Arabian Journal for Science and Engineering
https://doi.org/10.1007/s13369-018-3370-4
RESEARCH ARTICLE - ELECTRICAL ENGINEERING
Accelerated Opposition-Based Antlion Optimizer with Application to
Order Reduction of Linear Time-Invariant Systems
Shail Kumar Dinkar
1
· Kusum Deep
1
Received: 6 March 2018 / Accepted: 31 May 2018
© King Fahd University of Petroleum & Minerals 2018
Abstract
This paper proposes a novel variant of antlion optimizer (ALO), namely accelerated opposition-based antlion optimizer
(OB-ac-ALO). This modified version is conceptualized with opposition-based learning (OBL) model and integrated with
acceleration coefficient (ac). The OBL model approximates the original as well as opposite candidate solutions simultaneously
during evolution process. The implementation of OBL technique is collaborated with an exploitation acceleration coefficient
which is useful in local searching and tends to find global optimum efficiently. A position update equation is formulated using
these strategies. To validate the proposed technique, a broad set of 21 benchmark test suit of extensive variety of features is
chosen. To analyse the performance of proposed algorithm, various analysis metrics such as search history, trajectories and
average distance between search agents before and after improving the algorithm are performed. A nonparametric Wilcoxon
ranksum test is applied to show its statistical significance. It is applied to solve a real-world application for approximating the
higher-order linear time-invariant system to its corresponding lower-order invariant system. Three single-input single-output
problems have been considered in terms of integral square error.
Keywords Antlion optimizer · Opposition-based learning · Acceleration coefficient · Order reduction · Integral square error
List of symbols
H
ant
=
(
H
A,1
, H
A,2
,
... H
A,n
,..., H
A, N
)
T
Initial population of ant
H
A,n
=
H
1
A,n
,... H
d
A,n
,..., H
D
A,n
nth ant
H
d
A,n
d th variable of the nth ant
MH
ant
=
(
MH
A,1
, MH
A,2
... MH
A,n
,... MH
A, N
)
T
Fitness matrix of ant
MH
A,n
= f
H
1
A,n
,..., H
d
A,n
,
..., H
D
A,n
Fitness value of nth ant
H
antlion
=
H
AL,1
, H
AL,2
,
..., H
AL,n
,..., H
AL, N
T
Antlion population
B Shail Kumar Dinkar
shailkdinkar@gmail.com
Kusum Deep
kusumfma@iitr.ac.in
1
Department of Mathematics, Indian Institute of Technology
Roorkee, Roorkee, Uttarakhand, India
H
AL,n
=
H
1
AL,n
,...
H
d
AL,n
,... H
D
AL,n
nth antlion
H
d
AL,n
d th variable of the nth
antlion
MH
antlion
=
(
MH
AL,1
,...,
MH
AL,n
,..., MH
AL, N
)
Fitness matrix antlion
emax = 1,
emin - 0.00001
Fitness value of nth antlion
it
curr
, it
max
Current and maximum iter-
ation
LB, UB Lower and upper bound
H
sel
Selected antlion
H
elite
Elite (best) antlion
Rw
A
Random walk around H
sel
Rw
E
Random walk around H
elite
e
ac
Acceleration coefficient
emax = 1,
emin - 0.00001
Max and min value of con-
stant
G(s ) Original LTI system
s Complex variable
n Order of original system
123