SENSOR DEPLOYMENT USING
PARTICLE SWARM OPTIMIZATION
NIKITHA KUKUNURU
Asst. Professor, Dept. of C.S.E., GITAM University, Medak Dist, AP, India
BABU RAO THELLA
Asst. Professor, Dept. of Mech., GITAM University, Medak Dist, AP, India
RAJYA LAKSHMI DAVULURI
Professor, Dept. of I.T.,
GITAM University, Visakhapatnam, AP, India Abstract:
In Wireless Sensor Networks (WSN), sensors are randomly deployed in the sensor field which brings the coverage problem. It is a unique problem and in maximizing coverage, the sensors need to be placed in a position such that the sensing capability of the network is fully utilized to ensure high quality of service. This can be achieved with minimum number of sensor nodes having maximum coverage in the network and the nodes are within the communication range. In this paper, particle swarm algorithm was used to find the optimal positions of the sensors to determine the best coverage. This algorithm is an optimization technique which belongs to the fertile paradigm of swarm intelligence. It is a derivative free and is a very efficient global search algorithm with few algorithm parameters. Here, results are presented which shows that, PSO has good effect in solving coverage problem.
Keywords: Coverage Problem; Particle swarm optimization; Swarm intelligence; Wireless Sensor network.
1. Introduction
A wireless sensor network (WSN) is a group of low cost, low power, multifunctional and small size distributed networked sensors. These sensors work together to sense the environment with a little or no human intervention. PSO has been successfully used in numerous engineering applications like in training of neural networks to identify Parkinson's disease, extraction of rules from fuzzy networks, image identification, optimization of electric power distribution networks, structural optimization, inhabitant monitoring, environmental monitoring, monitoring deep oceans currents, smart home building and military applications among many others. One of the fundamental issues that arise in WSN is coverage area in addition to location identification, tracking, and deployment. In this coverage, the nodes have the effective responsibility to cover the predefined area. The most effective approach of sensor deployment is to place sensors in such a manner that the maximal network coverage is achieved. However, this approach may not be manually feasible in terms of deployment efforts, especially for a large WSN [Kennedy and Eberhart (1945)].
1.1. Sensor Coverage
A sensor placed on a location point (x1, y1) can cover a location point (x2, y2), if the Euclidean distance between these two points is
2 2 2 1 2 2
1
)
(
)
(
x
x
y
y
r
(1)j R j
R (2)
Where SRindicates, the sensor deployment point and Pj is the location point, distance refers to the Euclidean distance calculated as in "Eq. (1)". The objective is to minimize the F, such that the sensing range r, required to cover all the location points is minimum [Siba K. Udgata et al. (2009)].
2. Particle Swarm Optimization
Particle Swarm Optimization (PSO) is a population based stochastic search technique introduced by Kennedy and Eberhart in 1995 [Eberhart R. and Kennedy J. (1995)], [Jin-zhu Hu et al. (2009)], inspired by social behavior of bird flocking or fish schooling. It works in the same way as genetic algorithms and other evolutionary algorithms. Similar to evolution algorithm, PSO algorithm adopts a strategy based on particle swarm and parallel global random search. This algorithm determines search path according to the velocity and current position of particle without more complex evolution operation. PSO algorithm has better performance than early intelligent algorithms on calculation speed and memory occupation, and has less parameter and is easier to realize [Lin Lu et al. (2008)]. All these algorithms update a set of solutions (called swarm in the context of PSO) applying some operators and using the fitness information to guide the set of solutions for better regions of the search space.
PSO is a novel stochastic optimization algorithm based on the study of migration behaviors of bird flock in the process of searching food. In this process of searching food, each bird can find food through social collaboration of neighboring birds and the birds who have found food can guide other birds around them to fly to the food location. Once these birds also find food, they can guide more birds to find the location, which increases the possibility of bird flock finding food. PSO differs from these algorithms by simulating the social behavior and moment dynamics of a swarm and by not employing a survival of the fittest model [Marco Ferreira et al. (2008)]. Each swarm always moves to the own local optimum solution and the global optimum solution. Finally, swarm finds the good optimum solution.
Swarm Intelligence can be defined as the study of
“the emergent collective intelligence of groups of simple agents” [Firasath Riyaz (2005)].
Some research has been done about its improvement, applications and proposed [Eberhart R. and Kennedy J. (1995)], [Jin-zhu Hu et al. (2009)], [Shi Y. and Eberhart R. (1998)], [Siba K. Udgata et al. (2009)].
The ith particle of the swarm in a d-dimensional search space is represented by the position vector
).
,...
,
(
i1 i2 idi
x
x
x
x
The velocity of the particle is denoted by velocity vector
v
i
(
v
i1,
v
i2,...
v
id).
the bestvisited position for the particle is
p
ibest
(
p
i1,
p
i2,...
p
id)
and also the best position explored. The best value so far is global best i.e.,p
gbest
(
p
g1,
p
g2,...
p
gd)
[ Yong Wang et al. (2009)]. The below Fig.1 shows the searching nature of swarms based on social and cognition factors [Kershner, R. (1939)]. The velocity and positions of each particle are updated by the "Eq. (3)" and "Eq. (4)".)
(
*
()
*
)
(
*
()
*
)
(
*
)
1
(
i 1 ibest i 2 gbest ii
t
w
v
t
c
rand
p
x
c
rand
p
x
v
(3)Where, c1 and c2 are the cognitive and social factors (range between one and four) to control the effect of the “best” factors of particle. w is inertia weight which shows the effect of previous velocity vector on the new vector [
Firasath Riyaz (2005)
]. rand( ) values range from 0 to 1.v
i(
t
)
is the speed of the ith particle in the tth iteration. The second part of "Eq. (3)" thinks about particle own flying experience, represents cognition component. The third part considers group flying experience, represents the collaboration among particles giving the social component [Jin-zhu Hu et al. (2009)].)
1
(
)
(
)
1
(
t
x
t
v
t
x
i i i (4)Fig.1. Searching Diagram of PSO
3. Problem Formulation
The main objective of the present work paper is to minimize the distance between the neighboring nodes, maximizing coverage in the network, while simultaneously satisfying all constraints.
All sensor nodes are homogenous and have mobility.
We assume the deployed sensor nodes can fully cover the sensing field. Sensing coverage and communication coverage of each node is assumed to have a circular shape without any irregularity. The design variables are two-dimensional coordinates of the sensor nodes.
All the nodes cover equal sensing field areas [Singh M.P. and Gore M. M. (2005)]. The above are common assumptions for many sensor network applications.
4. Flow Chart
The flowchart contains a recursive iteration loop (generations) and can be described by the following pseudo code. Fitness F given in "Eq. (2)" depends on the Euclidian distance between the sensor node and the nearest centroid. Calculate fitness for each particle. Among the swarm, the particle with the least fitness is considered as the global best particle as it is closest to the optimum solution. The swarm is said to have accomplished the task if all the particles in it have acquired fitness less than or equal to the range of sensors incorporated in the network. In the particle swarm optimization algorithm, we perform the following actions:
1. Network information and algorithm parameters- inertia weight, learning factor, velocity boundary value, and the largest iterative number are initialized. Array of particles are initialized with random position and velocity vectors.
2. Find the distance of the interest point to its nearest sensor. Fitness is evaluated for every particle at its current position using Euclidian distance as in "Eq. (1)".
3. Minimize the fitness value; ideally the fitness value should be equal to zero, where the distance between the interests points with their nearest sensors are within the sensors’ sensing range. If the fitness of the particle is lesser than that of the best particle, then the particle would be the best particle for the next move, and the fitness of this particle is taken as best fitness.
4. Each particle is made to modify its current position, current velocity, the distance between current position
Cognit ion
X axis Y axis
Social
Pgbest
Vid( t + 1)
Xid( t + 1)
Xid
Vid
Pbest
5. If the next position of the particle is best, then the particle chooses a new position, otherwise, the same algorithm is continued.
6. This process is repeated in iterations, until all the particles communicate with each other and generate maximum coverage.
No Yes
No Yes
Initialize PSO parameters
Randomly initialize all particles velocities and positions
Set i=1, k=1
Stop Start
i>n
Update current position, current
velocity and distances
Criteria Satisfied
Output result i++
Set i=1, k++
Update particle i and best values
4.1.PSO Parameters
For the proposed method the number of particles are taken as 40 and the learning factors c1=c2=2. An inertia weight factor is linearly reduced as the search proceeds from 0.9 to 0.4 [Xiahui et a.l (2004)]. The maximum velocity and maximum iterations [Bo Li and RenYue Xiao (2007)] are taken as 50 and 300 respectively.
5. Results and Discussion
The initial population is created randomly and the objective function is calculated. The new sequence generation based on the initial sequence is illustrated in the following example. Considering, the following initial sequence, pibest and pgbest as follows:
Present: 2 6 3 5 4 1 pibest : 6 1 2 5 3 4 pgbest : 5 3 6 4 2 1
Assume c1=c2=1 and rand() =0.57. The pibest is generated by swapping the individuals of a present sequence. Present: 2 6 3 5 4 1 Swap: (2,6)
6 2 3 5 4 1 Swap: (2,1) 6 1 3 5 4 2 Swap: (3,2) 6 1 2 5 4 3 Swap: (4,3) 6 1 2 5 3 4--- pibest
Hence (2,6), (2,1), (3,2) and (4,3) are used for getting the pibest from present sequence. The pgbest is generated by swapping the individuals of a present sequence.
Present: 2 6 3 5 4 1 Swap: (2,5) 5 6 3 2 4 1 Swap: (6,3) 5 3 6 2 4 1 Swap: (2,4) 5 3 6 2 4 1---pgbest
Hence (2,5), (6,3) and (2,4) are used for getting the pgbest from present sequence. Velocity = 1*0.57{(2,6),(2,1),(3,2),(4,3)}+1*0.57{(2, 5), (6, 3),(2,4)}
The 57% of the changes in both the parts are considered. Hence the first two changes in both the parts (2,6),(2,1) and (2,5), (6,3) is considered. Hence the new velocity = (2,6),(2,1),(2,5), (6,3)
New sequence= present + velocity = 2 6 3 5 4 1+(2,6),(2,1),(2,5), (6,3)
Hence the sequence generated for the next generation is 3 1 6 2 4 5. Similarly for all the other particles, the new sequences are generated and objective function is evaluated.
Fig.2.b
Fig.2.c
Fig.2.d
PSO’s particles location of the target Fig.2.a randomly distributed particles; Fig.2.b Particles positions after 50 interactions; Fig.2.c Particles’ positions after 100 interactions and Fig.2.d Particles’ positions after 200 interactions.
It is proved theoretically [Men-Shen Tsai and Wu-Chang Wu (2008)] that the maximum efficient coverage is
(
3
3
/
2
)
r
2. The minimum of nodes is given as Sensing field/Maximum Coverage.The minimum number of nodes required to cover rectangular area (A) of 50x50 is 40.6. Conclusion
The proposed work has the ability to achieve optimal solution of coverage problem with minimum number of sensors in wireless sensor networks. This approach cultivates an innovative is idea in employing the PSO algorithm with enhanced fidelity. The results show that the PSO approach is effective and robust for efficient coverage problem of sensor deployment and is considered to give almost the optimal solution in WSN.
In future, the focus can be given to achieve 100% coverage with minimum number of sensors. The study of the 100% coverage using various optimal search techniques also presents several interesting challenges.
References
[1]. Bo Li and RenYue Xiao (2007): The Particle Swarm Optimization Algorithm: How to Select the Number of Iteration, IIH-MSP, vol. 2, pp. 191-196,ISBN: 0-7695-2994-1.
[2]. Eberhart R. and Kennedy J. (1995): A new Optimizer using Particle Swarm Theory, Proc. 6th
Int. Symposium on Micro Machine and Human Science, pp. 39-43.
[3]. Firasath Riyaz (2005): Evolving a Disjunctive Predator Prey Swarm using PSO: Adapting Swarms with Swarms, Thesis (M.S.)--Baylor University.
[4]. Jin-zhu Hu et al .(2009): Research on Particle Swarm Optimization with dynamic inertia weight. MASS `09, ISBN: 978-1-4244-4638. [5]. Lin Lu et al. (2008): An Improved Particle Swarm Optimization for Reconfiguration of Distribution Network, Fourth International
Conference on Natural Computation, IEEE Computer Society, And ISBN: 978-0-7695-3304-9.
[6]. Marco Ferreira et al. (2008): Detecting Protocol errors using particle swarm optimization with java pathfinder, High Performance Computing & Simulation Conference ©ECMS Waleed W. Smari (Ed.).
[7]. Men-Shen Tsai and Wu-Chang Wu (2008): A Novel Binary Coding Particle Swarm Optimization for Feeder Reconfiguration, Particle Swarm Optimization, Edited by Aleksandar Lazinicav p. cm. ISBN 978-953-7619-48-0.
[8]. Nor Azlina Bt. Ab Aziz et al (2007): Particle Swarm Optimization and Voronoi Diagram for Wireless Sensor Networks Coverage Optimization, International Conference on Intelligent and Advanced Systems.
[9]. Kennedy J. and Eberhart R. (1945): Particle swarm Optimization, Proc. IEEE Int. conf. on Neural Networks, pp 1942-1948. [10].Kershner, R. (1939): The Number of Circles Covering a Set” American Journal of Mathematics, Vol. 61, No. 3. (1939), pp. 665-671. [11].Shi Y. and Eberhart R. (1998): A Modified Particle Swarm Optimizer, Proc. IEEE Int. conf. on Evolutionary computation, pp 69-73. [12].Siba K. Udgata et al. (2009): Sensor Deployment in Irregular Terrain Using Artificial Bee Colony algorithm, NaBIC.
[13].Singh M.P. and Gore M. M. (2005): A Solution to Sensor Network Coverage Problem,0-7803-8964-6/05@2005 IEEE, ICPWC. [14].Xueqing Wang and Shuqin Zhang (2009): Research on Efficient Coverage Problem of Node in Wireless Sensor Networks, Second
International Symposium on Electronic Commerce and Security.
[15].Xiahui et a.l (2004): Recent advances in Particle Swarm, IEEE Transactions, 0-7803-8515-2104 02004.
