Arab J Sci Eng (2014) 39:6317–6325 DOI 10.1007/s13369-014-1292-3
RESEARCH ARTICLE - ELECTRICAL ENGINEERING
Sensor Node Placement in Wireless Sensor Network Using Multi-objective Territorial Predator Scent Marking Algorithm H. Zainol Abidin · N. M. Din · I. M. Yassin · H. A. Omar · N. A. M. Radzi · S. K. Sadon
Received: 29 May 2013 / Accepted: 30 September 2013 / Published online: 6 July 2014 © King Fahd University of Petroleum and Minerals 2014
Abstract Optimum sensor node placement for wireless sensor network (WSN) in a monitored area is needed for costeffective deployment. The location of sensor nodes must be able to offer maximum coverage and connectivity with minimum energy consumption. This paper proposes a sensor node placement approach that utilizes a new biologically inspired multi-objective optimization algorithm that imitates the behaviour of a territorial predator in marking their territories with their odours known as multi-objective territorial predator scent marking algorithm (MOTPSMA). The algorithm uses the maximum coverage and minimum energy consumption objective functions with subject to full connectivity. A simulation study has been carried out to compare the performance of the proposed algorithm with the multi-objective evolutionary algorithm with fuzzy dominance-based decomposition and an integer linear programming algorithm. Simulation results show that WSN deployed using the MOTPSMA sensor node placement algorithm outperforms the perfor-
mance of the other two algorithms in terms of coverage, connectivity and energy usage. Keywords Sensor node placement · Wireless sensor network · Coverage · Connectivity · Energy · Territorial predator scent marking algorithm · Biological inspired
H. Zainol Abidin (B) · I. M. Yassin · H. A. Omar Faculty of Electrical Engineering, Universiti Teknologi MARA, 40450 Shah Alam, Selangor, Malaysia e-mail:
[email protected] I. M. Yassin e-mail:
[email protected] H. A. Omar e-mail:
[email protected] N. M. Din · N. A. M. Radzi · S. K. Sadon Centre for Communications Service Convergence Technologies, College of Engineering, Universiti Tenaga Nasional, Jalan Ikram-Uniten, 43000 Kajang, Malaysia e-mail:
[email protected] N. A. M. Radzi e-mail:
[email protected] S. K. Sadon e-mail:
[email protected]
1 Introduction The special characteristics of wireless sensor network (WSN) allow them to be used in a wide range of applications, including environment monitoring, battlefield surveillance and health care. Another application and one of the most important areas of research is object tracking, in which wireless sensors monitor and report the locations of moving objects within the network [1]. WSN for target monitoring applications such as target tracking, landslide monitoring, forest fire detection and precision agriculture can be implemented
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using a fixed number of sensor nodes that are deployed to monitor one or more locations within a monitored area. One way to provide WSN with maximum coverage, connectivity and minimum energy consumption is through an effective planning mechanism in arranging the limited number of sensor nodes. For cost-effective deployment, it is critically important to determine optimal locations for the sensor nodes. The locations of the sensor nodes strongly affect the energy consumption, operational lifetime and sensing coverage [2]. Thus, careful sensor node placement is needed. Romoozi [3] stated that there is a trade-off between energy consumption of sensor nodes and network coverage. Closer sensor nodes will reduce the energy consumption, but the network coverage will become smaller. Most researchers nowadays prefer the artificial intelligence (AI)-based approaches particularly those based on biological inspired algorithms in solving optimization problems in WSN. This is because AI is proven to be able to give optimum solution for complex problems. Particle swarm optimization (PSO)-based algorithms for sensor node placement are mostly applied for sensor node placement. Some of these algorithms are virtual force directed co-evolutionary PSO (VFCPSO) [4], improved PSO (IPSO) [5] and intelligent single particle optimizer (ISPO) [6]. Aziz et al. in [7] and [8] optimized the sensor node coverage using PSO for optimal placement and Voronoi diagram to evaluate the fitness of the solution. Other sensor node placement algorithms that used biological inspired algorithms are genetic algorithm (GA) [9,10], artificial bee colony (ABC) [11], optimized artificial fish swarm algorithm (OAFSA) [12] and the glowworm swarm optimization algorithm (GSO) [13]. This paper introduces a sensor node placement algorithm for target monitoring by utilizing a new biologically inspired optimization algorithm known as territorial predator scent marking algorithm (TPSMA). This algorithm imitates the behaviour of a territorial predator in marking its territories with their odours. The sensor node placement problem could not be solved with a single optimal solution because the distance between two sensor nodes will affect the coverage and the energy consumption. Thus, our proposed algorithm considers a multi-objective optimization (MOO) concept that will be further discussed in Sect. 2. Our methodology is then presented in Sect. 3 followed by a simulation study in Sect. 4. Finally, based on the results obtained, a number of conclusions and recommendation for future work are pointed out in Sect. 5.
2 Related Work In many practical or real-life problems, there are several contradicting objectives that need to be optimized simultaneously [14]. Thus, it is no longer reliable to depend on a single
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optimal solution but rather a whole set of possible solutions of equivalent quality. The sensor node placement problem also falls in this category. As mentioned in the previous section, there is a trade-off between the coverage and the energy consumption affected by the distance between two sensor nodes. None of the AI-based works presented in previous section consider multi-objective optimization (MOO). Swarm intelligence (SI) that is based on information sharing of PSO and maintenance mechanism of an artificial immune system (AIS) to address coverage problems is given in reference [15]. This work can be considered as a MOO approach because their main objectives are to obtain maximum coverage probability with given number of sensor nodes and minimum number of sensor nodes with required coverage probability. Nevertheless, the objectives of this algorithm are not executed concurrently where the output for each objective will be different. Thus, there will be two sets of sensor node coordinates to be produced. Lizhong et al. [16] proposed a node distribution optimization algorithm based on multi-objective differential evolution algorithm (MDEA) that makes use of sensor radius adjustment and mobility of the sensor nodes to improve the WSN coverage. MDEA is used to optimize the distribution of the mobile sensor nodes in mobile WSN (MWSN) where the inputs are initial sensor node position and sensor node sensing range while the objectives are maximizing network coverage rate and network energy consumption of sensing. MDEA is also applied in paper [17] where the objectives are energy-related parameters. These two papers used the weighting method where they aggregate the multiple objectives into one objective function considering weights that can be fixed or dynamically changing during the optimization process. However, it is not always possible to find the appropriate weighted function [18]. The trend has shown that evolutionary algorithm (EA) has been enhanced for dealing with MOO problems [18]. MOEAs aim at finding a set of representative Pareto optimal solution in a single run. Most MOEAs are Pareto dominance based, where single objective EA frameworks are adopted and the fitness of each solution at each generation is mainly determined by its Pareto dominance relations with other solutions in the population. Most popular Pareto dominancebased algorithms are non-dominated sorting genetic algorithm-II (NSGA-II), strength Pareto evolutionary algorithm-II (SPEA-II) and Pareto-archived evolution strategy (PAES) [18]. Yuan et al. [19] and Sengupta et al. [20] proposed a sensor node placement algorithm that utilizes MOEA approach with decomposition and Pareto optimal concepts. Yuan et al. believed that MOEA is able to improve convergence speed and algorithm efficiency. MOEA approach in [19] considers network size, power consumption and processing time as their main objectives while Sengupta et al. in [20] suggested MOEA which take into consideration of coverage, lifetime,
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energy consumption as well as the connectivity. The aim of this work was to reduce the total cost of the sensor nodes without compromising the coverage and connectivity. MOEA is also applied to deploy MWSN [21] where the main objectives of this work are to minimize energy consumption and maximize the network coverage area. The energy consumption is reduced by minimizing the mobile sensor node distance travelled. Pradhan and Panda [22] proposed a sensor node placement algorithm that is based on multi-objective PSO with fuzzy logic-based strategy to select the best compromised solution on the Pareto front. The two objectives that are considered in this work are maximizing both coverage and lifetime. PSO with fuzzy logic is also proposed by Rani and Devarajan in [23] where three main objectives are passed on to a fuzzy logic engine the form the fuzzy rules. Following sections describe our TPSMA based sensor node placement algorithm using MOO.
3 Methodology 3.1 Territorial Predator Scent Marking Algorithm (TPSMA) Territorial predator such as tigers, bears and dogs can be defined as predators that consistently defend a specific area against animals from other species. The territory is chosen based on certain factor such as food resources. Most territorial predators use scent marking to indicate the boundaries of their territories which are also playing a role in territorial maintenance and as information sites for other members of the population [24]. Chemical or olfactory communication enables these animals to leave messages that are relatively long lasting and can be read later by conspecifics. Furthermore, it can also be used at night, underground or in dense vegetation [24]. Animal odours can facilitate communication between conspecifics according to four different functions, scent matching, reproductive signalling, temporal or spatial signalling and resource protection [25]. Scent matching allows a resident animal to distinguish other residents from intruders by recognizing their scent, thereby reducing the need for territorial encounters [25]. The marks may be deposited by urination, defecation, rubbing parts of bodies such as chin and foot, scratching, using glands and vegetation flattening [24]. For example, to identify its territory, the male tiger marks trees by spraying of urine and anal gland secretions, as well as marking trails with scat. Dogs and other canines scent mark by urinating and defecation, while cats scent mark by rubbing their faces and flanks against objects. Bear rubs their bodies that have scent glands against the substrate. There are two phases in TPSMA known as marking phase and matching phase.
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1 Marking Phase: Predator checks on all food resources on L locations and marks the location with the highest food resource level, L marked : ∀x = {1, 2, . . . , L} : (Rx |Rx ∈ Z [0, ∞))
(1)
Rx = F(x)
(2)
L marked = max (Rx )
(3)
where Rx = food resources level at location x, F(x) = objective function value and L marked = marked location 2 Matching Phase: Predator locates the marked location L marked . Assume that the predator locates L marked based on linear search behaviour as shown in the algorithm below [26]: procedure linear search (L marked : integer, R1 , R2 , . . . , R L : distinct integers) i:=1 while (i ≤ L ∧ L marked = Ri ) i := i + 1 if i ≤ L then location := i else location := 0 return location These phases are further illustrated in Fig. 1a, b, respectively. 3.2 WSN Sensor Node Placement Based on Multi-objective TPSMA (MOTPSMA) Territorial predator scent marking behaviour can be adopted in designing the sensor node placement algorithm where the territory of a sensor node can be scent marked based on a design objective such as maximum coverage, minimum uniformity, minimum energy consumption and maximum connectivity. This is done based on the scent marking behaviour where normally predator will scent mark the area due to certain factors such as food resources. Sensor node will identify its monitored location based on their marked territories that imitates the scent matching behaviour. As highlighted in the previous section, the sensor node placement problem can be considered as a MOO problem as there is a conflict between the coverage and the energy consumption of WSN. Closer sensor nodes will reduce the energy consumption, but the network coverage will become smaller. Based on this fact, it seems that the best trade-offs among the objectives can be defined in terms of Pareto optimality [14]. MOTPSMA is done based on decomposition by applying non-dominated Pareto optimal. Decomposition approach
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x = Rx
i = Lmarked
Rx
max(Rx) = Lmarked
(a) (b) Fig. 1 a Scent marking process. b Scent matching process
A ∈ P is considered to dominate anB ∈ P if and only if:
was developed based on a MOO algorithm which has been described in [18]. The algorithm decomposes a MOO problem into a number of single objective optimization subproblems and optimizes them simultaneously.
A decision vector other decision vector
3.3 Dominance and Pareto Optimal
Hence, a non-dominated Pareto optimal solution can be defined as follows: Let A ∈ P be an arbitrary decision vector
The concepts of dominance and Pareto optimal explained in this section are based on a paper written by Sengupta, S. et al. [20]. Consider a MOO problem with n objective functions ( f 1 , . . . f n ) with D decision variables (x1 , . . .x D ): Minimize: Y = f ( X ) = ( f 1 (x1 , . . . , x D ), . . . , f n (x1 , . . . , x D ))
(4)
subject to specific constraints: gi ( x ) ≤ 0, x ) = 0, h j (
i = 1, . . . , p j = p + 1, . . . , q
(5)
where Decision (parameter) vector, X = [x1 , . . . , x D ]T ∈ P Objective vector, Y = [y1 , . . . , yn ]T ∈ O
(6) (7)
P and O are the parameter space and objective space, respectively.
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≤ f i ( B) ∧ ∃ j ∈ {1, . . . , n} : ∀i ∈ {1, . . . , n} : f i ( A) < f j ( B) (8) f j ( A)
• The decision vector A is said to be non-dominated regarding the set P ⊆ P if and only if there is no vector P which can dominate A. • The decision (parameter) vector A is called Pareto opti non-dominated regarding the whole mal if and only if As parameter space P. 3.4 Problem Formulation A monitoring area is broken up into a number of small square tiles called monitoring locations. These monitoring locations are also the potential locations of sensor nodes. Thus, the number of monitoring locations is equal to the number of potential locations for sensor node. Each monitored location can only be equipped with one sensor node. The centre of each square tile is considered as the monitoring point and
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may be monitored by more than one sensor node. The area is obstacle free. The covering area of sensor nodes is assumed to be a circular area with a radius of RS that represents the sensing range. Monitoring points that are located within that circle is said to be covered by the sensor node. At least one sensor node would be able to cover a monitoring point. Sensor nodes are homogeneous static nodes where all sensor nodes will have similar sensing range, RS and communication range, RC . The number of sensor nodes must not exceed the number of monitoring locations, and at least one path must be there between each sensor node and the sink node to ensure connectivity. Two sensor nodes are said to be connected if the distance between them is less than RC . Each sensor node has a specific initial energy and energy consumed by each sensor node affects the network lifetime because it is related to the working time of a sensor node. Energy consumed by the sensor node consists of three parts [20]: • Maintenance energy: required for maintaining the sensor nodes in active state • Reception energy: depends on the number of sensor nodes from which it receives data for transmitting to sink node • Transmission energy: depends on the path in which the energy flows from the sensor node to the sink node 3.5 Mathematical/Placement Optimization Modelling
(9)
Description
N S
Number of sensor node index by i Set of sensor nodes
s
Sensor node
P
Number of sensor node potential locations
M
Set of monitoring points index by p
m
Monitoring point
x( j)
Variable that indicates whether the monitoring location j is equipped with a sensor node or not
ss
Sink node
EM
Sensor node maintenance energy
ET
Sensor node transmission energy
ER
Sensor node reception energy
RS
Sensing range
RC
Communication range
PiS
Cost of minimum path from a sensor node i to the sink node
αi
Number of sensor nodes from which the sensor node i receives data and transfer it to the sink node in multi-hop communication
L
Link between sensor nodes i and j
NCov
Number of uncovered points
Objective function 1, f 1 is the net energy consumed, E: Ei (11) f1 = E = The second objective is to maximize the area of coverage. Since we need to minimize energy, it is simpler to model the coverage as a minimization problem. Thus, coverage is expressed as a number of uncovered points (NCov) function that is determined as follows: 1 d(si , m p ) > Rs (12) N Cov p = 0 otherwise where d(si , p) is the Euclidean distance between monitoring point m p (xmp , ymp ) and sensor node i, si (xsi , ysi ). The Euclidean distance can be calculated as follows: (13) d(si , m p ) = (xsi − xm p )2 + (ysi − ym p )2 The objective function 2, f 2 is the sum of NCov for all monitoring points: f 2 = N Cov = N Cov p (14)
where ci = (xi , yi ) is the coordinate of si 3.6 MOO Formulation
p∈M
The first objective is to minimize the energy consumption. Energy consumed by each sensor node, E i , can be determined as follows [20]: E i = E Mi + E Ti × PiS + E Ri × αi
Parameters
i∈S
The parameters for the mathematical modelling are listed in Table 1. A two-dimensional area, Z 2 = {(x, y), 0 ≤ x ≤ l, 0 ≤ y ≤ l} where l is the length of the monitoring area, is deployed with N sensor nodes, with the sensor node set S = (s1 , s2 , . . . , s N ). The objective of this optimization process is to determine the coordinates of the sensor nodes in a two-dimensional area that satisfy the required goals. The decision variable is a set of positions of sensor nodes in the area as follows: C = (c1 , c2 , . . . , c N )
Table 1 Modelling parameters
(10)
The net multi-objective is: min Y = F( x ) = ( f1 , f2 )
(15)
There are two constraints of this optimization problem. First, the distance between any two sensor nodes must not exceed
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their RC and there must be at least a path from the sensor node to the sink node to ensure connectivity. Only one sensor node can be placed in each monitoring location. The monitoring locations are marked with x( p) as follows to indicate whether the location is equipped with a sensor node or not. ⎧ ⎨ 1 if location p has a sensor node x( p) = (16) ⎩ 0 otherwise ⎧ d(si , si−1 ) ≤ RC , i ∈ {1, 2, . . . , N } ⎪ ⎪ ⎨ const = αi ≥ 1, i ∈ {1, 2, . . . , N } (17) ⎪ ⎪ ⎩ x( p) = 0, p ∈ {1, 2, . . . , M}
are connected. An edge (i, j) belongs to G if the distance between sensor nodes i and j is within the RC . Dijkstra’s shortest path algorithm is applied from each of the sensor nodes to the sink node. The output returned by the algorithm is the cost of the path, which is used to determine PiS and the sequence of nodes in the path that will give αi . Sengupta et al. [20] stated that graph theory is able to reduce the huge computational effort in formulating the objective functions.
The problem is based on the assumptions listed in Lemma 1, 2 and 3 while the objectives are listed in Proposition 4 and 5. Problem 6 formalizes the optimization problem.
4.1 Simulation Network Model
Lemma 1 The area is obstacle free; the sensing and communication ranges of all sensor nodes are identical and assumed to have a circular coverage area. Lemma 2 Number of monitoring locations are equal to the number of sensor nodes potential locations. M=P
(18)
4 Simulation Study
A numerical simulation has been carried out using MATLAB and network simulator (NS2) on Linux platform to demonstrate the performance and the effectiveness of the proposed algorithm based on recent studies. Figure 2 depicts the monitoring area with 60 m × 60 m dimension and consists of 144 equal width monitored locations. The properties of the sensor nodes are listed in Table 2. Figure 3 shows the convergence rate for MOTPSMA. It can be seen that the algorithm totally converged when the
Lemma 3 Number of sensor nodes must not exceed the number of monitoring locations. N≤M
(19)
Proposition 4 All sensor nodes should communicate with each other and there must be at least a path from the sensor node to the sink node to ensure connectivity as shown in Eq. (17). Proposition 5 Monitoring points must be covered by at least one sensor node. ∀ p ∈ {1, . . . , M} ∧ ∃i ∈ {1, . . . , N } :
d ( p, si ) ≤ RS (20)
Problem 6 Place the sensor nodes that will give maximum coverage with minimum energy consumption with guaranteed connectivity. Each monitoring location can only be equipped with not more than one sensor node. The problem is represented by Eqs. (11), (14) and (15) subject to constraints in the Eq. (16) and (17).
Fig. 2 Simulation network model
Table 2 Sensor nodes properties
3.7 Connectivity, Graph and Dijkstra’s Algorithm Dijkstra’s algorithm [26] is used to check whether sensor nodes are connected to the sink node or not. Dijkstra’s algorithm gives the minimum cost, PiS , and the number of hops, αi , between the sensor nodes and the sink node. A graph G is created containing all sensor nodes while an adjacency matrix is created which contains the sensor nodes that
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Parameter
Value
Sensing range, RS Communication range, RC
15 m 15 m
Initial energy
1 Ah
Sensor node maintenance energy, E M
13 mA
Sensor node transmission energy, E T
20 mA/m
Sensor node reception energy, E R
2 mA
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Fig. 3 Convergence rate of MOTPSMA Fig. 5 Connectivity probability
Fig. 4 Coverage ratio
number of iterations reached 400. Thus, 400 iterations are considered in the simulation work. 4.2 Simulation Results WSN performance deployed with proposed sensor node placement algorithm is studied in terms of coverage ratio, connectivity probability and the average energy consumption. Simulation results are compared with results produced by MOEA/DFD [20] and integer linear programming (ILP)based algorithm which is focusing on minimizing the cost proposed by Deyab et al. [27]. The simulation results of proposed algorithm are compared with these two algorithms because they are recently studied and presenting the same network scenario. Figure 4 shows the coverage ratio of WSN for different number of sensor nodes. As expected, the coverage ratio of WSN will increase as the number of sensor nodes increases. Coverage ratio offered by MOTPSMA is higher than
Fig. 6 Average energy consumed by each sensor node for minimum of 95 % coverage
MOEA/DFD and Deyab’s algorithms which indicates that MOTPSMA would be able to offer higher coverage with fewer sensor nodes. It can be seen that MOTPSMA needs around 10 sensor nodes to get at least 95 % coverage compared to MOEA/DFD and Deyab’s that need 12 sensor nodes and 20 sensor nodes, respectively. In order to get 100 % coverage, MOTPSMA needs 24 sensor nodes compared to MOEA/DFD that needs 28 sensor nodes and Deyab’s algorithm that needs 30 sensor nodes. Thus, it can be concluded that MOTPSMA would be able to provide higher coverage with the lowest cost. Cost can be reduced around 16 % compared with MOEA/DFD and 14 % compared with Deyab’s algorithm for the minimum of 95 % coverage. In order to achieve 100 % coverage, MOTPSMA outperforms MOEA/DFD by 14 % and Deyab’s algorithm by 20 % in terms of the deployment cost. As depicted in Fig. 5, MOTPSMA is able to provide 100 % connectivity with the lowest number of sensor nodes while MOEA/DFD can be considered fully connected with a small
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Number of Nodes = 10
70
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60
60
50
50
40 30 20 10 0 -10 -20 -20 -10
Number of Nodes = 20
80
Y coordinate (m)
Y coordinate (m)
80
40 30 20 10 0 -10
0
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0
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(a)
(b)
Fig. 7 a Sensor node position for 10 sensor nodes deployed with MOTPSMA and b sensor node position for 20 sensor nodes deployed with MOTPSMA
number of sensor nodes compared with Deyab’s algorithm. This is because MOTPSMA and MOEA/DFD place the sensor nodes subject to full connectivity requirement. On the other hand, Deyab’s algorithm provides almost full connectivity when the number of sensor nodes gives at least 95 % coverage. As mentioned before, Deyab’s algorithm is focusing on minimizing the deployment cost and it is found that the lowest sensor nodes that they need in order to achieve full connectivity are around 24 sensor nodes. From the figure, it can be seen that the connectivity probability of Deyab’s algorithm is unstable at the beginning. It reaches a steady state when the number of sensor nodes gives approximately 95 % coverage. This is because, Deyab’s algorithm places the sensor nodes randomly without considering any location constraint as required by MOTPSMA and MOEA/DFD algorithms. Figure 6 depicts the average energy consumed by each sensor node when the minimum of 95 % coverage is achieved. The bar chart clearly shows that MOTPSMA has the lowest energy usage compared with MOEA/DFD and Deyab’s algorithm. MOTPSMA consumed the lowest energy because the objective of the algorithm is to place the sensor nodes at the location that gives the lowest energy usage without considering other energy-based criterion. On the other hand, Deyab’s algorithm only considers the deployment cost and did not consider the energy consumption. Figure 7 illustrates samples of sensor nodes’ positions. The stars show the monitored points while the dots indicate the sensor nodes. The circles show the coverage of the sensor nodes. Figure 7a shows WSN deployed with 10 sensor nodes while Fig. 7b shows 20 sensor nodes. As can be seen, more locations are covered when the number of sensor nodes deployed is increased.
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5 Conclusion and Future Works A multi-objective sensor node placement algorithm known as MOTPSMA has been developed in order to ensure that the WSN coverage and connectivity will be maximized with minimum energy consumption for effective monitoring. The simulation network model presented in this paper is an area that consists of several equal widths monitored locations. Based on the simulation results obtained, it can be concluded that WSN deployed with proposed MOTPSMA sensor nodes placement algorithm offers considerably higher coverage ratio, higher connectivity and lower energy consumption value compared with MOEA/DFD and Deyab’s algorithm. This result implies that WSN deployed with proposed algorithm is expected to provide higher coverage and fully connected with longer lifetime. This work will be further extended with other objective function to address other concern issues in deploying WSN. References 1. Zoghi, M.R.; Kahaei, M.H.: Sensor management under tracking accuracy and energy constraints in wireless sensor networks. Arab. J. Sci. Eng. 37, 721–734 (2012) 2. Oldewurtel, F.; Mähönen, P.: Analysis of enhanced deployment models for sensor networks. In: Proceedings of the 2010 IEEE 71st Vehicular Technology Conference, Taipei, Taiwan, pp. 1–5 (2010) 3. Romoozi, M.; Vahidipour, M.; Maghsoodi, S.: Genetic algorithm for energy efficient and coverage-preserved positioning in wireless sensor networks. In: Proceedings of the 2010 International Conference on Intelligent Computing and Cognitive Informatics, Kuala Lumpur, Malaysia, pp. 22–25 (2010) 4. Wang, X.; Wang, S.: Hierarchical deployment optimization for wireless sensor networks. IEEE Trans. Mob. Comput. 10, 1028– 1041 (2010)
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