Advanced Metaheuristics-Based Approach for Fuzzy Control Systems Tuning - Complex System Modelling and Control Through Intelligent Soft Computations - page 623

1 j N fit k

best k ¼ min ð 19 Þ

1 j N fit k

worst k ¼ max ð 20 Þ

To perform a good compromise between exploration and exploitation, authors of
GSA choose to reduce the number of agents with lapse of iterations in Eq. ( 11 ),
which will be modi

ed as:

X

rand j F ij ; d
k

F i ; d
k

¼ ð Þ

21

j 2 Kbest ; j 6¼ i

where Kbest is the set of the first K agents with best fitness and biggest mass that

will attract the others.
The algorithm parameter Kbest is a function of iterations with the initial value
K 0 , usually set to the total size of population N at the beginning, and linearly
decreasing with time. At the end of search, there will be just one agent applying
force to the others.
Finally, the steps of the original version of GSA, as described in Rashedi et al.
( 2009 ), can be summarized as follows:

1. Search space characterization: number of agents, dimension of problem, control
parameters G 0 , K 0 , …

2. Randomized generation of the initial population.
3. Fitness evaluation of agents.
4. Update the algorithm parameters G k , best k , worst k and M k for each agent and at

each iteration.
5. Calculation of the total force in different directions.
6. Calculation of acceleration and velocity.
7. Updating agents

'

position.

8. Repeat steps 3 - 7 until the stop criteria are reached.

3.3 Arti cial Bee Colony

The Arti cial Bee Colony (ABC) is a population-based metaheuristic optimization

algorithm introduced in 2005 by Karaboga ( 2005 ). The principle of such an algo-
rithm is based on the intelligent foraging behavior of honey bee swarm (Basturk and
Karaboga 2006 ; Karaboga 2005 ; Karaboga and Akay 2009 ; Karaboga and Basturk
2007 , 2008 ). The ABC algorithm has been enormously successful in various
industrial domains and a wide range of engineering applications as summarized in
Karaboga et al. ( 2012 ).