppose that there are N nodes and M targets (N>3M), the purpose of task allocation is to produce the smallest energy consumption in multi-target system. Suppose that Ω s ={s 1 ,s 2 ,…,s n ,…,s N },Ω t ={t 1 ,t 2 ,…,t m ,…,t M }, Ω c ={c 1 ,c 2, …, c m ,…,c M }, c m ={s m1 ,s m2 ,s m3 } (s m1 ,s m2 ,s m3 ∈Ω s ),where s n and t m is one of nodes and targets respectively. c m represents a dynamic tracking cluster composed of three nodes that use to track targets t m. The task allocation matrix is defined as (4):
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Advances in Information Sciences and Service Sciences Volume 2, Number 2, June 2010
a11 a12 a a22 A = 21 aM 1 aM 2
a1N a2 N aMN
(4)
The rows number and the columns number is respectively defined as the target number and the node number in the matrix A. a mn is 0-1 variables, a mn =1 represents the nth (n= 1,2,…,N) node is assigned to track the mth target (m = 1,2, ..., M), otherwise a mn =0. The solution set of node resource allocation problem determine each element c m ={s m1 ,s m2 ,s m3 } (s m1 ,s m2 ,s m3 ∈Ωs ) of Ω c in minimum energy criterion. Therefore, the mathematical model of the target tracking optimizing allocation can be described as objective function, which is expressed as formula (5): M
N
F = min ∑
∑a
M
mn1 m =1 n1 , n2 =1 n1 ≠ n2
N
a mn2 d n1n2 + ∑∑ a mn d mn
(5)
m =1 n =1
Constraint conditions: 1) The node s n can only be assigned to track the target t m or sleep. This can be solved that these multi-target tracking resource conflicts of many clusters. It is expressed as formula (6): M
∑a m =1
mn
≤ 1, n = 1,2,, N
(6)
2) The goal t m requires that the tracking cluster c m composed by three nodes to ensure positioning accuracy. It is expressed as formula (7): N
∑a n =1
mn
= 3, m = 1,2,, M
(7)
3) d mn is the distance between the target m and the chosen node n, d n1n2 is the distance between node n 1 and node n 2 in dynamic tracking cluster. The formula (5) shows that the communication distance in m dynamic tracking cluster is minimal.
3. Task allocation based on PSO 3.1 The PSO Description PSO simulates the bird flock predatory behavior, each bird will be abstracted as a massless and sizeless particle to represent a candidate solution of the problem, the "particles" moves regularly and finds the optimal solution after a number of iterations in the solution space. The PSO mathematical description as follows: Suppose that a D-dimensional target space, there are the N particles representing potential problems solutions form a group, of which the ith particle is expressed as a D-dimensional vector, X i =[x i1 ,x i2 ,…, x iD ], i= 1,2, ..., N; the ith particle position is X i in the D-dimensional search space, the flight speed is V i =[v i1 ,v i2 ,…,v iD ]; P i is defined as the searchable individual optimal location of the ith particle, P i =[p i1 ,p i2 ,…,p iD ]; P g is defined as the searchable global optimum, P g =[ p g1 , p g2 , …, p gD ]; The particle updates the speed and position in accordance with such formula (8)、(9) in each iteration: (8) vi , j (t + 1) = wvi , j (t ) + c1r1 ( pi , j − xi , j (t )) + c2 r2 ( pg , j − xi , j (t )) xi , j (t + 1) = xi , j (t ) + vi , j (t + 1) ，j=1,…,d
(9)
where i=1,2,3,…N; t is the iterative number; w is the weighting factor, c 1 ，c 2 is the learning factor, which adjust the flown maximum step size of the best individual particle and the best global particle respectively; r 1 ，r 2 is random number between [0,1]. Particles update through learn continuously, P g is get as a global optimal solution at last. We must note that task allocation of wireless sensor network is a discrete problem, the basic PSO is designed for the continuous problem, solving the task allocation
15
Node Task Allocation based on PSO in WSN Multi-target Tracking LIU Mei, HUANG Dao-ping, XU Xiao-ling needs to design a discrete PSO algorithm. Therefore, the discrete PSO particles and operations are defined. Particle position X represents a task allocation scheme, which can be expressed as X=(X 1 ;X 2 ;…;X j ;…; X M ), 1≤ j≤M; X j =(x j1 ,x j2 ,…, x ji ,…,x jN )，1≤i≤N。M is the target number, N is the nodes number. x ji =1 represents that the ith node distribute to track target j, x ji =0 represents that the ith node does not distribute to track target j.
3.2 Task Allocation based on PSO ① Initialization of PSO In the initialization of PSO, if there is not the priori condition, we assign randomly the initial solution according to the specific requirements. However, if we initialize PSO according to some priori conditions to search the optimal solution more quickly. Depending on the target tracking requirement, we ensure that the target can communicate within least three nodes at the communication radius at first. An effective tasks distribution of the initial program is produced according to the demand. There, we select the initial value that the nearest three distances between these nodes and the target to track targets. It ensured that the running result of PSO is not higher than the running results of the nearest neighbor at least. Assume that task allocation as follows matrix (10):
1 1 0 1 0 0 1 0 A = 0 0 0 0 0 0 0 0
0 0 1 0 0
(10)
From the matrix (8), according to the distribution scheme, the 1th, 2th and 4th nodes are assigned to track the target 1, the 3th node is assigned to track the target 2, the last one is assigned to track the target 3. ② Fitness Function, Individual and Global Extremum The fitness function as the evaluation criteria that need to be able to reflect the project objective of solving problem and constraint in PSO, since task allocation is constrained combinatorial optimization problem, so fitness function must deal with these constraints. The fitness function is therefore taken as the objective function. Meanwhile, condition is limited by according to the practical application. Second, the best position that particles have experienced are calculated as pb i (t), that is, particles that have experienced the best fitness position, by formula (11) to determine: pb (t ) pbi (t + 1) = i xi (t + 1)
f ( x1 (t + 1), x2 (t + 1),, xn (t + 1)) > pbi (t ) f ( x1 (t + 1), x2 (t + 1),, xn (t + 1)) ≤ pbi (t )
(11)
Finally, the best positions of all particles are calculated, that is the global best position by formula (12) to determine: (12) gb(t ) = min{ f ( pb1 (t )), f ( pb2 (t )),, f ( pbN (t ))} Particle velocity and position are evolved according to PSO formula. If the objective function fitness reaches a sufficient degree or a pre-set value, then the judge concluded, otherwise continue.
4. Simulation We simulate PSO algorithm with MATLAB 7.0. There are 60 sensors disposed randomly in 100m×100m sensing area and three targets is in uniform linear motion. The sensor’s detection radius is 20m. The sampling interval in simulation is 1s. Suppose that at least three nodes can detect each target all the time. The experiment using a set of parameters is as follows: PSO parameters are w = 1, c1 = c2 = 2, cycles n = 100; target trajectories and node distribution diagram are in Fig. 2, which display the node task allocation in a moment. The energy consumption comparison of task allocation between PSO and nearest neighbor algorithm is in Fig. 3.
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Advances in Information Sciences and Service Sciences Volume 2, Number 2, June 2010
Figure 2. Sensor nodes task allocation (12s) and target trajectories
Figure 3. Comparison of energy consumption in different methods The simulation results indicate that PSO is better than the nearest-neighbor algorithm as a whole, the energy consumption of nearest-neighbor algorithm is far greater than PSO when the nodes have more options and the distance between the nodes is far. When the node distribution is relatively dense and closer between target and nodes, if the distance between the node and the target and the distance between nodes and nodes are in close proximity, the result difference of nearest-neighbor algorithm and PSO is not significant. The calculations show that the average energy consumption index of the nearest neighbor algorithm and PSO is 152.83 and 142.083 in 20 sampling interval respectively. The energy consumption in PSO is reduced 7.03% compared with the nearest neighbor algorithm. In the practical application, the nodes distribution and the distance between targets and nodes will generally not be too intensive, PSO would be even better demonstrated its superiority.
5. Conclusion Discrete particle swarm optimization based on nearest neighbor algorithm realizes the optimal task allocation in muti-targets tracking in the minimum resources and the limited time, extends the network life as much as possible. It’s suit for resource-limited WSN.
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Node Task Allocation based on PSO in WSN Multi-target Tracking LIU Mei, HUANG Dao-ping, XU Xiao-ling
6. References [1] Tseng Yu-Chee, Sheng-Po Kuo, Hung-Wei Lee, Chi-Fu Huang. Location tracking in a wireless sensor network by mobile agents and its data fusion strategies[J]. The Computer Journal , 2004 ,47 (4) : 448-460 [2] L.M.Kaplan. Transmission Range Control during Autonomous Node Selection for Wireless Sensor Networks. Proceedings of IEEE Aerospace Conference, Big Sky,2004. IEEE, Piscataway: 2072~2087 [3] LIU Mei, LI Haihao, SHEN Yi. Research on Task Allocation Technique for Aerial Target Tracking Based on Wireless Sensor Network. Journal of Astronautics, 2007. 28(4):960-971 [4] LIU Mei, HUANG Daoping. Task Allocation Method of Sensor Node based on MEMSOM NN in WSN. Journal of South China University of Technology (Natural Science Edition). 2010, 38(6): 102-107 [5] Giannecchini S, Caccamo M, Shih C S. Collaborative resource allocation in wireless sensor networks [C]//Proc of the Euro Micro Conf. on Real2Time Systems (‘ECRTS’2004). Catania: IEEE Computer Society Press, 2004: 35 -44. [6] Kumar R, Wolenetz M, Agarwalla B, et al. DFuse: A framework for distributed data fusion[C]//Proc of the ACM Conf. on Embedded Networked Sensor Systems (‘SenSys’ 2003). Los Angeles: ACM Press, 2003: 114-125. [7] Frei,B.Faltings. Resource Allocation in Networks Using Abstraction and Constraint Satisfaction Techniques. Proceedings of Constraint Programming, 1999. IEEE, Piscataway: 204~218 [8] Heemin P, Mani B S. Energy-efficient task assignment framework for wireless sensor networks[R]. CENS Technical Reports, 2003.
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Node Task Allocation based on PSO in WSN Multi-target Tracking LIU Mei 1,2 HUANG Dao-ping1 XU Xiao-ling2 1 College of Automation Science and Engineering, South China University of Technology, Guangzhou, Guangdong, 510640, China 2 College of Computer and Electronic Information, Maoming University, Maoming 525000, China [email protected], [email protected] doi: 10.4156/aiss.vol2.issue2.2
Abstract Aiming at the task allocation in multi-target tracking of wireless sensor networks, the discrete particle swarm optimization based on nearest-neighbor is presented to reduce the communication energy consumption between nodes. First, task allocation is initialized with nearest neighbor algorithm. Then the fitness function is compared through change task allocation matrix to achieve task allocation. Simulation results show that task allocation based on particle swarm optimization can effectively reduce communication energy consumption than nearest neighbor optimization in the relatively sparse nodes coverage.
Keywords: Wireless Sensor Network (WSN), Task Allocation, Particle Swarm Optimization 1. Introduction Target tracking is an important application in wireless sensor networks. Task allocation is an important component of target tracking. It brings about challenge of the collaborative task allocation mechanism research due to the unique characteristics of dynamic topology and limited strictly resource in wireless sensor networks. It demands that task allocation mechanism is simple, effective and has a certain robustness, fault tolerance, scalability and dynamic adaptability. Therefore, the appropriate task allocation technology has a significant role in promoting target tracking research. In the existing task allocation research of multi-target tracking, the reference [1] only aims at the situation that tracks a target and the nodes are a special distribution of an equilateral triangle, chooses the nearest three nodes to realize target tracking and positioning, without considering these situations that these randomly distributed nodes and communication energy consumption and other factors. The reference [2] proposes a kind of autonomy node selection method while taking into account positioning accuracy and energy requirements, but does not consider the situation of multi-target tracking and resource conflicts. The reference [3] proposes dynamic alliance to realize collaborative task allocation and solve the resource conflict between a number of dynamic alliances in order to reduce the communication energy between the sensor nodes. Liu Mei[4] improves this algorithm by establishing combination performance index of tracking precision and energy consumption and initializing with the nearest neighbor method in Neurons to achieve the best compromise of system power, precision and real-time. Aiming at reducing the system communication energy consumption in task allocation of WSN, this paper realizes task allocation by particle swarm optimization. The paper shows mainly that: (1) The mathematical model of multi-target tracking node allocation is established, the communication energy consumption under the certain tracking accuracy is considered as the leading indicator of the optimized objective function; (2) The discrete particle swarm optimization is initialized by the nearest neighbor algorithm to obtain the optimal allocation result as quickly as possible.
2. Task allocation description of target tracking In the multi-target tracking, many dynamic tracking clusters are needed to track targets. These nodes allocation uses the minimum energy criterion. Taking into account the positioning accuracy, a dynamic tracking cluster needs at least three sensors to perform a target tracking. It also need that
13
Node Task Allocation based on PSO in WSN Multi-target Tracking LIU Mei, HUANG Dao-ping, XU Xiao-ling considers the sensor capacity constraints, a node only joins a cluster and a cluster only achieves a target tracking. In the overlapping coverage areas of the cluster, different tracking tasks need the same node resource, because a node can only join a cluster, which will produce the phenomenon of node resource competitive conflicts. Shown in Fig. 1, assuming that the two targets of T1 and T2 in the S1 node detection region (dotted circle) at some point, then S1 would need to be resolved whether to join the monitoring alliance and which monitoring alliance. In this case, we must optimize the critical nodes allocation to track targets. sensor node target S6
S5
S7
S9
S8 S4
T1
S10
S1 T2
S11
S3 S2
S12
Figure 1. Competition conflicts in nodes task allocation The node energy consumption consists of the sensing, data processing, communication between nodes. This paper utilizes the radio communication model. E Tx /E Rx denotes the energy consumption of the node transmit/receive information respectively, the node energy consumption of transmits by kbit data through distance d that comprises transmission circuit power consumption and power amplifier consumption, through the formula descript (1):
k × Eelec + k × ε amp × d 2 , d < d 0 ETx (k ,d ) = ETx elec (k ) + ETx amp (k,d ) = ′ × d 4 , d ≥ d0 k × Eelec + k × ε amp
(1)
The node energy consumption of transmitting kbit data can describe as the formula (2): (2) ERx (k )= ETx elec (k )= k × Eelec Where E Tx_elec describe as the energy consumption of the node transmit circuit, E Tx_amp describe as the energy consumption of the node amplifier circuit, E Rx_elec describe as the energy consumption of the node receiving circuit, E elec describe as receiving/sending circuit receives/sends every bit of energy consumption, ε amp and ε’ amp describe as energy consumption of the node amplifying circuit transmits every bits of signal in per unit area, d 0 is a threshold distance. The communication between nodes has a dominant position in energy consumption, so the algorithm only consider the communication energy consumption ignoring other energy consumption; the radio communication model is used in this paper, a distributed tracking fusion architecture is used, the total energy consumption is expressed as formula (3):
= E
∑ ∑
n∈Ωc k ≠ n , k∈Ωc
[lnε amp d nk4 + lnε ele ]
(3)
Where Ω c is a dynamic alliance composed by nodes; ε amp is needed energy of each bit in power amplifier；ε ele is needed energy of each bit in filters and other electronic devices; l n is the total quantity of data that transferred from the node n; d nk is the distance between the target n and the chosen node k. This shows that the total energy E depends primarily on d nk , the communication energy consumption minimum can be equivalent to the sum of d nk minimum. Suppose that there are N nodes and M targets (N>3M), the purpose of task allocation is to produce the smallest energy consumption in multi-target system. Suppose that Ω s ={s 1 ,s 2 ,…,s n ,…,s N },Ω t ={t 1 ,t 2 ,…,t m ,…,t M }, Ω c ={c 1 ,c 2, …, c m ,…,c M }, c m ={s m1 ,s m2 ,s m3 } (s m1 ,s m2 ,s m3 ∈Ω s ),where s n and t m is one of nodes and targets respectively. c m represents a dynamic tracking cluster composed of three nodes that use to track targets t m. The task allocation matrix is defined as (4):
14
Advances in Information Sciences and Service Sciences Volume 2, Number 2, June 2010
a11 a12 a a22 A = 21 aM 1 aM 2
a1N a2 N aMN
(4)
The rows number and the columns number is respectively defined as the target number and the node number in the matrix A. a mn is 0-1 variables, a mn =1 represents the nth (n= 1,2,…,N) node is assigned to track the mth target (m = 1,2, ..., M), otherwise a mn =0. The solution set of node resource allocation problem determine each element c m ={s m1 ,s m2 ,s m3 } (s m1 ,s m2 ,s m3 ∈Ωs ) of Ω c in minimum energy criterion. Therefore, the mathematical model of the target tracking optimizing allocation can be described as objective function, which is expressed as formula (5): M
N
F = min ∑
∑a
M
mn1 m =1 n1 , n2 =1 n1 ≠ n2
N
a mn2 d n1n2 + ∑∑ a mn d mn
(5)
m =1 n =1
Constraint conditions: 1) The node s n can only be assigned to track the target t m or sleep. This can be solved that these multi-target tracking resource conflicts of many clusters. It is expressed as formula (6): M
∑a m =1
mn
≤ 1, n = 1,2,, N
(6)
2) The goal t m requires that the tracking cluster c m composed by three nodes to ensure positioning accuracy. It is expressed as formula (7): N
∑a n =1
mn
= 3, m = 1,2,, M
(7)
3) d mn is the distance between the target m and the chosen node n, d n1n2 is the distance between node n 1 and node n 2 in dynamic tracking cluster. The formula (5) shows that the communication distance in m dynamic tracking cluster is minimal.
3. Task allocation based on PSO 3.1 The PSO Description PSO simulates the bird flock predatory behavior, each bird will be abstracted as a massless and sizeless particle to represent a candidate solution of the problem, the "particles" moves regularly and finds the optimal solution after a number of iterations in the solution space. The PSO mathematical description as follows: Suppose that a D-dimensional target space, there are the N particles representing potential problems solutions form a group, of which the ith particle is expressed as a D-dimensional vector, X i =[x i1 ,x i2 ,…, x iD ], i= 1,2, ..., N; the ith particle position is X i in the D-dimensional search space, the flight speed is V i =[v i1 ,v i2 ,…,v iD ]; P i is defined as the searchable individual optimal location of the ith particle, P i =[p i1 ,p i2 ,…,p iD ]; P g is defined as the searchable global optimum, P g =[ p g1 , p g2 , …, p gD ]; The particle updates the speed and position in accordance with such formula (8)、(9) in each iteration: (8) vi , j (t + 1) = wvi , j (t ) + c1r1 ( pi , j − xi , j (t )) + c2 r2 ( pg , j − xi , j (t )) xi , j (t + 1) = xi , j (t ) + vi , j (t + 1) ，j=1,…,d
(9)
where i=1,2,3,…N; t is the iterative number; w is the weighting factor, c 1 ，c 2 is the learning factor, which adjust the flown maximum step size of the best individual particle and the best global particle respectively; r 1 ，r 2 is random number between [0,1]. Particles update through learn continuously, P g is get as a global optimal solution at last. We must note that task allocation of wireless sensor network is a discrete problem, the basic PSO is designed for the continuous problem, solving the task allocation
15
Node Task Allocation based on PSO in WSN Multi-target Tracking LIU Mei, HUANG Dao-ping, XU Xiao-ling needs to design a discrete PSO algorithm. Therefore, the discrete PSO particles and operations are defined. Particle position X represents a task allocation scheme, which can be expressed as X=(X 1 ;X 2 ;…;X j ;…; X M ), 1≤ j≤M; X j =(x j1 ,x j2 ,…, x ji ,…,x jN )，1≤i≤N。M is the target number, N is the nodes number. x ji =1 represents that the ith node distribute to track target j, x ji =0 represents that the ith node does not distribute to track target j.
3.2 Task Allocation based on PSO ① Initialization of PSO In the initialization of PSO, if there is not the priori condition, we assign randomly the initial solution according to the specific requirements. However, if we initialize PSO according to some priori conditions to search the optimal solution more quickly. Depending on the target tracking requirement, we ensure that the target can communicate within least three nodes at the communication radius at first. An effective tasks distribution of the initial program is produced according to the demand. There, we select the initial value that the nearest three distances between these nodes and the target to track targets. It ensured that the running result of PSO is not higher than the running results of the nearest neighbor at least. Assume that task allocation as follows matrix (10):
1 1 0 1 0 0 1 0 A = 0 0 0 0 0 0 0 0
0 0 1 0 0
(10)
From the matrix (8), according to the distribution scheme, the 1th, 2th and 4th nodes are assigned to track the target 1, the 3th node is assigned to track the target 2, the last one is assigned to track the target 3. ② Fitness Function, Individual and Global Extremum The fitness function as the evaluation criteria that need to be able to reflect the project objective of solving problem and constraint in PSO, since task allocation is constrained combinatorial optimization problem, so fitness function must deal with these constraints. The fitness function is therefore taken as the objective function. Meanwhile, condition is limited by according to the practical application. Second, the best position that particles have experienced are calculated as pb i (t), that is, particles that have experienced the best fitness position, by formula (11) to determine: pb (t ) pbi (t + 1) = i xi (t + 1)
f ( x1 (t + 1), x2 (t + 1),, xn (t + 1)) > pbi (t ) f ( x1 (t + 1), x2 (t + 1),, xn (t + 1)) ≤ pbi (t )
(11)
Finally, the best positions of all particles are calculated, that is the global best position by formula (12) to determine: (12) gb(t ) = min{ f ( pb1 (t )), f ( pb2 (t )),, f ( pbN (t ))} Particle velocity and position are evolved according to PSO formula. If the objective function fitness reaches a sufficient degree or a pre-set value, then the judge concluded, otherwise continue.
4. Simulation We simulate PSO algorithm with MATLAB 7.0. There are 60 sensors disposed randomly in 100m×100m sensing area and three targets is in uniform linear motion. The sensor’s detection radius is 20m. The sampling interval in simulation is 1s. Suppose that at least three nodes can detect each target all the time. The experiment using a set of parameters is as follows: PSO parameters are w = 1, c1 = c2 = 2, cycles n = 100; target trajectories and node distribution diagram are in Fig. 2, which display the node task allocation in a moment. The energy consumption comparison of task allocation between PSO and nearest neighbor algorithm is in Fig. 3.
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Advances in Information Sciences and Service Sciences Volume 2, Number 2, June 2010
Figure 2. Sensor nodes task allocation (12s) and target trajectories
Figure 3. Comparison of energy consumption in different methods The simulation results indicate that PSO is better than the nearest-neighbor algorithm as a whole, the energy consumption of nearest-neighbor algorithm is far greater than PSO when the nodes have more options and the distance between the nodes is far. When the node distribution is relatively dense and closer between target and nodes, if the distance between the node and the target and the distance between nodes and nodes are in close proximity, the result difference of nearest-neighbor algorithm and PSO is not significant. The calculations show that the average energy consumption index of the nearest neighbor algorithm and PSO is 152.83 and 142.083 in 20 sampling interval respectively. The energy consumption in PSO is reduced 7.03% compared with the nearest neighbor algorithm. In the practical application, the nodes distribution and the distance between targets and nodes will generally not be too intensive, PSO would be even better demonstrated its superiority.
5. Conclusion Discrete particle swarm optimization based on nearest neighbor algorithm realizes the optimal task allocation in muti-targets tracking in the minimum resources and the limited time, extends the network life as much as possible. It’s suit for resource-limited WSN.
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Node Task Allocation based on PSO in WSN Multi-target Tracking LIU Mei, HUANG Dao-ping, XU Xiao-ling
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