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3 Solving Optimization Problem Using Advanced
Algorithms
In this section, the basic concepts as well as the algorithm steps of each proposed
advanced metaheuristic are described for solving the formulated PID-type FLC
tuning problem.
3.1 Differential Search Algorithm
The Differential Search Algorithm (DSA) is a recent population-based metaheu-
ristic optimization algorithm invented in 2012 by Civicioglu ( 2012 ). This global
and stochastic algorithm simulates the Brownian-like random-walk movement used
by an organism to migrate (Civicioglu 2012 ; Goswami and Chakraborty 2014 ;
Waghole and Tiwari 2014 ).
Migration behavior allows the living beings to move from a habitat where
capacity and diversity of natural sources are limited to a more ef
cient habitat. In
the migration movement, the migrating species of living beings constitute a
superorganism containing large number of individuals. Then it starts to change its
position by moving toward more fruitful areas using a Bownian-like random-walk
model. The population made up of random solutions of the respective problem
corresponds to an arti
cial superorganism
migrates to global minimum value of the problem. During this migration, the
arti
cial-superorganism migrating. The arti
cial-superorganism tests whether some randomly selected positions are suitable
temporarily. If such a position tested is suitable to stop over for a temporary time
during the migration, the members of the arti
cial-superorganism that made such
discovery immediately settle at the discovered position and continue their migration
from this position (Civicioglu 2012 ).
In DSA metaheuristic, a superorganism X k of N arti
cial-organisms making up,
at every generation k ¼
1
;
2
; ...; k max , an arti
cial-organism with members as much
as the size of the problem, de
ned as follows:
X k ¼
x i ; 1
k
x i ; 2
k
x i ; d
k
x i ; D
k
;
; ...;
; ...;
ð
3
Þ
A member of an arti
cial-organism, in initial position, is randomly de
ned by
using Eq. ( 4 ):
x i ; 0 ¼
x i ; d
x i ; d
low
x i ; d
low þ
rand 0
ðÞ
;
1
up
ð
4
Þ
finding a so called Stopover Site, which presents the
solution of optimization problem, at the areas remaining between the arti
In DSA, the mechanism of
cial-
organisms, is described by a Brownian-like random walk model. The principle is
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