Firefly Algorithm (FFA)
The firefly algorithm was inspired by the flashing light of fireflies
and developed by Xin-She Yang [15]. All the fireflies are considered
unisexual and their attraction is directly proportional to the intensity
of their flash. Therefore if a firefly particle had the choice of moving
towards either of two fireflies, it will be more attracted towards the
firefly with higher brightness and moves in that direction. If there are
no fireflies nearby, the firefly will move in a random direction. The
brightness of flash is associated with the fitness function. As a
firefly’s attractiveness is proportional to the light intensity seen by
adjacent fireflies, the attractiveness β of a firefly can be
defined as a function of the Cartesian distance r between the
fireflies [15,16]:
(35)
where β 0 is the attractiveness at r = 0
and γ is the absorption coefficient. The movement of a fireflyi is attracted to another more attractive (brighter) fireflyj is determined by
(36)
where α is the randomization parameter and ε is the vector of
random numbers taken from Gaussian distribution. At the end of all
generations, the firefly with the highest brightness i.e. the best
fitness value is concluded as the optimal solution to the problem