 Open Access
 Total Downloads : 58
 Authors : Naveen Sihag
 Paper ID : IJERTV7IS020082
 Volume & Issue : Volume 07, Issue 02 (February 2018)
 DOI : http://dx.doi.org/10.17577/IJERTV7IS020082
 Published (First Online): 05032018
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
A Novel Adaptive Ant Lion Optimizer for Global Numerical Optimization
Naveen Sihag1
Ph.D. Scholar Department of Computer Engineering, Rajasthan Technical University Kota,
Rajasthan 324002, India1
Abstract – A novel bioinspired optimization algorithm based on the hunting process of Ant Lions in nature is known the Ant Lion optimizer (ALO) Algorithm in contrast to metaheuristics; main feature is randomization having a relevant role in both exploration and exploitation in optimization problem. A novel randomization technique termed adaptive technique is integrated with ALO and exercised on unconstraint test benchmark function and localization of partial discharge in transformer like geometry. ALO algorithm has quality feature that it uses simple mathematical equation to update position of Ants towards targeted optimal solution over the end of maximum iteration limit. Integration of new randomization adaptive technique provides potential that AALO algorithm to attain global optimal solution and faster convergence with less parameter dependency. Adaptive ALO (AALO) solutions are evaluated and results shows its competitively better performance over standard ALO optimization algorithms.
Keywords: Metaheuristic; Ant Lion optimizer; Adaptive technique; Global optimal; Hunting; Sensor Position.

INTRODUCTION
The ALO technique reflects the intellectual activities of antlions in hunting ants in environment. The ALO algorithm [1] inspired by hunting process and it is the interface between antlions and ants in the trap. To model such interfaces, ants have to travel over the exploration space, and antlions are permitted to pursuit them and become fitter using traps.
In the metaheuristic algorithms, randomization play a very important role in both exploration and exploitation where more strengthen randomization techniques are Markov chains, Levy flights and Gaussian or normal distribution and new technique is adaptive technique. So metaheuristic algorithms on integrated with adaptive technique results in less computational time to reach optimum solution, local minima avoidance and faster convergence.
In past, many optimization algorithms based on gradient search for solving linear and nonlinear equation but in gradient search method value of objective function and constraint unstable and multiple peaks if problem having more than one local optimum.
Population based ALO is a metaheuristic optimization algorithm has an ability to avoid local optima and get global optimal solution that make it appropriate for practical applications without structural modifications in algorithm for solving different constrained or unconstraint optimization problems. ALO integrated with adaptive technique reduces the computational times for highly complex problems.
Paper under literature review are: Adaptive Cuckoo Search Algorithm (ACSA) [2] [3], QGA [4], Acoustic Partial discharge (PD)
[5] [6], HGAPSO [7], PSACO [8], HSABA [9], PBILKH [10], KHQPSO [11], IFAHS [12], HS/FA [13], CKH [14], HS/BA [15], HPSACO [16], CSKH [17], HSCSS [18], PSOHS [19], DEKH [20], HS/CS [21], HSBBO [22], CSSPSO [23] etc.Recently trend of optimization is to improve performance of metaheuristic algorithms [24] by integrating with chaos theory, Levy flights strategy, Adaptive randomization technique, Evolutionary boundary handling scheme, and genetic operators like as crossover and mutation. Popular genetic operators used in KH [25] that can accelerate its global convergence speed. Evolutionary constraint handling scheme is used in Interior Search Algorithm (ISA) [26] that avoid upper and lower limits of variables.
The remainder of this paper is organized as follows: The next Section describes the Ant Lion optimizer and its algebraic equations are given in Section 2. Section 3 includes description of Adaptive technique. Section 4 consists of simulation results of unconstrained benchmark test function, convergence curve and tables of results compared with source algorithm. In Section 5 PD localization by acoustic emission, in section 6 conclusion is drawn. Finally, acknowledgment gives regards detail and at the end, references are written.

ANTLION OPTIMIZER
The ALO technique proposed by Seyedali Mirjalili that reflects the intellectual activities of antlions in hunting ants in environment. To model such interfaces, ants have to travel over the exploration space, and antlions are permitted to pursuit them and become fitter using traps [1].

Operators of ALO algorithm
As ants travel randomly in nature when searching for food, a random walk is selected for demonstrating ants movement and it is given by following equation:
X(t)=[0, cumsum(2r(t_1)1),cumsum(2r(t_2)1),,cumsum(2r(t_n)1)] (1)
Where, cumsum computes the cumulative sum, n is the maximum no. of iteration, t is the step of random walk (iteration), and r(t)
is a stochastic function defined as follows:
0 rand 0.5
r(t) 1 rand 0.5
Where, t is the step of random walk and rand represents a random number created by uniform distribution in the interval of [0, 1]. The location of ants are kept and used during optimization in the given matrix:
A11
A12
. . A1d
A A . . A
21 22 2d
M Ant
. . . . .
. . . . .
(2)
An1
An2 . .
And
Where: M Ant
= the matrix for storing the location of every ants,
Aij = the value for jth variable (dimension) of ith ant, n = the no.
of ants and d = the total no. of variables.
For calculating individual ant, a fitness function is used in optimisation and subsequent matrix saves the fitness value of each ants:
f A11, A12 ,…, A1d
f A21, A22 ,…, A2d
M :
(3)
OA
:
Where,
f An1, An2 ,…, And
MOA = the matrix for storing the each ant fitness,
Aij = the value of jth variable of ith ant, n = the total no. of ants and f =
the objective function.
So we suppose that ants as well as the antlions are hiding somewhere in the search area. So as to store their locations and fitness values, the following matrices are used:
AL11 AL12 . . AL1d
AL AL . . AL
21 22 2d
M Antlion
. . . . .
. . . . .
(4)
ALn1
ALn2 . .
ALnd
Where: M Antlion = the matrix for storing the location of individual antlion, ants and d = the no. of variables.
ALij = the value of jth variable of ith antlion, n = no. of
f AL11, AL12 ,…, AL1d
f AL21, AL22 ,…, AL2d
M :
(5)
OAL
:
f ALn1, ALn2 ,…, ALnd
Where, M OAL = the matrix for storing the fitness of individual antlion, and f = the objective function.
ALij = the value of jth variable of ith antlion, n = no. of ants

Random Walk of Ants
Each of the behaviors is mathematically modeled as:
The Random walks of ants is calculated as follows equation (6)
(xt x ) * (d ct )
xt i i i i c
(6)
i i
i (d t a ) i
Where, ai = the minimal of random walk of ith variable, bi = the Maximum of random walk in ith variable.

Trapping in Antlions pits
The Trapping in ant lions pits is calculated as follows equation (7) and equation (8)
i j
ct Antliont ct
i j
dt Antliont dt

Sliding Ants towards Antlion
The Sliding ants towards ant lion calculated as follows equation (9) and equation (10)
t ct
(7)
(8)
c (9)
I
t
d t
d (10)
I
Where, I = ratio, ct = the minimal of total variables at tth iteration, and dt = the vector containing the maximum of total variables at
tth iteration.

Catching prey and rebuilding the pit
Catching prey and rebuilding the pits calculated as follows equation (11)
Antliont
Anttif [ f (Antt )] f (Antliont )
(11)
j i i j
j i
Where, t = the current iteration, Antlion t= the location of chosen jth antlion at tth iteration, and Ant t= the location of ith ant at tth
iteration.

Elitism
Elitism of ant lion calculated using roulette wheel as follows equation (12)
t Rt

Rt
Anti
A E
A
E
2
(12)
Where,
Rt = the random walk nearby the antlion chosen by means of the roulette wheel at tth iteration,
Rt = the random walk
nearby the elite at tth iteration,
Antt = the location of ith ant at tth iteration.
i


ADAPTIVE ALO ALGORITHM
In the metaheuristic algorithms, randomization play a very important role in both exploration and exploitation where more randomization techniques are Markov chains, Levy flights and Gaussian or normal distribution and new technique is adaptive technique. Adaptive technique used by Pauline Ong in Cuckoo Search Algorithm (CSA) [2] and shows improvement in results of CSA algorithms. The Adaptive technique [3] includes best features like it consists of less parameter dependency, not required to define initial parameter and step size or position towards optimum solution is adaptively changes according to its functional fitness value o15ver the course of iteration. So meteheuristic algorithms on integrated with adaptive technique results in less computational time to reach optimum solution, local minima avoidance and faster convergence.
i t
t 1 t
1 ((bestf (t) fi(t)) (bestf (t) worstf (t)))
Xi
Where
X randn *
(13)
X t 1 new solution of ith dimension in tth iteration
i
f (t) is the fitness value

SIMULATION RESULTS FOR UNCONSTRAINT TEST BENCHMARK FUNCTION Table 1: Benchmark Test functions
No. Name Function Dim Range Fmin
f x x * R x
F1 Sphere n
2
i
10 [100, 0
100]
F2 Schwefel 2.22
i1
n n
f x x x
* R x
10 [10, 0
10]
F3 Schwefel 1.2
i1
i i
10
[100, 100]
0
10
[100, 0
100]
10
[30, 0
10
[100, 0
100]
10
[1.28, 0
1.28]
i1
2
n i
f x x j * R x
i1 j 1
i
F4 Schwefel 2.21
f x max x
F5
Rosenbrocks
Function f
n1 2 2
x 100x x
i1 i
F6
Step Function
n 2
f
x x 0.5 * R
F7
Quartic Function
n
i
i1
,1 i n
2
xi 1
* R x
30]
i x
i1
i
f x ix4 random0,1* R x
F8 Schwefel 2.26
i1
F x n x sin
x *R x
10 [500,
500]
( 418.9829*5
F9 Rastrigin
i i
i1
n
i i
F x x2 10cos 2 x 10 * R x
)
10 [5.12, 0
5.12]
F10 Ackleys Function
i1
F x 20exp 0.2
n
1 2
x
i
10 [32, 0
32]
1 n
n i1
exp n cos 2 xi 20 e * R x
F11 Griewank Function
i1
1 n n x
10 [600, 0
F x
x2 cos
i
1* R x
600]
i
4000 i1
i1
i
F12 Penalty 1
n1
10sin y y 12
10 [50, 0
50]
F x
1 i
i1
n 110sin2 y
y
12
y 1 xi 1 ,
i 4
k x
i1

am
n
x a
i
u(x , a, k, m)
i i
0 a xi a
k x

a m
x a
i i
F13 Penalty 2
10 [50, 0
n
sin2 3 x x 12 50]
1 i
i1
i
F x 0.11 sin2 3 x 1
x 12 1 sin2 2 x
n
n
n
F14 De Joung (Shekels Foxholes)
u xi , 5,100, 4* R x
i1
1
2 [65.536, 1
65.536]
1 25 1
F x
500 j 1
2
6
j xi aij
i1
F15 Kowaliks Function
11 xi bi bi x2
4 [5,5] 0.00030
2
2
f x ai b 2 b x

x
F16 Shekel
i1
10
i i
3 4
T
1
4 [0,10] 10.5363
f x X ai X ai
i1

ci
F17 Cube function
F18 Matyas function
f x 100(x x3 )2 (1 x )2
1 2 1 2
2 1 1
f (x) 0.26(x2 x2 ) 0.48x x
30 [100, 0
100
30 [30, 0
30]
F19 Powell function
D2 (x
10x )2 5(x
x )2 4 [30, 0
f (x) i1
i i1
i2
30]
i1 (x 2x
)4 10(x
x )4
i i1
i1
i2
F20 Beale Function
1.5 x1 x x2
2.25 x x x2
230
[100, 0100]
1 1 2
2
f (x) 1
2.625 x x x3 2
F21 levy13 function
1 1 2
2
sin2 3 x x 1 1 sin2 3 x
2
30
1 1
[10, 010]
f (x)
x
12 1 sin2 2 x
2 2
Table 2: Internal Parameters
Parameter Name
Search Agents no.
Max. Iteration no.
No. of Evolution
F1F21
30
500
2030
Acoustic PD Localization
40
200
20
Note: Scale specified on axis, Not specified means axis are linear scale
F1 F2
F3 F4
F5 F6
F7
F8
F9 F10
F11 F12
F13 F14
F15 F16
F17 F18
F19 F20
F21
Fig. 1: Convergence Curve of Benchmark Test Function
Table 3: Result for benchmark functions
Fun.
AntLion optimizer (ALO)
Adaptive AntLion Optimizer (AALO)
Ave
Best
S.D.
Ave
Best
S.D.
F1
1.1018E08
8.5917E09
3.4308E09
6.9926E09
5.5958E09
3.4308E09
F2
1.35
0.0011442
1.9076
0.2666
0.00052061
1.9076
F3
0.05592
0.0061171
0.070433
0.012982
0.00077882
0.070433
F4
0.0028435
0.00058981
0.0031871
0.0011557
0.00025095
0.0031871
F5
8.8444
8.2563
0.83172
1.5002
7.6731E06
0.83172
F6
2.1803E08
1.0074E08
1.6588E08
1.0207E08
9.4448E09
1.6588E08
F7
0.014989
0.0062663
0.012335
0.027139
0.0046907
0.012335
F8
2692.5959
3459.3448
1084.3467
2850.0459
3656.8455
1084.3467
F9
26.3663
25.8689
0.70354
22.884
19.8992
0.70354
F10
0.5776
5.544E05
0.81677
5.4147E05
5.2544E05
0.81677
F11
0.1576
0.14525
0.017463
0.2165
0.1328
0.017463
F12
1.5235
0.98867
0.75642
0.31478
0.31101
0.75642
F13
3.9475E07
3.3722E07
8.1357E08
2.0961E07
4.28E08
8.1357E08
F14
3.9604
1.992
2.7837
2.4871
1.992
2.7837
F15
0.010793
0.0011281
0.013668
0.00074227
0.00073769
6.4749E06
F23
3.8354
3.8354
5.8935E12
6.6715
10.5364
5.4658
F28
3.5236
2.4015E11
4.9831
5.8609E11
2.3499E11
4.9652E11
F31
6.0627E14
2.4656E14
5.0871E14
9.7097E15
2.403E16
1.3392E14
F34
9.6533E06
5.7193E06
5.636E06
1.0075E05
3.4594E06
9.3556E06


ACOUSTIC PD LOCALIZATION SENSOR POSITION
Dielectric breakdown in transformers is most frequently initiated by partial discharges. The consequences of these types of occurrences can be hazardous if not detected in a timely fashion. Regular PD analysis gives an accurate indication of the status of the deterioration process. So it is possible to foretell developing fault condition by online monitoring and precautionary tests. It is very much essential to have information of PD level and location to plan maintenance of electrical equipment. A famous method of understanding the health of the transformer is by studying the partial discharge signals. Monitoring of transformer can be either online or offline. The primary established techniques for electrical PD detection by measuring current or Radio Frequency (RF) pulses. Suppression of interference is one of the main challenges in detecting PDs, either while the transformer is offline or on line in a noisy environment. The offline PD detection methods only provide snapshots in time of part of the transformers condition. On the other hand, no standards have yet been developed for online electrical monitoring of PDs.
It is well known that the occurrence of discharge results in discharge current or voltage pulse, electromagnetic impulse radiation, ultrasonic impulse radiation and visible or ultraviolet light emission. Accordingly, there are several detection methods that have been developed to measure those phenomena respectively. Acoustic detection is one of them which is very famous nowadays.
PD generates acoustic waves in range of 20 kHz to 1 MHz. External system and internal system are two categories of acoustic detection techniques based on sensor location in transformer. External system is widely accepted as sensors are mounted outside of the transformer. An obvious advantage of the acoustic method is that it can locate the site of a PD by algorithms. Electromagnetic interference may cause corruption of signals captured by piezoelectric sensors.
A main objective is to determine the position of the PD source based on signals captured by sensor array inside the transformer tank as shown in Fig. 3. Each sensor will capture acoustic signals at different time as shown in Fig. 4. Time Difference of Arrival (TDOA) algorithm has been implemented to find location of partial discharge source.
PDE equation in homogeneous medium for propagation of acoustic wave:
2 P 22
2 2 P 2 P 2 P
t2
P x2 y2 z2
(14)
Where: P (x, y, z, t) pressure wave field; function of space and time; x, y, z Cartesian coordinates (mm) and v is acoustic wave velocity (m/s).
Sensor 4
x
Sensor 3
z
PD source
Sensor 1
Sensor 5
Sensor 2
y
Fig. 2: Visualization of PD source and sensor arrangement
U(t) PD
onset
T
S1 S2 S3 Sn
t21
t31
tn1
PD
Source
Time
Fig. 3: Schematic of acoustic time differences in reference to electrical PD signal Table 4: Transformer dimension and Coordination position of sensor
Element 
Xaxis (mm) 
Yaxis (mm) 
Zaxis (mm) 
Transformer Dimension 
5000 
3000 
4000 
Actual PD source 
4500 
2600 
3700 
Sensor (S1) 
2500 
0 
2000 
Sensor (S2) 
2500 
1500 
4000 
Sensor (S3) 
5000 
1500 
2000 
Sensor (S4) 
2500 
3000 
2000 
Sensor (S5) 
0 
1500 
2000 
t1 =2600 microseconds ( Reference ) 
1() = [ 1600, 1500, 1900, 3524.69] 1 , = 2,3,4,5, And sensor 1 is assumed as reference paper [6]. Problem Formulation:
21 31
1000 1003 , 1100 1003 ,
(15)
41 51
700 1003 , 924.69 1003 ,
P x x 2 y y 2 z z 2 0.5
(16)
1 1 1
0.5
a x x 2 y y 2 z z 2 P ;
(17)
2 2 2
e 21
2 2 2 0.5
b x x3 y y3 z z3
P e31 ;
(18)
2 2 2 0.5
c x x4 y y4 z z4 /p>
P e41 ;
(19)
0.5
d x x 2 y y 2 z z 2 P ;
(20)
5 5 5
e 51
Min
{D (x, y, z, )} a2 b2 c2 d 2 ;
(21)
f e
Subjected to
0 x xmax
0 y ymax
0 z zmax
(22)
1200 e 1500, (m / s
Where:
, , and are transformer tank dimension and equality sound velocity.
Calculated PD source is Pc (xc , yc , zc ) comprehensive distance error of it with actual PD source
P(x, y, z) is
R x x
2 y y
2 z z
2 0.5
(23)
c c c
Error of each coordinate is formulated:
r
Lact Lcal Lact
100%
(24)
Maximum deviation Dmax
xact xcal
Dmax
max yact ycal
(25)
z
act zcal
Where; , ,, , , , actual and calculated coordinates respectively.
Table 5: Comparison of the results of PD localization
Coordinate (mm) 
Actual PD source 
ALO 
AALO 
GA 
X 
4500 
4381.7459 
4381.7465 
4223.76 
Y 
2600 
2469.6026 
2469.603 
2391.71 
z 
3700 
3647.4901 
3647.4905 
3503.04 
Table 6: Error analysis
Error 
ALO 
AALO 
GA 
Error of x% 
2.627 
2.627 
6.14 
Error of y% 
5.015 
5.322 
8.01 
Error of z% 
1.419 
1.419 
5.32 
D max /mm 
130.3974 
130.397 
276.24 
Comprehensive Error(del R/mm) 
183.6975 
183.6968 
398.10 
CONCLUSION
Ant Lion Optimizer have an ability to find out optimum solution with constrained handling which includes both equality and inequality constraints. While obtaining optimum solution constraint limits should not be violated. Randomization plays an important role in both exploration and exploitation. Adaptive technique causes faster convergence, randomness, and stochastic behavior for improving solutions. Adaptive technique also used for random walk in search space when no neighboring solution exits to converse towards optimal solution. Acoustic PD source localization method based on AALO algorithm is feasible. PD localization by AALO gives better result than ALO algorithm and also accurate in compare to GA. The ALO result of various unconstrained problems proves that it is also an effective method in solving challenging problems with unknown search space.
ACKNOWLEDGMENT
The authors would also like to thank Prof. Seyedali Mirjalili for his valuable comments and support. http://www.alimirjalili.com/ALO.html.
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