1604
IEEE COMMUNICATIONS LETTERS, VOL. 16, NO. 10, OCTOBER 2012
Sensor Deployment of Wireless Sensor Networks Based on Ant Colony Optimization with Three Classes of Ant Transitions Xuxun Liu
Abstract—The problem of minimum-cost and connectivityguaranteed grid coverage (MCGC) is one of the most critical issues for the implementation of wireless sensor networks (WSNs). In this paper, a novel algorithm, ant colony optimization with three classes of ant transitions (ACO-TCAT) is proposed to decrease inferior solutions and narrow the searching range of the algorithm and finally to solve this problem. Simulation results are conducted to demonstrate the effectiveness of our proposed approach. Index Terms—Wireless sensor networks, sensor deployment, ant colony optimization, three classes of ant transitions.
I. I NTRODUCTION
S
ENSOR deployment is one of the fundamental problems in wireless sensor networks (WSNs). It is a key requirement that the connected system can cover the sensing field with redundancy and the system cost must be minimized in WSNs. Thus, the problem of minimum-cost and connectivityguaranteed grid coverage (MCGC) is full of challenges. This challenging problem is to design an algorithm which can get high quality solutions with low system cost, which is defined by the total number of sensors deployed in the network. Sensor deployment in WSNs is divided into two kinds of methods, i.e., those based on continued points and those based on grid. Due to a variety of advantages, such as flexibility, extendibility and implementability, the latter has become an active branch of sensor deployment in WSNs. Grid coverage for surveillance and target location in WSNs has been presented at the early time in [1]. It has been proved to be NP-Complete for deploying a network to k-cover points with minimum sensors. A resource-bounded optimization framework has been presented for grid coverage of the sensor field in [2], and the algorithm is aimed at optimizing the number of sensors and determining their placement to support such WSNs. In [3], the similar method has been presented and the algorithm is targeted at an average coverage as well as at maximizing the coverage of the most vulnerable grid points, but in both [2] and [3], the storage and computing cost is too much on account of the large number of grid array. Based on simulated annealing (SA) in [4], the grid-based sensor placement problem is formulated as a combinatorial optimization problem in WSNs, but the position affection of the sink and the connectivity problem has not been taken Manuscript received May 4, 2012. The associate editor coordinating the review of this letter and approving it for publication was Y.-D. Lin. This work was partly supported by the National Natural Science Foundation of China (Grant No. 61001112) and the Fundamental Research Funds for the Central Universities (Grant No. 2011ZM0030). The author is with the School of Electronic and Information Engineering, South China University of Technology, Guangzhou, 510641, China (e-mail:
[email protected]). Digital Object Identifier 10.1109/LCOMM.2012.090312.120977
into account. Furthermore, genetic algorithm (GA) has been presented for grid-based sensor deployment in [5], [6], but the node communications problem has not been taken into consideration. In addition, ant colony optimization (ACO) is also used for sensor deployment in [7], but the large searching range of the algorithm insults in lots of inferior solutions and slow convergence. According to our survey, each of the above methods has certain limitations and grid-based sensor deployment in WSNs has not been solved by mathematic optimization methodology. ACO is a well-known algorithm where ants are stochastic constructive procedures that build solutions while walking on a construction graph. Such search behavior makes ACO effective for solving combinatorial optimization problems, such as traveling salesman problem (TSP), etc. [8]. The problem of MCGC is also an applicable combinatorial optimization problem, thus ACO can be suitable for solving this problem. In this paper, a novel algorithm, ant colony optimization with three classes of ant transitions (ACO-TCAT) is proposed and the goal of the algorithm is to improve the quality of the solution space and raise the searching speed, and finally better solve the problem of MCGC. Different from other algorithms such as EasiDesign [7] with only one class of ant transition, our algorithm possess three classes of ant transitions. The diversity of classes of ant transitions can significantly narrow the searching range of the algorithm and markedly decrease inferior solutions, and finally achieve the goal of our approach. II. P ROBLEM D ESCRIPTION In the binary WSN model, the sensing field comprises discrete grid points on which sensors can be deployed and can detect the points of interest (PoIs) within the sensing radius. All the candidate points are separated from the sink, the PoIs, and the obstacles. The problem of MCGC is to search a solution, i.e., a set of points, from the candidate grid points which exclude the sink, the PoIs, and the obstacles, so that a sensor is deployed on each point of the set and all the PoIs can be covered by at least k sensors deployed on the points of the set. Each member of the set is named a point of solution (PoS). For the problem of MCGC, the number of PoSs should be minimized and every PoS should be connected to the sink. As an example, Fig.1 illustrated the WSN model and a solution to the problem of MCGC in WSNs. III. A LGORITHM D ESCRIPTION The algorithm of ACO-TCAT is based on ACO. In ACOTCAT, in the beginning the ant is on the sink located randomly in the network. The ant moves from a grid point to another
c 2012 IEEE 1089-7798/12$31.00
LIU: SENSOR DEPLOYMENT OF WIRELESS SENSOR NETWORKS BASED ON ANT COLONY OPTIMIZATION WITH THREE CLASSES OF ANT . . .
PoI
PoI
PoI
m1 sink
sink
PoS
sink
PoI
PoS m2
m1
m3
m2
sink
m4
obstacle
m5 m7 obstacle
Fig. 1.
Fig. 2.
step by step and a sensor is deployed on each grid point visited by the ant. The set of all grid points visited by the ant is a solution of the problem of MCGC. In other words, each grid point visited by the ant is a PoS. ACO-TCAT comprises of three classes of ant transitions, named ant transition of Class I (ATC-I), ant transition of Class II (ATC-II), and ant transition of Class III (ATC-III) respectively. A. Ant Transition of Class I ATC-I, similar to EasiDesign [7], is the ordinary transition of ACO where the ant moves step by step with probability. Definition 1 (ECPs): ECPs (effective candidate points) are defined as such points on which the sensor can cover at least one uncovered PoI. Definition 2 (NCPs): NCPs (non-effective candidate points) are defined as such points on which the sensor can’t cover any uncovered PoI. i (I)): In ATC-I, the set of candidate Definition 3 (Scandidate i points for the ant on point i, Scandidate (I), is defined as SECP(i) , if SECP(i) = φ i Scandidate (I) = (1) φ otherwise where SECP(i) is the set of ECPs within the communication radius of point i. In ATC-I, each ant chooses the next point with a probability according to the pheromone intensity and the heuristic desirability. For the t-th iteration, the transition probability of the ant from point i to point j is as follows [τij (t)]α [ηij (t)]β α β (I) [τir (t)] [ηir (t)]
m4 m5 m6
m6
(a) ATC-ĉ and ATC-Ċ
(b) After sensor deployment
Description of the problem of MCGC.
pij (t) =
PoS m3
obstacle
obstacle
(a) Before sensor deployment
1605
(2)
i r∈Scandidate
where the variable τij (t) is the pheromone intensity on edge (i, j), the variable ηij (t) is the heuristic value of transition from point i to point j. The parameters α and β are constants, which determine the relative influence of the pheromone and the heuristic on the decision of the ant. As shown from formula (1), NCPs have been eliminated and the efficiency of ACO-TCAT has been enhanced in ATC-I. In addition, sensors on the adjacent PoSs can communicate with each other because each step is within the communication radius. By continuous transitions, all the sensors on all the PoSs can be connected together and the connectivity of the
(b) ATC-ĉ and ATC-ċ
Three classes of ant transitions in ACO-TCAT.
system is guaranteed. In addition, in the beginning the ant is on the sink located randomly in the network, hence the connectivity of the system is guaranteed for different sink locations. B. Ant Transition of Class II In ATC-I, the ant only chooses ECPs, but if there is no such i kind of points, i.e., Scandidate (I) = φ , ATC-II is proposed in this paper to be applied in ACO-TCAT. Definition 4 (ESPs): ESPs (effective selected points) are defined as such PoSs within the communication radius of which there exists at least one ECP. Definition 5 (NSPs): NSPs (non-effective selected points) are defined as such PoSs within the communication radius of which there doesn’t exist any ECP. i (II)): In ATC-II, the set of candidate Definition 6 (Scandidate i points for the ant on point i, Scandidate (II), is defined as SESP, if SESP = φ i Scandidate (II) = (3) φ otherwise where SESP is the set of ESPs throughout the network. In ATC-II, the ant on point i stochastically chooses a PoS, i (II) and transfers to it. As shown in point j, from Scandidate formula (3), NSPs have been eliminated and the efficiency of ACO-TCAT has been enhanced in ATC-II. Fig.2 illustrated the three classes of ant transitions in ACOTCAT. The shadow of circular is the sensing region of the sensor which is in the center and the communication radius is equal to the sensing radius. By ATC-I in Fig.2(a), the ant transfers from point m1 to point m2 , point m3 , · · · , m7 in turn, but it is “routeless” on point m7 . Then ATC-II makes the ant transfer from point m7 to the ESP, point m2 , directly. In ATC-II, the ant can transfer to ESPs, which are in the vicinities of ECPs, elsewhere quickly. Furthermore, the connectivity of the system is guaranteed by continuous transitions with each step going back to one PoS which belongs to a connected system. C. Ant Transition of Class III i (I) = φ If neither ATC-I nor ATC-II fails, i.e., Scandidate i and Scandidate(II) = φ, ATC-III is proposed in this paper to be applied in ACO-TCAT.
1606
IEEE COMMUNICATIONS LETTERS, VOL. 16, NO. 10, OCTOBER 2012
TABLE I ACO-TCAT WITH C OMPUTATIONAL C OMPLEXITY Steps
Contents
the ant on point i, the class of ant transition, ϕ, is determined by the set of candidate points, as follows
Complexity O(n2 + m)
(1)
Initialize all parameters
(2)
Each ant transfers to the next point based on one of the three classes of ant transitions
(3)
Each ant updates the set of PoSs
O(m)
(4)
Each ant updates the set of candidate points for ant transition of Class I
O(m)
(5)
Each ant updates the set of candidate points for ant transition of Class II
O(m)
(6)
Each ant updates the set of candidate points for ant transition of Class III
O(m)
(7)
Each ant judges whether a complete solution is built. If it is not built, the algorithm goes back to step (2)
O(m)
(8)
The solutions built by ants are evaluated
O(m)
(9)
The intensity of pheromone on all edges is updated
O(n2 )
(10)
The iterating times are computed. If the maximum iterating times, Cmax , is not reached, the algorithm goes back to step (2)
O(m)
(11)
The best solution is achieved
O(1)
O(m)
Definition 7 (RCPs): RCPs (residual candidate points) are defined as such candidate points excluding PoSs in the set of all initial candidate points. i (III)): In ATC-III, the set of candiDefinition 8 (Scandidate i (III), is defined date points for the ant on point i, Scandidate as SRCP(i) , if SRCP(i) = φ i Scandidate (III) = (4) φ otherwise where SRCP(i) is the set of RCPs within the communication radius of point i. In ATC-III, the ant on point i stochastically chooses a point i (III) and transfers to it as a PoS. The set j from Scandidate i Scandidate(III) doesn’t comprise any ECP, but can lead the ant to ECPs ultimately. As shown in Fig.2(b), the ant transfers from point m1 to point m2 , point m3 , and point m4 in turn by ATC-I, but it is “routeless” again on point m4 . Then ATC-III makes the ant transfer from point m4 to the RCPs, point m5 and point m6 , in turn. Distinctly, ECPs exist within the communication radius of point m6 and the ant can transfer from point m6 to it as the next step by ATC-I. In ATC-III, the ant can eventually transfer to ECPs elsewhere conveniently. Moreover, similar to that in ATC-I, the connectivity of the system in ATC-III is guaranteed by continuous transitions with each step within the communication radius. D. The Full Algorithm of ACO-TCAT The algorithm, ACO-TCAT, with computational complexity is summarized in Table I for N = n × n grid points in the sensor field, and m ants are used. The ant transfers to another point step by step until all PoIs are covered by all sensors on the PoSs and a solution is achieved. After each step, some correlative information is updated. Let Ψ = (ϕ1 , ϕ2 , ϕ3 ) denote a sequence of classes of ant transitions, i.e., ATC-I, ATC-II, and ATC-III respectively. For
⎧ i ⎪ ⎨ϕ1 , if Scandidate(I) = φ i i ϕ = ϕ2 , if Scandidate (I) = φ, Scandidate (II) = φ ⎪ ⎩ ϕ3 , otherwise
(5)
In ATC-I, the variable ηij (t) in formula (2) is defined as
ηij (t) = L +
l(m)
(6)
m∈SECP(j)
where l(m) is defined as a constant 1, i.e., l(m) ≡ 1
(7)
and the constant L, L > 0, is used to prohibit ηij (t) = 0. It is mirrored that ηij (t) denotes the approximate number of potential ECPs and the PoS has the potential capability of covering more uncovered PoIs. After the ant finishes a tour, the pheromone intensity on every edge (i, j) is updated in terms of τij (t + 1) = (1 − ρ)τij (t) + Δτij (t)
(8)
where ρ ∈ (0, 1) is the pheromone evaporation parameter, and the added pheromone trail amount Δτij (t) is given by Δτij (t) =
C total(t)
(9)
where the function total(t) is the number of total PoSs in the solution, C is a constant and C > 0. The function total(t) in formula (9) contains the global optimization. Obviously, the pheromone updating rule has the potential capability of using less total sensors. In order to prohibit algorithm stagnation or premature convergence in different scales of networks, the pheromone constraining process [7] is adopted in ACO-TACT to constrain the pheromone value within the imposed limits, i.e., τmin ≤ τij ≤ τmax . An individual period for the constraining process of the pheromone value is also adopted. The period, denoted as Tc , is counted in the number of iteration of the algorithm. The period Tc differs in different scales of networks in ACO-TCAT. For small-scale networks, the ant is easy to be attracted by the earlier paths, thus Tc is given a relatively small value to constrain the pheromone value with high frequency. However, the ant is not easy to be attracted by the earlier paths in large-scale networks, hence Tc is given a relatively large value to constrain the pheromone value with low frequency. For a better solution, different from that of the other approaches such as [7], ρ varies in different periods in ACOTCAT. In the first half period, ρ is assigned a relatively small value to achieve a small difference in the pheromone intensity of all edges and finally to work out extensive solutions. However, ρ is assigned a relatively large value to get a large difference in the pheromone intensity of all edges and fast convergence of the algorithm in the last half period.
0
80
0
EasiDesign ACO-TCAT
20 40 60 The number of PoIs (a) Rs=Rc=10m
80
Average steps for an iteration 30 35 40 45 50 55 60
0
Fig. 4.
20 40 60 The number of PoIs (a) Rs=Rc=10m
MAX_AVG_COV MAX_MIN_COV ACO-TCAT 20 40 60 The number of PoIs (b) Rs=Rc=15m
80
The number of sensors in a solution of different algorithms.
Average steps for an iteration 40 45 50 55 60 65 70
Fig. 3.
MAX_AVG_COV MAX_MIN_COV ACO-TCAT
The number of sensors in a solution 10 15 20 25 30 35 40 45 50
The number of sensors in a solution 30 35 40 45 50 55 60 65 70
LIU: SENSOR DEPLOYMENT OF WIRELESS SENSOR NETWORKS BASED ON ANT COLONY OPTIMIZATION WITH THREE CLASSES OF ANT . . .
0
EasiDesign ACO-TCAT
1607
MIN COV [3]. As shown in this figure, the number of sensors in a solution increases as the increase of PoIs, in that more sensors are demanded with the increase of PoIs. Evidently, sensors in ACO-TCAT are much less than that in the others. Less sensors are demanded in Fig.3(b) than that in Fig.3(a) in this figure, due to the ability of covering more PoIs by sensors with the increase of sensing radius and communication radius. Fig.4 shows the Performance comparison between our algorithm, ACO-TCAT, and the other algorithm, EasiDesign [7]. As shown in this figure, average steps by an ant for an iteration in different algorithms increase with the increase of PoIs, because more sensors are demanded with the increase of the PoIs. Average steps by an ant for an iteration in ACO-TCAT is much less than that in the other, because three classes of ant transitions in ACO-TCAT are applied to reduce the candidate points and redundant steps as soon as possible. V. C ONCLUSION
20 40 60 The number of PoIs (b) Rs=Rc=15m
80
Average steps by an ant for an iteration in different algorithms.
IV. P ERFORMANCE E VALUATION A. Computational Complexity In [3], two deployment methods for WSN are introduced. The first one, MAX AVG COV, attempts to maximize the average coverage of the grid points, but the second one, MAX MIN COV, attempts to maximize the coverage of the grid point that is covered least effectively. Unfortunately, the two methods suffer from high computational complexity, O(n4 ) [3]. According to Table I, the computational cost of ACO-TCAT is O(n2 ). EasiDesign [7] has only one class of ant transition, but it is obvious that EasiDesign and ACO-TCAT have the equal computational complexity, O(n2 ), which is much lower than that of MAX AVG COV and MAX MIN COV. B. Experiment and Analysis The effectiveness of the algorithm is tested under Visual C++. The experiment was for a 2-dimensional square area of 100m×100m, with grid of 21 points in each dimension. The sensing radius Rs and communication radius Rc are chosen as Rs =Rc =10m and Rs =Rc =15m respectively in different cases. Other parameters are assigned as α=2, β=3, Tc =22, ρ=0.08 and 0.15 respectively in the first half time and the latter. In addition, the number of iterations is 200 and 10 ants are used. Fig.3 shows the performance comparison among ACOTCAT, and other algorithms, MAX AVG COV and MAX
In this paper, a novel algorithm, ACO-TCAT is proposed for the problem of MCGC. Different from other algorithms with only one class of ant transition, ACO-TCAT embodies three classes of ant transitions. The diversity of classes of ant transitions is applied to decrease inferior solutions and narrow the searching range of the algorithm, and finally to improve the quality of the solution space and raise the searching speed observably. Moreover, our algorithm can deal with different scales of networks. Furthermore, the connectivity of the system is guaranteed for different sink locations and the system cost is minimized. R EFERENCES [1] W. C Ke, B. H Liu, and M. J. Tsai, “Constructing a wireless sensor network to fully cover critical grids by deploying minimum sensors on grid points is NP-Complete,” IEEE Trans. Computers, vol. 56, no. 5, PP. 710–715, May 2007. [2] S. S. Dhillon, K. Chakrabarty, and S. S. Ivengar, “Sensor placement for grid coverage under imprecise detections,” in Proc. 2002 International Conference on Information Fusion, pp. 1581–1587. [3] S. S. Dhillon and K. Chakrabarty, “Sensor placement for effective coverage and surveillance in distributed sensor networks,” in Proc. 2003 IEEE Conference on Wireless Communications and Networking, pp. 1609–1614. [4] F. Y. S. Lin and P. L. Chiu, “A near-optimal sensor placement algorithm to achieve complete coverage/discrimination in sensor networks,” IEEE Commun. Lett., vol. 9, no. 1, pp. 43–45, Jan. 2005. [5] D. B. Jourdan and O. L. Weck, “Layout optimization for a wireless sensor network using a multi-objective genetic algorithm,” in Proc. 2004 IEEE Vehicular Technology Conference – Fall, pp. 2466–2470. [6] Y. Xu and X. Yao, “A GA approach to the optimal placement of sensors in wireless sensor networks with obstacles and preferences,” in Proc. 2006 IEEE Conference on Consumer Communications and Networking, pp. 127–131. [7] D. Li, W. Liu, and L. Cui, “EasiDesign: an improved ant colony algorithm for sensor deployment in real sensor network system,” in Proc. 2010 IEEE Globecom, pp. 1–5. [8] M. Dorigo and T. Stutzle, Ant Colony Optimization. MIT Press, 2004.
