International Journal of Engineering, Applied and Management Sciences Paradigms (IJEAM)
Volume 54 Issue 3 June 2019 364 ISSN 2320-6608
Enhancing the lifetime of network using Hybrid
Artificial Bee Colony – Nelder Mead (HABC-
NM) in coverage connected node
placement problem of target based WSN
Poonguzhali1, P.Bhavani
2, R.Ramachandiran
3
1,2,3Department of Computer Science and Engineering,
Sri Manakula Vinayagar Engineering College, Puducherry, India.
Abstract- Major concern in wireless sensor networks is to maximize network lifetime (in terms of rounds) while
maintaining a high quality of services (QoS) at each round such as target coverage and network connectivity. Due to the
power scarcity of sensors, a mechanism that can efficiently utilize energy has a great impact on extending network
lifetime. Most existing works concentrate on scheduling sensors between sleep and active modes to maximize network
lifetime while maintaining target/area coverage and network connectivity is a great challenge.To meet the challenges of
the existing work an effective Nelder-Mead (NM) mathematical model has been incorporated with Ant Bee Colony (ABC)
algorithm. The performance of proposed method will be tested in the test bed 3. Finally the obtained results are discussed
and the results will show the significance of proposed method on comparing existing algorithms.
Keywords- QoS(Quality of Service); ABC(Ant Bee Colony); NM (Nelder- Mead)
I. INTRODUCTION
A Wireless Sensor Network (WSN) can be defined as a collection of limited power based sensors with the ability to
cover an area/ a single point target and communicate the collected data to sink node (base station) either via single-
hop or through multi-hop [2, 3]. WSN is used for monitoring the physical and environmental changes such as
weather, wind, clouds, natural calamities etc. WSN has been considered or appreciated for its ability to cross the
domain which can also be stated as cross-multidisciplinary, highly cohesive with respect to the addressed problem,
which holds the recent trend with cutting edge knowledge regarding research field. It enables the user to access the
region where a human interference is difficult or sometimes which is impossible. This gives an API kind technology
by which the future generation shall process the information in more effective manner than now. This technology
has been addressed as most predominating technology of 21st century.
WSN has been considered as a most prominent network in wireless technology where sensing and collection of data
are more effective and also reliable in a wireless based system. This agility and ability of processing and
transformation of data in WSN leads the technology to get adapted and used in cross domain fields too. This type of
structure reduces the human effort in monitoring a region or an environment. The key domains of application of
WSN are discussed below. Figure 1 demonstrates the overview of WSN which consists of sensor nodes, sink nodes,
data transformation paths, relay nodes, etc.
Figure1. Overview of Wireless Sensor Network
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Military applications: In military applications WSN has been used as an artificial based application. WSN is used to
track the battlefield, which can be also termed for communication, controlling, etc.
1.1 Target Based WSN
In target based WSN, the sensor nodes are deployed in the region that are to be sensed either in ad-hoc or
predetermined manner. Usually, ad-hoc type of deployment happens in the regions such as deep forest, volcano, etc.
These sensor nodes expect localization of nodes first before data aggregation. In predetermined deployment of
sensor nodes, the deployment position will be computed in prior to actual deployment. During the computation to
search for better or optimal positions with maximum coverage and less number of sensor nodes usage is an
optimization task to be handled. The existing challenges in deployment of sensor nodes are 1) each sensor nodes
holds limited amount of transmission range. 2) The sensors are equipped with limited power resources on which
once the power gets drained the node dies and data transmission is under debate. 3) Hazardous external properties
can damage the sensor nodes where an alternate sensor may give a backup and keep the network to be alive. This
states that the issue of covering target nodes and maintaining connectivity between sensors are important in target
based WSN.
1.2. coverage WSN
Coverage represents at least number of sensor nodes required for monitoring every single target in WSN. A
sensor node may reside in another cover set but each target should be covered at least by sensors. One among the
methodology is to subdivide the given region into parts and place sensors in each region. This method
completes the coverage issue but addressing the concept of minimal sensor usage is a missing factor in it.
1.3 Coverage Connected sensor nodes
Wireless Sensor Networks has an immense amount of research aspects since its application range is vast. In
applications such as monitoring the surroundings, military border monitoring, warning of disasters, tracking the
targets etc. In these applications the targets nodes are to be covered and the gathered information should be
transformed to the base station for further processing either via single or multi-hop connection.
The conventional approaches fixes one sensor node to cover a target and the information are collected from the
sensor nodes. This become a successful task until the sensor nodes drain the battery source. Once the sensor node
fails to communicate the sensed data to base station due to insufficient power source, not only that particular target
data will be missed out but also the communication path where this drained sensor node is used for communication
purpose also will get affected and the entire network fails at this stage. This issue can be solved when more than one
number of sensor nodes are used for covering the targets and more number of sensor nodes are used for
communication between sensor nodes to base station. Thus in coverage, represents the number of sensor nodes
that are used to cover a target and in connected represents the number of sensor nodes that covers other sensor
node for recovery from node failure.
II. RELATED WORK
Liu and Zheng proposed theCoverage of target nodes in WSN, guarantees the sensing data to be covered accurately
without any loss in it. Coverage are even classified into point based coverage and region based coverage.
Connectivity between sensor nodes deals with the adequacy on which the communication between sources to
destination occurs. In this chapter, the research contributions of researchers on WSN coverage and connectivity
problems and its solving methodologies. This literature study has been done in two folds.
Carde et.al., extended their work where the sensors participate in one individual can also be used to cover other
targets in the same region. Hence this approach addresses multiple coverage uses using sensors.They proposed two
different methodologies for efficiently handling the coverage issue in WSN based on residual energy and the
accessible nodes for covering the targets.
Hongwu, Zhang et. al., proposed a heuristic greedy optimum coverage algorithm (HG-OCA). In HG-OCA, we first
design a network model in which power supplies of sensor nodes follow a normal distribution. Next, we analyze
energy model of target coverage, educe three rules to reduce network scale, present the concept of the key target and
the prior coverage of key target. Moreover, we choose sensor with most energy utility as active sensor. In the end,
we present HG-OCA to extend network lifetime, based on minimizing energy consumption of key target and
maximizing energy efficiency of sensor node. Measurement results show that the new algorithm could increase 80%
longer network lifetime and achieve more adaptability and stability.
International Journal of Engineering, Applied and Management Sciences Paradigms (IJEAM)
Volume 54 Issue 3 June 2019 366 ISSN 2320-6608
Gu et. al., discussed the two important contributions. The first contribution is to have two lifetime upper bounds,
which could be used to justify performance of previously proposed heuristic algorithms. One upper bound is based
on the relaxation and reformulation technique while the other is derived by relaxing coverage constraints. We study
the interesting connection between those two bounds and thus endow them with physical meanings. The second
contribution is proposing a column generation based (CG) approach. The objective is to find an optimal schedule,
defined as a time table specifying from what time up to what time which sensor watches which targets while the
maximum lifetime has been obtained. We also offer an in-depth theoretic analysis as well as several novel
techniques to further optimize the approach. Numerical results not only demonstrate that the lifetime upper bounds
are very tight, but also verify that the proposed CG based approach constantly yields the optimal or near optimal
solution.
Zhao and Gurusamy proposed an algorithm CWGC which states the connected target coverage problem. This paper
consists of the theoretical analysis of the target coverage problem and then this problem has been modelled as
maximum cover tree problem. The theoretical analysis has been done in order to prove that the handled problem is
NP complete. They proposed two concepts namely greedy based method and approximation algorithm for
effectively solving target coverage problem. The considered factors of this paper are connectivity between sensors,
coverage of target nodes and real-time energy consumption model which is based on the distance between nodes.
Greedy method has been used to select the edges or the paths where the residual energy is high at each instance.
However, on applying this method the algorithm expects a recompilation of weights between the nodes when a new
cover set is generated.
Lu, Mingming et. al., this paper generalizes the sleep/active mode by adjusting sensing range to maximize total
number of rounds and presents a distributed heuristic to address this problem.
This paper is organized as follows. Section 1 describes introduction about the wireless sensor network, k coverage
connected nodes. Section 2 explains the literature review. Section 3 describes the proposed work. Experimental
results and discussion are described in the section 4. Finally, section 5 concludes the paper.
III. PROPOSED WORK
3.1. Nelder-Mead Method
Nelder-Mead (NM) algorithm also known as simplex search algorithm which was introduced in the year 1965 for
solving multidimensional optimization problem without taking the derivatives of them. Derivatives gives precise
results for optimization problems but the computational cost is expensive. NM Method was originally developed for
soling unconstrained optimization problems. Since it does not use derivative forms this method can be easily
adaptable for non-smooth functions.
NM method consists of four steps for achieving best solution from the given points or coordinates. The four steps
includes reflection, contraction, expansion a shrinkage. At initial stage a simplex transformation method is followed
in NM method in which the four steps which are discussed above will be a subcategory.
Ordering
Calculate the best ( ), second best ( ) and the worst points ( ) from the given position in the search space using
simplex method. For a maximization problem the computation will be as follows.
; ;
3.2. Centroid
Compute the centroid between and
International Journal of Engineering, Applied and Management Sciences Paradigms (IJEAM)
Volume 54 Issue 3 June 2019 367 ISSN 2320-6608
3.3. Transformation
The transformation from one region in the search space to the other best position has been carried out in four steps
as it is discussed above. Initially the worst point will be replaced any of the best points using the above-mentioned
methods. The four steps are controlled by four different parameters namely using respectively. the control
parametric values are .
3.4 Reflection
Determine the reflection point using the calculated centroid and best point as follows
Compute the fitness value of point using the fitness function such that
The computed will be replaced by the worst solution if it satisfies the below Equation
3.5 Expansion
Determine the expansion point using the calculated centroid and reference point as follows
Compute the fitness value of point using the fitness function such that
The computed will be replaced by the reference point if it satisfies the below Equation
3.6 Contraction
If the computed reference point is lesser than the second-best position ( ) determine the contraction point
using and
Outside: If then determine
Compute the fitness value of point using the fitness function such that
The computed will be replaced by the referenced point if it satisfies the below Equation
Or else the shrink transformation will be called on for carrying the transformation process.
International Journal of Engineering, Applied and Management Sciences Paradigms (IJEAM)
Volume 54 Issue 3 June 2019 368 ISSN 2320-6608
Inside: If then determine
Compute the fitness value of point using the fitness function such that
The computed will be replaced by the best points if it satisfies the below Equation
Or else the shrink transformation will be called on for carrying the transformation process.
Shrink
Calculate new points using random points between best and neighborhood points
Compute the fitness value of point using the fitness function such that
3.7 .ABC-NM for Coverage Connected Problem
ABC-NM pseudocode shows the hybrid version of ABC algorithm and mathematical Nelder Mead method for
solving connected coverage problem. The objectives of the connected coverage problem will be stated in 4.3.1. the
proposed concept will be given in Algorithm 4.1.
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IV. EXPERIMENTAL RESULTS AND DISCUSSION
The proposed algorithm has been implemented in MATLAB v9 in a system with Intel core i7 processor with 3.2
GHz clock speed with 4GB RAM and 1TB HDD. The problem of coverage and connected node placement has
been designed and implemented in MATLAB using three different grid scenarios under different region: WSN1 -
300 300 meters, WSN2 - 500 500 meters and WSN3 - 700 700 meters. The sink nodes positions for WSN1,
WSN2 and WSN3 are (300, 150), (500,250) and (700,350) respectively.
Table 1. Parameter Settings
Parameters For 100 Targets For 200 Targets
Grid Size
300X300,
500X500,
700X700
300X300,
500X500,
700X700
Available Positions 100, 150, 200, 250 200, 250, 300, 350
Communication Range 50 meters 25 meters
Sensing Range 40 meters 20 meters
Population Size 50 50
Iteration 1000 1500
1, 2 1, 2
Table 2 shows the simulated values of F on 100 target nodes with different number of available potential positions.
The simulation has been carried out on six different algorithms with the same simulation parameters.
Table 2. F-Value on 100 target nodes with varied #potential positions
Range Dimension PP Greedy Mini et
al GA-R GA-G HPG
ABC-
NM
k=1,
m=1
300X300
100 0.46 0.32 0.29 0.28 0.26 0.24
150 0.29 0.21 0.18 0.18 0.17 0.15
200 0.2 0.15 0.13 0.13 0.13 0.11
250 0.15 0.11 0.1 0.1 0.09 0.08
500X500
100 0.59 0.56 0.55 0.53 0.49 0.48
150 0.37 0.36 0.35 0.35 0.31 0.31
200 0.27 0.26 0.26 0.26 0.23 0.23
250 0.21 0.2 0.19 0.19 0.17 0.18
700X700
100 0.75 0.72 0.71 0.69 0.65 0.64
150 0.47 0.46 0.45 0.45 0.41 0.41
200 0.34 0.33 0.33 0.34 0.3 0.29
250 0.25 0.24 0.24 0.24 0.23 0.22
k=1,
m=2
300X300
100 0.49 0.37 0.34 0.31 0.34 0.26
150 0.32 0.22 0.2 0.19 0.21 0.17
200 0.23 0.15 0.12 0.14 0.13 0.13
250 0.17 0.11 0.09 0.1 0.1 0.09
500X500
100 0.6 0.59 0.58 0.55 0.53 0.5
150 0.4 0.39 0.38 0.33 0.34 0.33
200 0.29 0.29 0.27 0.23 0.25 0.25
250 0.22 0.22 0.21 0.18 0.18 0.18
700X700
100 0.75 0.74 0.73 0.7 0.68 0.65
150 0.47 0.46 0.45 0.4 0.41 0.41
200 0.34 0.34 0.32 0.28 0.3 0.29
250 0.25 0.25 0.24 0.21 0.23 0.22
k=2,
m=1 300X300
100 0.44 0.3 0.27 0.27 0.24 0.23
150 0.27 0.18 0.18 0.17 0.15 0.14
200 0.18 0.13 0.12 0.13 0.1 0.11
250 0.14 0.1 0.09 0.1 0.08 0.08
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Volume 54 Issue 3 June 2019 373 ISSN 2320-6608
500X500
100 0.57 0.55 0.53 0.51 0.49 0.47
150 0.37 0.35 0.35 0.33 0.31 0.31
200 0.27 0.25 0.23 0.24 0.23 0.23
250 0.2 0.19 0.18 0.19 0.18 0.18
700X700
100 0.75 0.73 0.71 0.69 0.67 0.65
150 0.47 0.46 0.45 0.44 0.42 0.41
200 0.34 0.33 0.3 0.32 0.3 0.29
250 0.25 0.24 0.23 0.24 0.23 0.22
k=2,
m=2
300X300
100 0.42 0.29 0.27 0.26 0.24 0.23
150 0.27 0.19 0.17 0.15 0.16 0.15
200 0.19 0.13 0.13 0.11 0.1 0.11
250 0.13 0.1 0.1 0.08 0.08 0.09
500X500
100 0.55 0.53 0.5 0.47 0.46 0.43
150 0.34 0.33 0.33 0.31 0.29 0.29
200 0.25 0.25 0.25 0.23 0.29 0.21
250 0.2 0.19 0.2 0.18 0.17 0.16
700X700
100 0.75 0.73 0.7 0.67 0.66 0.63
150 0.47 0.47 0.47 0.45 0.43 0.41
200 0.34 0.34 0.34 0.32 0.3 0.29
250 0.25 0.24 0.25 0.23 0.23 0.22
Table 3 shows the simulated values of F on 200 target nodes with different number of available potential positions.
The simulation has been carried out on six different algorithms with the same simulation parameters.
Table 3. F-Value on 200 target nodes with varied #potential positions
Range Dimension PP Greedy Mini et
al GA-R GA-G HPG
ABC-
NM
k=1,
m=1
300X300
200 0.46 0.32 0.29 0.28 0.26 0.12
250 0.22 0.16 0.14 0.14 0.13 0.09
300 0.13 0.1 0.09 0.08 0.08 0.07
350 0.09 0.07 0.06 0.06 0.06 0.06
500X500
200 0.59 0.56 0.55 0.53 0.49 0.24
250 0.28 0.27 0.27 0.26 0.23 0.18
300 0.18 0.17 0.17 0.17 0.15 0.15
350 0.13 0.12 0.12 0.12 0.11 0.13
700X700
200 0.38 0.35 0.34 0.32 0.28 0.32
250 0.28 0.27 0.27 0.26 0.23 0.25
300 0.23 0.22 0.22 0.22 0.2 0.19
350 0.18 0.17 0.17 0.17 0.16 0.16
k=1,
m=2
300X300
200 0.49 0.37 0.34 0.31 0.34 0.13
250 0.24 0.17 0.15 0.15 0.16 0.1
300 0.15 0.1 0.08 0.09 0.09 0.08
350 0.11 0.07 0.06 0.07 0.06 0.07
500X500
200 0.61 0.59 0.58 0.55 0.53 0.25
250 0.3 0.29 0.29 0.25 0.26 0.2
300 0.19 0.19 0.18 0.15 0.16 0.16
350 0.14 0.14 0.13 0.11 0.12 0.13
700X700
200 0.38 0.36 0.35 0.32 0.3 0.33
250 0.28 0.27 0.27 0.23 0.24 0.25
300 0.23 0.22 0.21 0.19 0.2 0.19
350 0.18 0.18 0.17 0.15 0.16 0.16
k=2,
m=1 300X300
200 0.44 0.3 0.27 0.27 0.24 0.12
250 0.2 0.14 0.14 0.13 0.12 0.08
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300 0.12 0.09 0.08 0.09 0.07 0.07
350 0.09 0.07 0.06 0.06 0.05 0.06
500X500
200 0.57 0.55 0.53 0.51 0.49 0.24
250 0.28 0.27 0.26 0.25 0.24 0.18
300 0.18 0.17 0.15 0.16 0.15 0.15
350 0.13 0.12 0.11 0.12 0.11 0.13
700X700
200 0.38 0.36 0.34 0.32 0.3 0.33
250 0.28 0.27 0.27 0.26 0.24 0.25
300 0.23 0.22 0.2 0.21 0.2 0.19
350 0.18 0.17 0.17 0.18 0.16 0.16
k=2,
m=2
300X300
200 0.42 0.29 0.27 0.26 0.24 0.12
250 0.21 0.14 0.13 0.11 0.12 0.09
300 0.13 0.09 0.09 0.07 0.07 0.07
350 0.08 0.06 0.06 0.05 0.05 0.06
500X500
200 0.55 0.53 0.5 0.47 0.46 0.22
250 0.26 0.25 0.25 0.24 0.22 0.17
300 0.17 0.16 0.16 0.15 0.14 0.14
350 0.13 0.12 0.12 0.11 0.11 0.11
700X700
200 0.38 0.36 0.33 0.3 0.29 0.32
250 0.28 0.28 0.28 0.26 0.25 0.25
300 0.23 0.22 0.22 0.21 0.2 0.19
350 0.18 0.18 0.18 0.17 0.16 0.16
On comparing the mean of F-values for 100 target nodes our proposed ABC-NM outperforms existing algorithms
with 84% against Greedy, 29% against Mini, 17% against GA-R, 14% against GA-G and 9% against HPG on
300X300 grid size. On 500X500 grid ABC-NM outperforms existing algorithms with 20% against Greedy, 16%
against Mini, 13% against GA-R, 7% against GA-G and 2% against HPG. On 700X700 grid ABC-NM outperforms
existing algorithms with 16% against Greedy, 13% against Mini, 11% against GA-R, 7% against GA-G and 3%
against HPG.
On comparing the mean of F-values for 200 target nodes our proposed ABC-NM outperforms existing algorithms
with 100% against Greedy, 83% against Mini, 66% against GA-R, 60% against GA-G and 54% against HPG on
300X300 grid size. On 500X500 grid ABC-NM outperforms existing algorithms with 69% against Greedy, 62%
against Mini, 57% against GA-R, 49% against GA-G and 43% against HPG. On 700X700 grid ABC-NM
outperforms existing algorithms with 16% against Greedy, 11% against Mini, 8% against GA-R, 3% against GA-G.
However proposed ABC-NM performance has been degraded by 4% against HPG.
Table 4 shows the computational time on 100 target nodes with different number of available potential positions.
The simulation has been carried out on six different algorithms with the same simulation parameters.
Table 4.Computational Time on 100 target nodes with varied #potential positions
bb Dimension PP Greedy Mini et
al GA-R GA-G HPG
ABC-
NM
k=1,
m=1
300X300
100 5.71 5.94 4.19 6.48 4.64 5.27
150 6.04 5.41 6.49 6.02 6.76 4.09
200 6.42 5.08 5.33 5.03 4.65 5.65
250 4.82 5.08 5.4 5.02 5.22 5.48
500X500
100 10.23 8.11 8.93 9.34 8.67 8.9
150 9.15 11.36 9.84 9.85 8.55 8.1
200 9.09 11.04 11.52 8.72 10.26 7.83
250 8.29 8.3 9.09 8.33 10.71 9.93
700X700
100 13.93 13.08 13.29 12.72 13.16 11.83
150 11.37 11.63 12.92 14.72 12.72 11.2
200 14.74 11.74 12.7 13.45 12.25 14.89
250 14.93 14.33 11.36 14.69 14.74 12.15
k=1, 300X300 100 4.29 5.34 5.11 6.5 5.76 6.95
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m=2 150 6.65 5.68 4.86 5.54 4.75 6.62
200 6.65 5.48 6.63 6.91 5.18 4.05
250 4.69 5.15 6.81 6.79 4.74 4.71
500X500
100 8.02 7.28 10.35 8.54 8.81 9.28
150 8.11 10.91 9.43 9.02 8.12 9.04
200 8.25 8.98 11.23 10.88 9.06 9.04
250 10.41 12.34 10.04 10.41 8.64 8.52
700X700
100 13.23 11.09 13.36 13.19 13.75 14.01
150 12.78 13.71 12.28 13.86 11.33 13.48
200 13.8 11.28 14.07 14.63 12.43 11.4
250 13.26 14.7 14.51 11.59 11.2 13.81
k=2,
m=1
300X300
100 4.32 5.97 5.51 6.17 4.24 5.45
150 5.21 5.21 5.25 6.77 4.17 4.94
200 6.47 5.37 4.95 5.25 4.3 4.59
250 5.46 5.81 5.42 5.01 4.23 4.4
500X500
100 8.69 9.36 9.03 9.35 8.13 7.55
150 9.03 11.41 11.13 8.02 10.03 7.07
200 9.98 7.39 8.92 9.49 9.27 7.91
250 8.52 12.55 10.47 10.25 9.46 9.15
700X700
100 12.16 13.16 12.11 13.15 13.88 11.66
150 11.59 11.72 14.4 14.93 11 14.75
200 14.52 11.58 12.16 14.22 14.47 11.53
250 12.54 11.76 14.02 11.86 11.25 11.8
k=2,
m=2
300X300
100 4.07 5.49 4.82 5.19 4.99 4.82
150 6.51 5.69 4.45 6.81 6.94 4.27
200 6.67 5.82 6.28 5.12 4.96 6.42
250 6.49 6 6.27 6.86 6.31 4.73
500X500
100 9.67 12.04 9.03 10.8 9.18 9.29
150 9.34 7.57 11.13 9.27 10.99 7.05
200 10.91 10.87 8.92 8.69 10.89 9.51
250 10.43 10.69 10.47 8.61 8.17 7.87
700X700
100 14.28 11.58 13.55 12.12 11.92 14.31
150 12.81 12.14 14.47 13.49 14.03 11.79
200 12.25 13.15 12.82 14.73 12.26 13.25
250 13.69 14.58 12.76 12.4 12.23 13.75
Table 5 shows the computational time on 200 target nodes with different number of available potential positions.
The simulation has been carried out on six different algorithms with the same simulation parameters.
Table 5. Computational Time on 200 target nodes with varied #potential positions\
Range Dimension PP Greedy Mini et
al GA-R GA-G HPG
ABC-
NM
k=1,
m=1
300X300
200 7.84 8.23 7.05 8.85 7.68 8.71
250 7.26 8.37 7.88 8.2 7.36 8.83
300 7.18 8.48 8.31 8.55 7.23 8.73
350 8.43 7.22 7.98 7.57 8.92 8.75
500X500
200 12.83 12.55 10.32 10.59 10.19 10.48
250 13 12.53 10.57 10.69 11.6 11.96
300 11.86 11.28 12.07 11.75 12.09 12.93
350 10.61 10.15 10.04 11.2 11.95 12.49
700X700
200 19.58 17.18 17.71 17.74 18.86 18.51
250 19.41 17.96 17.31 19.1 17.47 19.37
300 19.9 19.06 18.48 18.55 18.26 17.98
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350 19.26 18.66 18.24 19.78 17.04 18.55
k=1,
m=2
300X300
200 7.88 8.94 8.25 8.72 8.59 8.34
250 7 7.09 8.25 7.06 8.23 7.35
300 8.8 7.57 7.34 7.2 8.12 8.37
350 8.62 7.8 8.77 8.02 8.21 8.73
500X500
200 11.91 12.88 11.93 10.1 12.59 10.55
250 11.74 11.23 12.14 11.93 12.82 12.81
300 10.38 12.89 11.51 11.12 10.88 10.08
350 12.44 11.26 11.93 11.66 12.07 10.02
700X700
200 19.59 18.9 17.69 19.34 18.5 18.53
250 18.93 17.09 18.59 19.59 17.1 18.35
300 18.88 17.47 18.49 19.96 17.96 17.18
350 17.57 19.31 19.19 17.1 19.8 18.43
k=2,
m=1
300X300
200 7.94 8.4 8.27 7.16 7.74 7.34
250 8.83 8.88 7.76 7.41 7.85 7.21
300 7.1 8.65 7.3 8.94 7.48 7.97
350 8.1 7.15 8 8.69 8.67 8.26
500X500
200 11.31 10.23 11.11 12.68 12.19 12.62
250 12.5 10.28 10.25 11 10.14 11.51
300 10.2 12.42 12.98 12.88 10.17 11.8
350 12.01 11.74 10.02 11.49 11.07 10.18
700X700
200 19.62 19.47 19.72 18.49 19.69 19.29
250 18.84 18.52 19.39 17.96 18.27 18.84
300 17.12 19.43 19.69 18.9 18.72 17.83
350 19.88 18.35 19.95 19.41 18.03 17.81
k=2,
m=2
300X300
200 8.51 8.64 7.55 8.19 7.26 8.58
250 8.64 7.06 7.21 7.15 8.2 7.73
300 8.12 8.23 8.12 7.21 7.69 7.78
350 8.11 7.01 8.11 8.94 8.95 7.51
500X500
200 12.23 10.16 11.08 12.97 10.05 10.4
250 11.92 12.69 10.82 12.04 12.08 12.03
300 11.09 12.49 12.53 11.74 10.84 11.52
350 12.48 12.69 13 11.43 10.34 12.59
700X700
200 17.6 19.74 17.3 18.83 17.34 17.08
250 17.31 18.93 17.6 17.49 18.72 17.64
300 17.07 19.9 17.54 18.38 17.64 17.85
350 19.29 19.37 18.22 17.93 18.91 18.66
On comparing the mean of computational time for 100 target nodes our proposed ABC-NM outperforms existing
algorithms with 10% against Greedy, 7% against Mini, 6% against GA-R, 16% against GA-G on 300X300 grid.
However, it takes high computational time against HPG with 1%. On 500X500 grid ABC-NM outperforms existing
algorithms with 9% against Greedy, 18% against Mini, 17% against GA-R, 10% against GA-G and 9% against
HPG. On 700X700 grid ABC-NM outperforms existing algorithms with 3% against Greedy, 13% against Mini, 3%
against GA-R, 5% against. Also, ABC-NM shows a degrade of 2% against Min, et al. and 1% against HPG.
On comparing the mean of computational time for 200 target nodes our proposed ABC-NM outperforms existing
algorithms with 2% against Greedy, 2% against Mini, 66% against GA-R, 1% against GA-G and shows high
computational time with 1% against GA-R and 2% against HPG on 500X500 grid size. On 700X700 grid ABC-NM
outperforms existing algorithms with 3% against Greedy, 3% against Mini, 1% against GA-R, 2% against GA-G.
However proposed ABC-NM performance has been degraded by 0.3% against HPG. On 300X300 grid in all the
instances proposed ABC-NM takes high computational time.
Table 6 shows the simulated results in terms of average coverage of each sensor on 100 target nodes with different
number of available potential positions. The simulation has been carried out on six different algorithms with the
same simulation parameters.
International Journal of Engineering, Applied and Management Sciences Paradigms (IJEAM)
Volume 54 Issue 3 June 2019 377 ISSN 2320-6608
Table 6. Average Coverage on 100 target nodes with varied #potential positions
Range Dimension PP Greedy Mini et
al GA-R GA-G HPG
ABC-
NM
k=1,
m=1
300X300
100 2.17 3.13 3.45 3.57 3.85 4.17
150 2.33 3.23 3.70 3.70 4.00 4.35
200 2.56 3.45 3.85 4.00 4.00 4.76
250 2.70 3.57 4.17 4.17 4.35 4.76
500X500
100 1.69 1.79 1.82 1.89 2.04 2.08
150 1.79 1.85 1.89 1.92 2.17 2.17
200 1.89 1.96 1.96 1.92 2.22 2.17
250 1.92 2.04 2.08 2.08 2.33 2.22
700X700
100 1.33 1.39 1.41 1.45 1.54 1.56
150 1.41 1.45 1.47 1.49 1.64 1.61
200 1.47 1.52 1.52 1.49 1.67 1.72
250 1.59 1.67 1.69 1.69 1.75 1.82
k=1,
m=2
300X300
100 2.04 2.70 2.94 3.23 2.94 3.85
150 2.08 3.03 3.33 3.45 3.23 4.00
200 2.17 3.45 4.17 3.57 3.85 4.00
250 2.38 3.70 4.55 3.85 4.00 4.35
500X500
100 1.67 1.69 1.72 1.82 1.89 2.00
150 1.67 1.72 1.75 2.04 1.96 2.04
200 1.72 1.75 1.85 2.17 2.04 2.04
250 1.79 1.82 1.92 2.22 2.17 2.17
700X700
100 1.33 1.35 1.37 1.43 1.47 1.54
150 1.41 1.45 1.47 1.67 1.61 1.61
200 1.47 1.49 1.56 1.79 1.67 1.72
250 1.59 1.61 1.69 1.92 1.75 1.82
k=2,
m=1
300X300
100 2.27 3.33 3.70 3.70 4.17 4.35
150 2.50 3.70 3.70 3.85 4.35 4.76
200 2.78 3.85 4.17 3.85 5.00 4.76
250 2.94 3.85 4.35 4.17 5.26 5.00
500X500
100 1.75 1.82 1.89 1.96 2.04 2.13
150 1.82 1.89 1.92 2.00 2.13 2.17
200 1.89 2.00 2.22 2.08 2.17 2.17
250 2.00 2.13 2.22 2.08 2.27 2.22
700X700
100 1.33 1.37 1.41 1.45 1.49 1.54
150 1.41 1.45 1.47 1.52 1.59 1.61
200 1.47 1.54 1.67 1.59 1.67 1.72
250 1.59 1.67 1.72 1.64 1.75 1.82
k=2,
m=2
300X300
100 2.38 3.45 3.70 3.85 4.17 4.35
150 2.44 3.57 3.85 4.55 4.17 4.35
200 2.63 3.85 3.85 4.76 5.00 4.55
250 3.03 4.00 4.17 5.26 5.00 4.55
500X500
100 1.82 1.89 2.00 2.13 2.17 2.33
150 1.96 2.00 2.00 2.13 2.27 2.33
200 2.00 2.04 2.04 2.22 2.33 2.38
250 2.00 2.08 2.04 2.27 2.33 2.50
700X700
100 1.33 1.37 1.43 1.49 1.52 1.59
150 1.41 1.43 1.43 1.49 1.56 1.61
200 1.47 1.49 1.49 1.59 1.67 1.72
250 1.59 1.64 1.61 1.75 1.75 1.82
International Journal of Engineering, Applied and Management Sciences Paradigms (IJEAM)
Volume 54 Issue 3 June 2019 378 ISSN 2320-6608
Table 7 shows the simulated results in terms of average coverage of each sensor on 200 target nodes with different
number of available potential positions. The simulation has been carried out on six different algorithms with the
same simulation parameters.
Table 7. Average Coverage on 200 target nodes with varied #potential positions
Range Dimension PP Greedy Mini et
al GA-R GA-G HPG
ABC-
NM
k=1,
m=1
300X300
200 2.17 3.13 3.45 3.57 3.85 4.17
250 3.72 5.16 5.93 5.93 6.40 6.96
300 5.13 6.90 7.69 8.00 8.00 9.52
350 6.18 8.16 9.52 9.52 9.94 10.88
500X500
200 1.69 1.79 1.82 1.89 2.04 2.08
250 2.86 2.96 3.02 3.08 3.48 3.48
300 3.77 3.92 3.92 3.85 4.44 4.35
350 4.40 4.66 4.76 4.76 5.32 5.08
700X700
200 2.67 2.90 2.99 3.17 3.64 3.77
250 2.82 2.92 2.97 3.03 3.42 3.23
300 2.94 3.03 3.03 2.99 3.33 3.45
350 3.17 3.31 3.36 3.36 3.51 3.64
k=1,
m=2
300X300
200 2.04 2.70 2.94 3.23 2.94 3.85
250 3.33 4.85 5.33 5.52 5.16 6.40
300 4.35 6.90 8.33 7.14 7.69 8.00
350 5.44 8.47 10.39 8.79 9.14 9.94
500X500
200 1.64 1.69 1.72 1.82 1.89 2.00
250 2.67 2.76 2.81 3.27 3.14 3.27
300 3.45 3.51 3.70 4.35 4.08 4.08
350 4.08 4.16 4.40 5.08 4.97 4.97
700X700
200 2.67 2.82 2.90 3.17 3.39 3.77
250 2.82 2.92 2.97 3.49 3.35 3.23
300 2.94 2.99 3.13 3.57 3.33 3.45
350 3.17 3.22 3.36 3.75 3.51 3.64
k=2,
m=1
300X300
200 2.27 3.33 3.70 3.70 4.17 4.35
250 4.00 5.93 5.93 6.15 6.96 7.62
300 5.56 7.69 8.33 7.69 10.00 9.52
350 6.72 8.79 9.94 9.52 12.03 11.43
500X500
200 1.75 1.82 1.89 1.96 2.04 2.13
250 2.91 3.02 3.08 3.20 3.40 3.48
300 3.77 4.00 4.44 4.17 4.35 4.35
350 4.57 4.86 5.08 4.76 5.19 5.08
700X700
200 2.67 2.82 2.99 3.17 3.39 3.64
250 2.82 2.92 2.97 3.09 3.28 3.23
300 2.94 3.08 3.33 3.17 3.33 3.45
350 3.17 3.31 3.41 3.27 3.51 3.64
k=2,
m=2
300X300
200 2.38 3.45 3.70 3.85 4.17 4.35
250 3.90 5.71 6.15 7.27 6.67 6.96
300 5.26 7.69 7.69 9.52 10.00 9.09
350 6.93 9.14 9.52 12.03 11.43 10.39
500X500
200 1.82 1.89 2.00 2.13 2.17 2.33
250 3.14 3.20 3.20 3.40 3.64 3.72
300 4.00 4.08 4.08 4.44 4.65 4.76
350 4.57 4.76 4.66 5.19 5.32 5.71
700X700 200 2.67 2.82 3.08 3.39 3.51 3.92
250 2.82 2.87 2.87 3.03 3.21 3.23
International Journal of Engineering, Applied and Management Sciences Paradigms (IJEAM)
Volume 54 Issue 3 June 2019 379 ISSN 2320-6608
300 2.94 2.99 2.99 3.17 3.33 3.45
350 3.17 3.27 3.22 3.46 3.51 3.64
On comparing the mean of average value for 100 target nodes our proposed ABC-NM outperforms existing
algorithms with 44% against Greedy, 21% against Mini, 13% against GA-R, 10% against GA-G and 5% against
HPG on 300X300 grid size. On 500X500 grid ABC-NM outperforms existing algorithms with 16% against Greedy,
13% against Mini, 11% against GA-R, 6% against GA-G and 2% against HPG. On 700X700 grid ABC-NM
outperforms existing algorithms with 14% against Greedy, 11% against Mini, 9% against GA-R, 5% against GA-G
and 3% against HPG.
On comparing the mean of F-values for 200 target nodes our proposed ABC-NM outperforms existing algorithms
with 44% against Greedy, 21% against Mini, 12% against GA-R, 10% against GA-G and 4% against HPG on
300X300 grid size. On 500X500 grid ABC-NM outperforms existing algorithms with 16% against Greedy, 13%
against Mini, 10% against GA-R, 6% against GA-G and 1% against HPG. On 700X700 grid ABC-NM outperforms
existing algorithms with 18% against Greedy, 15% against Mini, 12% against GA-R, 7% against GA-G and 3%
against HPG.
Table 8 shows the simulated results in terms of connection cost of each sensor on 100 target nodes with different
number of available potential positions. The simulation has been carried out on six different algorithms with the
same simulation parameters.
Table 8. Connection Cost on 100 target nodes with varied #potential positions
Range Dimension PP Greedy Mini et
al GA-R GA-G HPG
ABC-
NM
k=1,
m=1
300X300
100 0.85 0.86 0.88 0.90 0.91 0.97
150 0.83 0.85 0.87 0.88 0.91 0.95
200 0.78 0.86 0.85 0.85 0.89 0.95
250 0.79 0.83 0.85 0.84 0.88 0.94
500X500
100 0.96 0.96 0.97 0.98 0.98 0.98
150 0.97 0.96 0.97 0.97 0.97 0.98
200 0.96 0.95 0.98 0.96 0.97 0.97
250 0.97 0.96 0.97 0.96 0.96 0.98
700X700
100 0.98 0.99 0.98 0.99 0.98 0.99
150 0.98 0.97 0.99 0.99 0.99 1.00
200 0.98 0.99 0.98 1.00 0.99 0.99
250 0.97 0.97 0.99 0.98 0.98 0.98
k=1,
m=2
300X300
100 0.85 0.92 0.91 0.93 0.94 0.97
150 0.86 0.91 0.89 0.90 0.91 0.97
200 0.84 0.86 0.88 0.85 0.89 0.97
250 0.83 0.86 0.87 0.81 0.88 0.96
500X500
100 0.97 0.98 0.98 0.98 0.98 0.99
150 0.97 0.97 0.98 0.97 0.97 0.98
200 0.97 0.97 0.97 0.97 0.97 0.98
250 0.96 0.96 0.96 0.97 0.97 0.97
700X700
100 0.98 0.98 0.98 1.00 0.98 0.99
150 0.99 0.99 0.98 0.99 0.99 0.99
200 0.99 0.98 0.97 0.98 0.98 0.99
250 0.98 0.97 0.98 0.98 0.99 0.98
k=2,
m=1
300X300
100 0.83 0.84 0.87 0.87 0.91 0.96
150 0.79 0.81 0.87 0.87 0.87 0.94
200 0.78 0.76 0.86 0.83 0.86 0.94
250 0.76 0.73 0.83 0.82 0.87 0.92
500X500
100 0.96 0.97 0.97 0.97 0.99 0.97
150 0.97 0.96 0.96 0.98 0.97 0.98
200 0.96 0.96 0.97 0.97 0.97 0.97
250 0.97 0.97 0.98 0.97 0.97 0.96
International Journal of Engineering, Applied and Management Sciences Paradigms (IJEAM)
Volume 54 Issue 3 June 2019 380 ISSN 2320-6608
700X700
100 0.98 0.99 0.99 1.00 0.98 0.99
150 0.98 0.99 0.99 0.99 1.00 0.99
200 0.98 0.98 0.99 0.98 0.99 1.00
250 0.99 0.98 0.98 0.98 0.97 0.99
k=2,
m=2
300X300
100 0.83 0.84 0.87 0.87 0.88 0.95
150 0.82 0.83 0.80 0.85 0.87 0.95
200 0.81 0.75 0.78 0.86 0.87 0.94
250 0.81 0.77 0.74 0.83 0.86 0.92
500X500
100 0.95 0.96 0.97 0.98 0.98 0.98
150 0.96 0.95 0.96 0.96 0.98 0.97
200 0.95 0.95 0.96 0.96 0.96 0.97
250 0.95 0.96 0.97 0.96 0.97 0.97
700X700
100 0.99 0.99 0.99 1.00 0.98 0.99
150 0.99 0.98 1.00 0.99 0.99 0.98
200 0.98 0.98 0.98 0.98 0.98 0.99
250 0.98 0.97 0.98 0.98 0.99 0.99
Table 9 shows the simulated results in terms of connection cost of each sensor on 200 target nodes with different
number of available potential positions. The simulation has been carried out on six different algorithms with the
same simulation parameters.
Table 9.Connection Cost on 200 target nodes with varied #potential positions
Range Dimension PP Greedy Mini et
al GA-R GA-G HPG
ABC-
NM
k=1,
m=1
300X300
200 0.92 0.93 0.95 0.95 0.96 0.98
250 0.76 0.80 0.83 0.83 0.87 0.93
300 0.55 0.69 0.69 0.71 0.77 0.87
350 0.41 0.51 0.55 0.56 0.67 0.82
500X500
200 0.98 0.99 0.99 0.99 0.99 0.99
250 0.95 0.95 0.95 0.96 0.96 0.97
300 0.91 0.91 0.94 0.92 0.93 0.94
350 0.88 0.86 0.90 0.89 0.90 0.91
700X700
200 0.93 0.94 0.95 0.96 0.97 0.97
250 0.95 0.95 0.96 0.96 0.96 0.96
300 0.94 0.95 0.96 0.96 0.96 0.96
350 0.94 0.94 0.95 0.95 0.95 0.96
k=1,
m=2
300X300
200 0.93 0.96 0.96 0.97 0.97 0.99
250 0.80 0.87 0.85 0.87 0.89 0.95
300 0.68 0.71 0.75 0.66 0.77 0.91
350 0.52 0.59 0.62 0.47 0.65 0.86
500X500
200 0.99 0.99 0.99 0.99 0.99 0.99
250 0.95 0.96 0.95 0.97 0.97 0.97
300 0.92 0.92 0.91 0.94 0.94 0.95
350 0.88 0.88 0.88 0.91 0.92 0.92
700X700
200 0.93 0.94 0.96 0.97 0.96 0.97
250 0.96 0.95 0.94 0.96 0.96 0.96
300 0.95 0.95 0.94 0.95 0.96 0.96
350 0.94 0.94 0.94 0.95 0.95 0.96
k=2,
m=1
300X300
200 0.91 0.92 0.94 0.94 0.95 0.98
250 0.72 0.76 0.81 0.83 0.83 0.92
300 0.55 0.50 0.71 0.66 0.71 0.85
350 0.35 0.28 0.56 0.51 0.62 0.78
500X500 200 0.98 0.99 0.98 0.99 0.99 0.99
250 0.95 0.95 0.95 0.95 0.96 0.96
International Journal of Engineering, Applied and Management Sciences Paradigms (IJEAM)
Volume 54 Issue 3 June 2019 381 ISSN 2320-6608
300 0.91 0.91 0.92 0.90 0.93 0.94
350 0.88 0.87 0.90 0.87 0.88 0.90
700X700
200 0.94 0.95 0.95 0.96 0.96 0.97
250 0.96 0.95 0.96 0.96 0.96 0.97
300 0.95 0.95 0.95 0.95 0.96 0.96
350 0.94 0.94 0.95 0.95 0.95 0.96
k=2,
m=2
300X300
200 0.91 0.92 0.93 0.93 0.94 0.97
250 0.77 0.78 0.74 0.82 0.84 0.93
300 0.59 0.51 0.55 0.71 0.71 0.87
350 0.47 0.35 0.28 0.56 0.59 0.77
500X500
200 0.98 0.98 0.98 0.99 0.99 0.99
250 0.94 0.94 0.95 0.95 0.96 0.96
300 0.89 0.89 0.91 0.92 0.92 0.93
350 0.84 0.87 0.87 0.90 0.89 0.90
700X700
200 0.93 0.94 0.95 0.95 0.97 0.97
250 0.96 0.95 0.96 0.96 0.97 0.97
300 0.95 0.95 0.96 0.96 0.96 0.96
350 0.94 0.95 0.95 0.96 0.95 0.96
On comparing the mean of connection cost for 100 target nodes our proposed ABC-NM outperforms existing
algorithms with 14% against Greedy, 13% against Mini, 11% against GA-R, 9% against GA-G and 7% against HPG
on 300X300 grid size. On 500X500 grid ABC-NM outperforms existing algorithms with 1% against Greedy, 1%
against Mini, 1% against GA-R, 1% against GA-G and performs equally with HPG. On 700X700 grid ABC-NM
outperforms existing algorithms with 1% against Greedy, 1% against Mini, and equally performs with GA-R, GA-G
and HPG.
On comparing the mean of connection cost for 200 target nodes our proposed ABC-NM outperforms existing
algorithms with 25% against Greedy, 23% against Mini, 18% against GA-R, 17% against GA-G and 12% against
HPG on 300X300 grid size. On 500X500 grid ABC-NM outperforms existing algorithms with 2% against Greedy,
2% against Mini, 2% against GA-R, 1% against GA-G and equally performs with HPG. On 700X700 grid ABC-NM
outperforms existing algorithms with 2% against Greedy, 2% against Mini, 1% against GA-R, 1% against GA-G and
equal performance with HPG.
Table 10 shows the simulated results in terms of coverage cost of each sensor on 100 target nodes with different
number of available potential positions. The simulation has been carried out on six different algorithms with the
same simulation parameters.
Table 10.Coverage Cost on 100 target nodes with varied #potential positions
Range Dimension PP Greedy Mini et
al GA-R GA-G HPG
ABC-
NM
k=1,
m=1
300X300
100 0.95 0.90 0.88 0.87 0.85 0.83
150 0.95 0.90 0.86 0.86 0.84 0.81
200 0.93 0.88 0.85 0.84 0.84 0.77
250 0.93 0.87 0.83 0.83 0.81 0.77
500X500
100 0.97 0.97 0.97 0.96 0.96 0.96
150 0.97 0.97 0.96 0.96 0.95 0.95
200 0.96 0.96 0.96 0.96 0.95 0.95
250 0.96 0.96 0.96 0.96 0.95 0.95
700X700
100 0.98 0.98 0.98 0.98 0.98 0.98
150 0.98 0.98 0.98 0.98 0.97 0.97
200 0.98 0.98 0.98 0.98 0.97 0.97
250 0.97 0.97 0.97 0.97 0.97 0.97
k=1,
m=2
300X300
100 0.96 0.93 0.91 0.90 0.91 0.85
150 0.96 0.91 0.89 0.88 0.90 0.84
200 0.95 0.88 0.83 0.87 0.85 0.84
250 0.94 0.86 0.79 0.85 0.84 0.81
500X500 100 0.97 0.97 0.97 0.97 0.96 0.96
International Journal of Engineering, Applied and Management Sciences Paradigms (IJEAM)
Volume 54 Issue 3 June 2019 382 ISSN 2320-6608
150 0.97 0.97 0.97 0.96 0.96 0.96
200 0.97 0.97 0.97 0.95 0.96 0.96
250 0.97 0.97 0.96 0.95 0.95 0.95
700X700
100 0.98 0.98 0.98 0.98 0.98 0.98
150 0.98 0.98 0.98 0.97 0.97 0.97
200 0.98 0.98 0.98 0.97 0.97 0.97
250 0.97 0.97 0.97 0.96 0.97 0.97
k=2,
m=1
300X300
100 0.95 0.89 0.86 0.86 0.83 0.81
150 0.94 0.86 0.86 0.85 0.81 0.77
200 0.92 0.85 0.83 0.85 0.75 0.77
250 0.91 0.85 0.81 0.83 0.72 0.75
500X500
100 0.97 0.97 0.96 0.96 0.96 0.95
150 0.97 0.96 0.96 0.96 0.95 0.95
200 0.96 0.96 0.95 0.96 0.95 0.95
250 0.96 0.95 0.95 0.96 0.95 0.95
700X700
100 0.98 0.98 0.98 0.98 0.98 0.98
150 0.98 0.98 0.98 0.98 0.97 0.97
200 0.98 0.98 0.97 0.97 0.97 0.97
250 0.97 0.97 0.97 0.97 0.97 0.97
k=2,
m=2
300X300
100 0.94 0.88 0.86 0.85 0.83 0.81
150 0.94 0.87 0.85 0.79 0.83 0.81
200 0.93 0.85 0.85 0.77 0.75 0.79
250 0.91 0.84 0.83 0.72 0.75 0.79
500X500
100 0.97 0.96 0.96 0.95 0.95 0.95
150 0.96 0.96 0.96 0.95 0.95 0.95
200 0.96 0.96 0.96 0.95 0.95 0.94
250 0.96 0.96 0.96 0.95 0.95 0.94
700X700
100 0.98 0.98 0.98 0.98 0.98 0.97
150 0.98 0.98 0.98 0.98 0.98 0.97
200 0.98 0.98 0.98 0.97 0.97 0.97
250 0.97 0.97 0.97 0.97 0.97 0.97
Table 11 shows the simulated results in terms of coverage cost of each sensor on 200 target nodes with different
number of available potential positions. The simulation has been carried out on six different algorithms with the
same simulation parameters.
Table 11. Coverage Cost on 200 target nodes with varied #potential positions
Range Dimension PP Greedy Mini et
al GA-R GA-G HPG
ABC-
NM
k=1,
m=1
300X300
200 0.98 0.95 0.94 0.94 0.93 0.91
250 0.93 0.87 0.82 0.82 0.80 0.76
300 0.87 0.76 0.70 0.68 0.68 0.55
350 0.81 0.67 0.55 0.55 0.51 0.41
500X500
200 0.99 0.98 0.98 0.98 0.98 0.98
250 0.96 0.96 0.95 0.95 0.94 0.94
300 0.93 0.92 0.92 0.93 0.90 0.91
350 0.90 0.89 0.89 0.89 0.86 0.87
700X700
200 0.96 0.96 0.96 0.95 0.93 0.93
250 0.96 0.96 0.96 0.95 0.94 0.95
300 0.96 0.95 0.95 0.96 0.94 0.94
350 0.95 0.95 0.94 0.94 0.94 0.93
k=1,
m=2 300X300
200 0.98 0.96 0.96 0.95 0.96 0.93
250 0.94 0.88 0.86 0.85 0.87 0.80
International Journal of Engineering, Applied and Management Sciences Paradigms (IJEAM)
Volume 54 Issue 3 June 2019 383 ISSN 2320-6608
300 0.91 0.76 0.65 0.74 0.70 0.68
350 0.85 0.64 0.46 0.61 0.58 0.51
500X500
200 0.99 0.99 0.99 0.98 0.98 0.98
250 0.96 0.96 0.96 0.95 0.95 0.95
300 0.94 0.94 0.93 0.91 0.92 0.92
350 0.92 0.91 0.90 0.87 0.88 0.88
700X700
200 0.96 0.96 0.96 0.95 0.94 0.93
250 0.96 0.96 0.96 0.94 0.94 0.95
300 0.96 0.96 0.95 0.94 0.94 0.94
350 0.95 0.95 0.94 0.93 0.94 0.93
k=2,
m=1
300X300
200 0.97 0.94 0.93 0.93 0.91 0.91
250 0.92 0.82 0.82 0.81 0.76 0.71
300 0.85 0.70 0.65 0.70 0.50 0.55
350 0.77 0.61 0.51 0.55 0.28 0.35
500X500
200 0.98 0.98 0.98 0.98 0.98 0.98
250 0.96 0.95 0.95 0.95 0.94 0.94
300 0.93 0.92 0.90 0.91 0.91 0.91
350 0.90 0.88 0.87 0.89 0.87 0.87
700X700
200 0.96 0.96 0.96 0.95 0.94 0.93
250 0.96 0.96 0.96 0.95 0.95 0.95
300 0.96 0.95 0.94 0.95 0.94 0.94
350 0.95 0.95 0.94 0.95 0.94 0.93
k=2,
m=2
300X300
200 0.97 0.94 0.93 0.93 0.91 0.91
250 0.92 0.84 0.81 0.74 0.78 0.76
300 0.86 0.70 0.70 0.55 0.50 0.59
350 0.76 0.58 0.55 0.28 0.35 0.46
500X500
200 0.98 0.98 0.98 0.98 0.98 0.97
250 0.95 0.95 0.95 0.94 0.93 0.93
300 0.92 0.92 0.92 0.90 0.89 0.89
350 0.90 0.89 0.89 0.87 0.86 0.84
700X700
200 0.96 0.96 0.95 0.94 0.94 0.92
250 0.96 0.96 0.96 0.95 0.95 0.95
300 0.96 0.96 0.96 0.95 0.94 0.94
350 0.95 0.95 0.95 0.94 0.94 0.93
On addressing coverage cost, proposed ABC-NM shows a minimal deflection when compared with other existing
algorithms on both 100 and 200 target tables Table 10 and Table 11. However, the proposed ABC-NM satisfies a
complete coverage without any compromise in network lifetime.
Table 12 shows the simulated results in terms of network lifetime on 100 target nodes with different number of
available potential positions. The simulation has been carried out on six different algorithms with the same
simulation parameters.
Table 12. Network Lifetime on 100 target nodes with varied #potential positions
Range Dimension PP Greedy Mini et
al GA-R GA-G HPG
ABC-
NM
k=1,
m=1
300X300
100 722 1073 839 1034 1132 1151
150 761 898 937 839 1034 1229
200 663 781 995 722 1210 995
250 761 898 742 839 995 1171
500X500
100 550 655 615 518 615 655
150 501 558 590 607 623 655
200 518 582 590 582 550 623
250 526 510 526 566 558 631
700X700 100 390 486 414 378 546 474
International Journal of Engineering, Applied and Management Sciences Paradigms (IJEAM)
Volume 54 Issue 3 June 2019 384 ISSN 2320-6608
150 468 426 432 366 486 384
200 408 570 588 558 558 582
250 438 462 522 498 462 522
k=1,
m=2
300X300
100 689 972 1042 972 1113 1254
150 742 760 830 919 1025 1042
200 707 901 618 866 989 1025
250 601 654 601 707 919 1113
500X500
100 490 533 526 548 598 569
150 432 512 562 447 533 548
200 432 591 504 461 548 562
250 440 504 519 411 476 540
700X700
100 320 393 366 370 425 393
150 352 430 462 389 398 345
200 311 370 302 251 411 419
250 311 398 411 347 402 386
k=2,
m=1
300X300
100 620 788 821 637 1072 855
150 519 838 670 754 888 737
200 586 804 670 771 888 855
250 654 821 788 654 821 855
500X500
100 430 450 423 437 551 531
150 383 517 417 484 464 511
200 383 497 457 457 484 538
250 423 450 423 477 417 531
700X700
100 290 273 259 293 297 335
150 266 283 242 245 283 269
200 245 259 214 180 283 325
250 242 276 262 276 259 283
k=2,
m=2
300X300
100 580 836 887 614 1126 819
150 716 904 853 631 972 1058
200 597 699 751 648 904 921
250 648 734 802 529 785 921
500X500
100 390 415 390 365 484 497
150 365 415 409 403 409 465
200 384 440 371 421 396 453
250 333 421 377 352 390 409
700X700
100 250 340 352 352 352 340
150 301 363 371 375 328 336
200 270 297 273 273 305 328
250 289 270 246 254 285 340
Figure 2. Network Lifetime for 500X500 GRID on 100 Target Nodes
International Journal of Engineering, Applied and Management Sciences Paradigms (IJEAM)
Volume 54 Issue 3 June 2019 385 ISSN 2320-6608
Figure 2 shows the lifetime of WSN under different and values of 500X500 Grid for 100 target nodes. For
value (1,1), (2,1) and (2,2) it outperforms all existing methods and for values (1,2) proposed ABC-NM outperforms
other existing algorithms and HPG gives a near optimal network lifetime as like ABC-NM.
Figure 3. Network Lifetime for 700X700 GRID on 100 Target Nodes
Figure 3 shows the lifetime of WSN under different and values of 300X300 Grid for 100 target nodes. For
value (2,1) and (2,2) it outperforms all existing methods and for values (1,1) and (1,2) proposed ABC-NM
outperforms other existing algorithms except HPG.
Figure 4. Network Lifetime for 300X300 GRID on 200 Target Nodes
Figure 4 shows the lifetime of WSN under different and values of 300X300 Grid for 200 target nodes. For
value (1,1), (1,2), (2,1) and (2,2) it outperforms all existing methods.
Figure 5. Network Lifetime for 500X500 GRID on 200 Target Nodes
International Journal of Engineering, Applied and Management Sciences Paradigms (IJEAM)
Volume 54 Issue 3 June 2019 386 ISSN 2320-6608
Figure 5 shows the lifetime of WSN under different and values of 500X500 Grid for 200 target nodes. For
value (1,1), (1,2), (2,1) and (2,2) it outperforms all existing methods. This states that on performing on more number
of target nodes (i.e. when more number of combinations leads to converge towards global optimal combination
solution).
Figure 6. Network Lifetime for 700X700 GRID on 200 Target Nodes
Figure 6 shows the lifetime of WSN under different and values of 700X700 Grid for 200 target nodes. For
value (1,1), (1,2), (2,1) and (2,2) it outperforms all existing methods.
V. CONCLUSION
A major concern in wireless sensor networks is to maximize network lifetime (in terms of rounds) while maintaining
a high quality of services (QoS) at each round such as target coverage and network connectivity. Due to the power
scarcity of sensors, a mechanism that can efficiently utilize energy has a great impact on extending network lifetime.
Most existing works concentrate on scheduling sensors between sleep and active modes to maximize network
lifetime while maintaining target/area coverage and network connectivity. To enhance the lifetime of the network,
ABC-NM has been proposed. The proposed algorithm gives better lifetime of the network by conducting various
benchmark results.
VI. REFERENCE [1] Liu, Zheng. "Maximizing network lifetime for target coverage problem in heterogeneous wireless sensor networks." Mobile Ad-Hoc and
Sensor Networks (2007): 457-468.
[2] Cardei, Mihaela, My T. Thai, Yingshu Li, and Weili Wu. "Energy-efficient target coverage in wireless sensor networks." In INFOCOM
2005. 24th annual joint conference of the IEEE computer and communications societies. Proceedings IEEE, Vol. 3, pp. 1976-1984. IEEE, 2005.
[3] Hongwu, Zhang, Wang Hongyuan, Feng Hongcai, Liu Bing, and Gui Bingxiang. "A heuristic greedy optimum algorithm for target coverage
in wireless sensor networks." In Circuits, Communications and Systems, 2009. PACCS'09. Pacific-Asia Conference on, pp. 39-42. IEEE, 2009.
[4] Gu, Yu, Jie Li, Baohua Zhao, and Yusheng Ji. "Target coverage problem in wireless sensor networks: A column generation based
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[6] Lu, Mingming, Jie Wu, Mihaela Cardei, and Minglu Li. "Energy-efficient connected coverage of discrete targets in wireless sensor networks." Networking and mobile computing (2005): 43-52.