Advanced Metaheuristics-Based Approach for Fuzzy Control Systems Tuning - Complex System Modelling and Control Through Intelligent Soft Computations - page 621

Precup et al. ( 2011 ), Rashedi et al. ( 2009 ). The search agents are a set of masses which
interact with each other based on the Newtonian gravity and the law of motion.
Several applications of this algorithm in various areas of engineering are
investigated (Nobahari et al. 2011 ; Precup et al. 2011 ; Rao and Savsani 2012 ). In
GSA, the particles, called also agents, are considered as bodies and their perfor-
mance is measured by their masses. All these bodies attract each other by the
gravity force that causes a global movement of all objects towards the objects with
heavier masses. These agents correspond to the optimum solutions in the search
space (Rashedi et al. 2009 ). Indeed, each agent presents a solution of optimization
problem and is characterised by its position, inertial mass, active and passive
gravitational masses. The GSA is navigated by properly adjusting the gravitational
and inertia masses leading masses to be attracted by the heaviest object.
The position of the mass corresponds to a solution of the problem, and its
gravitational and inertial masses are determined using a cost function. The
exploitation capability of this algorithm is guaranteed by the movement of the
heavy masses, more slowly than the lighter ones.
Let us consider a population with N agents. The position of the ith agent at
iteration time k is de

ned as:

X k ¼ x i ; 1

k

x i ; 2
k

x i ; d
k

x i ; D
k

; ; ...; ; ...; ð 8 Þ

where x i ; d k presents the position of the ith particle in the dth dimension of search
space of size D.
At a speci c time “ t ” , denoted by the actual iteration “ k ” , the force acting on

mass “ i ” from mass “ j ” is given as follows:

G k M p k

M aj
k

F ij ; d
k

x j ; k x i ; d

k

¼ ð 9 Þ

R i k þ e

where M aj

k is the active gravitational mass related to agent j, M pi k is the passive
gravitational mass related to agent i, G k is the gravitational constant at time k, e is a

small constant, and R i k is the Euclidian distance between two agents i and j,de ned as:

2

R i k ¼ X k X k ; ð 10 Þ

To give a stochastic characteristic to this algorithm, authors of GSA suppose that
the total force that acts on agent i is a randomly weighted sum of jth components of
the forces exerted from other bodies, given as follows (Rashedi et al. 2009 ):

X

N

F i ; d
k

rand j F ij ; d
k

¼ ð 11 Þ

j ¼ 1 ; j 6¼ i

where rand j is a random number in the interval [0, 1].