Node Localization in Wireless Sensor Network by Ant Lion Optimization

Ant Lion Optimization

Thi-Kien Dao¹, Jeng-Shyang Pan^1,2,Trong-The Nguyen^1,3*, Shu-Chuan Chu², Huu-Trung Tran³, Trinh-Dong Nguyen³, Ngoc-Thanh Vu⁴

1Fujian Provincial Key Lab of Big Data Mining and Applications Fujian University of Technology, Fujian, China

2College of Computer Science and Engineering, Shandong University of Science and Technology, Qingdao, China

3University of Management and Technology, Haiphong, Vietnam

4University of Medicine and Pharmacy Haiphong, Vietnam

1101405123@nkust.edu.tw,jspan@cc.kuas.edu.tw,

*vnthe@hpu.edu.vn, scchu0803@gmail.com, trungth@hpu.edu.vn, dongnt@hpu.edu.vn,

vnthanh@hpmu.edu.vn

Abstract. Node location is a critical demand in some popularity of Wireless sen- sor network (WSN) applications. This paper proposes a node location identifica- tion in WSN based on a combined Ant Lion Optimizer (ALO) with a typical model of localization. The fitness function is modeled mathematically based on estimating distances of the WSN nodes. The updating solutions of the population are figured out for position correcting to improve the node positioning accuracy.

The effects of parameters like node density and communicating range is verified in the experiments to evaluate the performance of the proposed method in terms of concerning average localization error and success ratio. Compared to the re- sults of the test with Cuckoo Search (CS) and Particle swarm optimization (PSO) shows that the proposed approach effectively offers a better competitor in finding location accuracy.

Keywords: Ant Lion Optimizer; Localization; Wireless Sensor Network;

Positioning accuracy

1 Introduction

Wireless sensor networks (WSNs) have a wide spectrum of applications in fields such as monitoring, surveillance, domestic, etc.,[1][2] [3]. WSNs consist of hundreds of de- ployed sensor nodes [4] [5]. The advantages, e.g., low cost, wireless, and small size, WSNs have become a widening popular with developing potential applications in fields of military and industry [6][7]. The positioning node is a critical demand in some WSN applications [8][9]. The positioning approaches, e.g., the range-free and range-based,

are widening used in capturing the required location information. In the real-time situ- ation at the same time, obtaining the exact location of the sensor node also ensures the efficient execution of the routing and coverage algorithms of the network. The posi- tioning estimation for sensor nodes has significance for deploying a WSN application.

The localization is optimized by finding the best solution to the node positions in the WSN. Heuristic algorithms are a promising tool to produce acceptable solutions by doing trials and errors in complex practical problems. The improvements in optimiza- tion algorithms have forwarded proposing an answer to the shortcomings of various localization algorithms. An application of the heuristic algorithm as the Genetic algo- rithm (GA) to improve the node localization problem in WSN based on was introduced in [10]. The applied Particle swarm optimization (PSO) and cuckoo search (CS) to the DV-distance approach by estimation node position in WSN for localization effect was found in [11][12] respectively. The improved node location accuracy effectively by the DV-Hop algorithm was introduced in [13]. The relationship sensor node to the neighbor node was established to calculate the node location using the flower algorithm (FPA) was found in [14]. The work [15] introduced to the coded node information into the matrix for node localization. The applied Firefly algorithm (FA) to the node location in WSN was achieved good results in [16]. The methods mentioned above had achieved excellent results of location accuracy in WSN. However, efficiency performance still exists the limitation whenever it deployed in a highly complex environment.

A recently heuristic algorithm inspired by ant lions hunting behavior called Ant Lion Optimizer (ALO) [17] that offers competitive results in various challenging engineer- ing, and constrained real problems. The proof of its exploring search space, avoiding local optima, and converging rate are to provide better results in optimization solutions.

In this paper, the estimated positioning node in WSN is carried out by applying ALO.

The Pareto distance of sensor nodes is figured out by optimizing node localization.

2 Statement of WSN Localization Problem

The least-square equation is used in the DV-Hop method [11] [13] to compute the node coordinates. The cumulative error is used to measure the positioning accuracy. The possible errors can be calculated to model the node position as follows.

   

   

   



































2 2

2 2 2 2 2

2 1 2 1 1

n y y n x

n x d

y y x x d

y y x x d



(1)

where (𝑥, 𝑦) is the coordinates of unknown position node in the network area; (𝑥_𝑖, 𝑦_𝑖) is the coordinates of reference node; 𝑑_𝑖 is the distance of the unknown position node to the reference node; 𝑖 = 1, 2, … , 𝑛. Eq.(1) is presented as a following linear equation.

𝐴 × 𝑋 = 𝑏 (2)

In Eq. (2), 𝐴 is a matrix of least-square equation that expressed as follows.

 

 

 

 

 

  ^{ }







 







 





 











yn yn

yn y

yn y

xn xn

xn x

xn x A

1 2 1

1 2 1

2   (3)

Let 𝑋 be a vector that can be expressed as:





 y

X x (4)

Let 𝑏 be a coefficient that stated as:

 

 





 

 





 



 



 























2 2

1 2 2

1 2 2

1

2 2 2 2 2 2 2 2 2

2 2 1 2 2 1 2 2 1

dn dn yn yn xn xn

dn n d

y n y

x x

dn n d

y n y

x x b

 (5)

The above-constructed equations are under ideal theory conditions, but, in practice, problems would have noise or the distance measurement incorrect..

Let N be an error vector with n-1 dimensions, Eq(2) would be expressed as 𝐴 × 𝑋 + 𝑁 = 𝑏, the matrix X will get more accuracy whenever 𝑁 minimized.

 

^{ATA ATb}

X

1

 (6)

where 𝑏 is a parameter as a factor of the solution 𝑋; 𝑑𝑛 is determined by 𝑏. If the value of 𝑑𝑛 is large, the least-square equation would calculate the coordinates of specific nodes complicatedly. To deal with this issue, the node location problem in the environ- ment with significant errors is transformed into a constrained optimization problem.

The above equation should be re-expressed as follows.

   

   

   

































2 2 2

...

2 2 2 2 2 2

2 1 2 1 2 1

yn n y

x n x d

y y x x d

y y x x d

(7)

The measurement of distance error between nodes is formulated as follows:

i di

ri  



(8)

where 𝜀𝑖 is an error variable of ranging nodes 𝑟𝑖. The actual distance from the reference node 𝑖 to the unknown node of the network is expressed as follows with 𝑖 = 1,2, … , 𝑛:

   

   

   



















































2 2 2 2 2 2 2 2

2

...

2 2 2 2 2 2 2

2 2

2 2 2

2 1 2 1 2 1 2

1 2

1 2 1













d y n y

x n x dn

d y y x x d

d y y x x d

(9)

  

²



^{2 2}

1 n

fi i xxi  yyi di

 (10)

where 𝑓𝑖 is the ranging error when calculated it between the unknown node and the reference node. Therefore, the target function with (𝑥, 𝑦) is defined as follows.

 

^

   

    

 n

i x xi y yi di

y x f

1

2 2

, 2 (11)

The obtained value of the objective function 𝑓(𝑥, 𝑦) is small that the coordinate value is closer to the solution with the actual cost. Thus, the problem of node localization is transformed into a multi-dimensional constrained optimization problem. The global op- timization of the Ant lion optimizer is applied to find out the correct node locations in WSN.

3 Ant Lion Optimizer

The Ant lion optimizer (ALO) was inspired by the interaction between ant lions and trapped ants in nature [17]. For these interactions, first, we consider an ant as a moving agent in the search space, which is then allowed to be hunted by the ant lion. Since the ant’s motion is random, it is a method following equation.

𝑋(𝑡) = [0, 𝑐𝑢𝑚𝑠𝑢𝑚(2𝑟 (𝑡₁) − 1) 𝑐𝑢𝑚𝑠𝑢𝑚(2𝑟(𝑡₂) − 1)

… 𝑐𝑢𝑚𝑠𝑢𝑚(2𝑟(𝑡𝑛) − 1)] (12) where 𝑐𝑢𝑚𝑠𝑢𝑚 is the cumulative sum; n represents the maximum iteration; t denotes the random walk step (iteration t at this time); and r(t) is a random function calculated as follow.

𝑟(𝑡) = {1 𝑖𝑓 𝑟𝑎𝑛𝑑 > 0.5

0 𝑖𝑓 𝑟𝑎𝑛𝑑 ≤ 0.5 (13) In Eq.(13), t denotes the random walk step and rand is the random number in the interval [0, -1]. Ants’ location is stored in the following matrix and used during optimization.

𝑀𝐴𝑛𝑡= [

𝐴1,1

𝐴_2,1

⋮

⋮ 𝐴𝑛,1

𝐴1,2

𝐴_2,2

⋮

⋮ 𝐴𝑛,1

……

⋮

⋯⋮

……

⋮

⋯⋮ 𝐴1,𝑑

𝐴_2,𝑑

⋮

⋮ 𝐴𝑛,𝑑]

(14)

where 𝑀𝐴𝑛𝑡 specifies the location of each ant; 𝐴𝑖𝑗 specifies the 𝑗-th variable of the i-th ant; n is the number of ants and d represents the number of variables. To evaluate any ant, an objective function is used during optimization. Then, these functions are stored in accordance to Equation (11):

M𝑂𝐴 = [

𝑓(𝐴11, 𝐴12, ⋯ , 𝐴1𝑑) 𝑓(𝐴₂₁, 𝐴₂₂, ⋯ , 𝐴_2𝑑)

⋮

⋮

𝑓(𝐴𝑛1, 𝐴𝑛2, ⋯ , 𝐴𝑛𝑑)]

(15)

where 𝑀𝑂𝐴 stores the value of the objective function of each ant. Suppose ant lions are hiding in a space. In order to store this location and its corresponding objective function, the matrices presented in Eq.s (14) and (15) are expressed as follows.

M_{𝐴𝑛𝑡𝑙𝑖𝑜𝑛} = [

𝐴𝐿_1,1 𝐴𝐿2,1

⋮

⋮ 𝐴𝐿_𝑛,1

𝐴𝐿_1,2 𝐴𝐿2,2

⋮

⋮ 𝐴𝐿_𝑛,1

……

⋮

⋯⋮

……

⋮

⋯⋮ 𝐴𝐿_1,𝑑 𝐴𝐿2,𝑑

⋮

⋮ 𝐴𝐿_𝑛,𝑑]

(16)

M𝑂𝐴𝐿= [

𝑓(𝐴𝐿1,1, 𝐴𝐿1,2, ⋯ , 𝐴𝐿1,𝑑) 𝑓(𝐴𝐿_2,1, 𝐴𝐿_2,2, ⋯ , 𝐴𝐿_2,𝑑)

⋮

⋮

𝑓(𝐴𝐿_𝑛,1, 𝐴𝐿_𝑛,2, ⋯ , 𝐴𝐿_𝑛,𝑑) ]

(17)

where M_{𝐴𝑛𝑡𝑙𝑖𝑜𝑛} and M_𝑂𝐴𝐿 respectively specify the location matrix and the objective function matrix of each ant lion. Furthermore, 𝐴𝐿_𝑖,𝑗 shows the 𝑖th dimension value of the 𝑗th ant lion; n is the number of ant lion; and d is a number of variables. Ants are normalized by Equation (16) so that they can walk randomly in the search space.

𝑋_𝑖^𝑡=(𝑋_𝑖^𝑡− 𝑎𝑖) × (𝑑_𝑖^𝑡− 𝑐_𝑖^𝑡)

(𝑏_𝑖− 𝑎_𝑖) + 𝑐_𝑖 (18)

where 𝑎_𝑖 is the random walk with the 𝑖th variable; 𝑏_𝑖 presents the maximum random walk of the 𝑖th variable; 𝑐_𝑖^𝑡 is the minimum of ith variable in iterations 𝑡; and 𝑑_𝑖^𝑡 is the maximum of ith variable in iteration 𝑡. Eq.(13) is applied to each iteration to ensure that random walk occurs in the search space. Accordingly, the ant’s walk is influenced by the ant lion’s traps. This is expressed in mathematical terms as equations (19) and (20):

𝑐_𝑖^𝑡= 𝐴𝑛𝑡𝑙𝑖𝑜𝑛_𝑗^𝑡+ 𝑐^𝑡 (19)

𝑑_𝑖^𝑡= 𝐴𝑛𝑡𝑙𝑖𝑜𝑛_𝑗^𝑡+ 𝑑^𝑡 (20)

In Eq.s (19) and (20), 𝑐𝑡 is the minimum value of all the variables in iteration t; 𝑑𝑡

represents a vector of the maximum of all variables in iterations 𝑡; 𝑐_𝑖^𝑡 is the minimum value of all variables for the ith ant; 𝑑_𝑖^𝑡 denotes the vector of the maximum of all vari- ables for the ith ant; and 𝐴𝑛𝑡𝑙𝑖𝑜𝑛_𝑗^𝑡 represents the location of the jth ant lion at iteration t. When an ant gets trapped, the ant lion throws stones to the edges of the pit. The Eq.s (21) and (22) represent the mathematical method for this.

𝑐^𝑡=𝑐^𝑡

𝐼 (21)

𝑑^𝑡=𝑑^𝑡

𝐼 (22)

where 𝐼 is a constant ratio; 𝑐_𝑡 is the minimum of all variables at iteration 𝑡; and 𝑑_𝑡 is the vector of the maximum value of the variables at iteration t, which is defined as Eq:

(23):

𝐼 = 10^𝑤𝑡

𝑇 (23)

where 𝑡 is the iteration in progress, 𝑇 is the maximum number of iterations, and 𝑤 is constant. In the final stage of hunting, the prey gets trapped down and is placed in the ant lion’s mouth. Then, the ant lion takes the prey into the sand and eats it. In this algorithm, it is assumed that the hunt is done when an ant enters the sand. Therefore, the location of the ant lion should be updated according to the location where it has hunted the ant to increase the chance of a new hunt (Eq. (24)).

𝐴𝑛𝑡𝑙𝑖𝑜𝑛_𝑗^𝑡= 𝐴𝑛𝑡_𝑗^𝑡 𝑖𝑓 𝑓(𝐴𝑛𝑡_𝑖^𝑡) > 𝑓(𝐴𝑛𝑡𝑙𝑖𝑜𝑛_𝑗^𝑡) (24) where t represents iteration of a runs; 𝐴𝑛𝑡𝑙𝑖𝑜𝑛_𝑗^𝑡 is location of the jth ant lion at iteration t; and 𝐴𝑛𝑡_𝑗^𝑡 represents location of the ith ant at iteration t. Then, the best ant lion is stored and considered as an elite member. Therefore, it is assumed that each ant ap- proaches an ant lion based on the structure of a rotating wheel. Eq. (25) shows the elite simulation.

𝐴𝑛𝑡_𝑗^𝑡 =𝑅_𝐴^𝑡+ 𝑅_𝐸^𝑡

2 (25)

where 𝑅_𝐴^𝑡 is the variable of random walk around the ant lions by rotating wheel at iter- ation t; 𝑅_𝐸^𝑡 is the random walk around the elite at iteration t; and 𝐴𝑛𝑡_𝑗^𝑡 denotes the lo- cation of the ith ant at iteration 𝑡.

4 Localization WSN based on ALO

4.1 Objective Function

The fitness value of the objective function directly determines the position of ant-loins.

This subsection presents the comparison to the solution of an unknown node with each individual in the ant-lion swarms. The objective function is modeled as follows.

    

²



^{2 2}

, ⁿ1

fitness x y i xxi  yyi di

 (26)

where the coordinate of (𝑥, 𝑦) is a coordinate of unknown nodes, (𝑥_𝑖, 𝑦𝑖) is the coordi- nates of the 𝑖 reference node; 𝑛 is number reference odes; 𝑑𝑖 is the node distance be- tween the unknown and the reference nodes.

4.2 Correcting Position Factor

The central position of the newly formed swarm of agent is selected as the global opti- mum. The accuracy of location optimization would be improved of such chosen agent to a certain extent, but due to the iterative error and positional deviation of the agents.

In response to this issue, the position correction factor is suggested in the ant-lion swarm of a landmark of the operation search stage for improving the selection formula of the optimal position in the period of the ant-loin searching to optimize the localiza- tion accuracy of the ant-lion swarms.



best worse



¹

best n N p

 

    ^ 

 

 

  ⁽²⁷⁾

where



is a parameter of position of agents;_bestand_worseare the best and worse of agent positions that calculated as follows.

1, best

worse n

n p n p





 

  (28)

Suppose 1 1 n i pi

 andpi 0.1best 2andμworsebest 2. This proposed fac- tor is applied to Eq.(18) for solution of position correction as follows.

       

     

Xi t fitness Xi t Xc t

Np t fitness Xi t

  

 



 (29)

The position correction factor with iteration can identify the solution according to the best fitness values in the new population. The best-obtained optimization value could be found in shorten searching time.

Processing steps are described as follows:

Step 1: Set up the localization model above mentioned, and apply ALO to the solu- tion of the transformed model for the optimization problem.

Step 2: Initialize randomly position of ant lions, ants, and set the maximum number of iterations Itmax

Step 3: Objective function Eq.(26) is computed with the population based on classi- fied distances.

Step 4: Select randomly the individual from the first rank based on the sorting Step 5: Apply correcting factor 𝛿 to update agent’s position 𝑋_𝑖^𝑡 in the position up-

date Eq.(29).

Step 6:

Termination condition if it is not met, go to 3 Step and increase the number of iterations. Otherwise, it ends and the output as the global best is obtained with approximately optimal nodes position.

Given the excellent optimization ability of ALO combined with the model of three- point positioning, the node localization optimization is executed, and the tested locali- zation of the node is determined by solving the problem of the constrained optimization problem.

5 Simulation Results

The ALO is applied to estimate the location of the unknown nodes in WSN by optimiz- ing the objective function in Eq. (26). The semulation results of the proposed scheme are compared with the PSO[11], and SC[12] methods. The supposed network with N is unknown nodes (𝑁 = 100, 200, 300) and 𝑀 is the anchor nodes (𝑀 = 10, 20, 30) ran- domly deployed in area size of 𝑍 × 𝑍 (𝑍 = 100, 200,300) sensing field. The specific parameters for the setting simulation environment of deployment nework is listed in Table 1.

Table 1. Setting parameters to environment of simulation Parame-

ters Description Instance

Z Region size /m² 100×100

M No. of the reference nodes 100

N No. of the unknown nodes 30

R Communication radius / m 60

Itermax No. of runs / times 200 Distribu-

tion type Node distribution Random

distribution Fig.1 shows a GUI of the setting parameters of the network deployment in the location area, the reference node ratio, the communication radius, and the node density.

a. (x=200, y =200) b. (x=100, y =100)

Fig. 1. A GUI of the proposed scheme for the node localization in WSN for setting parameters of network deployment.

In order to evaluate the positioning accuracy of the proposed method performance quickly, a parameter is used for measuring the ranging error that is a measurement as a significant influence on the localization accuracy. The specific expression of mean er- rors has expressed the following efficiency of node locations.

  

²



²

1 ,

N

xi xi yi yi Er i

N R

   

 



(30) where 𝑥̅ , 𝑦_𝑖 ̅_𝑖 is the coordinates of estimated node 𝑖, and (𝑥_𝑖, 𝑦_𝑖) is the coordinates of estimated unknown nodes. 𝑁 is number of the unknown nodes, and 𝑅 is the communi- cation radius. Figure 2 displays the comparison of the curve of error fluctuation of the proposed method with the other techniques, e.g., CS and PSO, for optimizing the posi- tioning nodes. The line of the error fluctuation ratio of the proposed scheme is the out- performance of the others.

Fig. 2. Comparison of three methods for the positioning errors (the proposed approach, PSO, and CS methods).

Table 2 displays the effects of measurement of the density of the nodes in the net- work to localization accuracy. The number of the referencing node rate is about 20%, and the radio range of communication radius is fixed 25 m, the total nodes of the net- work are changed differently. Seen that increased number of reference nodes and the radio range of communication usually produce the localization accuracy more satisfac- tory, but the deployed network has cost more.

Table 2. The localization accuracy is impacted by the rate of nodes density of the network

Approaches Total number of nodes

80 100 120 140 160 180 200 CS 32.20.% 27.20.% 22.10.% 21.01.% 19.90% 19.90.% 17.90.%

PSO 30.90% 26.40.% 21.10.% 19.90% 18.80% 16.99.% 16.97.%

ALO 27.80% 25.80% 20.01% 19.01% 18.10% 16.67.% 16.29.%

Figure 3 depicts a comparison of the error curve as average positioning errors of the proposed with PSO and CS methods. The deployed area of nodes affects the localiza- tion accuracy that increases the area of the location area is more obtained efficiency.

Observably, if the number of nodes is over 150, the impact on accuracy over the error is not too much. In the real node location process, the relationship between the area and the density of nodes is measured effectively.

Fig. 3. Comparison of the error of curve as average positioning errors of the proposed scheme ALO with the PSO, and CS methods.

Observably, the rate of localization errors is obtained by the proposed methods that are lower than the errors generated by both of the PSO and CS. Table 3 shows the relation- ship between the positioning errors and the referencing node. The errors do not increase as the referencing node rate increases because of the rise of known nodes around un- known nodes resulting in getting more accuracy of localization.

Table 3. The variety referenced node rate effects for positioning errors

Approaches Referenced node rates

5.% 10.% 15.% 20.% 25.% 30.%

CS 32.% 27.% 23.% 21.% 20.% 20.%

PSO 27.% 22.% 20.% 20.% 19.% 18.%

ALO 25% 21% 19% 20% 19% 18%

Observed, the outcomes of the proposed method for optimization positioning node are better accuracy than the CS and PS methods.

6 Conclusion

In this paper, we proposed a solution to Wireless Sensor Network (WSN) node locali- zation based on combined Ant Lion Optimizer (ALO) with a typical localization model.

The node location problem was transformed into a positioning model in WSN as the objective function. The adaptive fitness value based on estimated distances was applied to make a model of the localizing node. We introduced a correcting factor for updating solutions to enhance ability, effectively searching forward to a promising area over each iteration that also reduces the positioning error effectively. The experiments were con- ducted to test the proposed method with the effects of parameters, e.g., node density and communicating range in terms of mean localization errors and success ratio. Com- pared results with the Cuckoo Search (CS) and Particle swarm optimization (PSO) ap- proaches show that the proposed method provides the improvement of the location ac- curacy effectively and reduces the cumulative errors.

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