Cuckoo Search Algorithm (CS)
Cuckoo search algorithm is based on the obligate brood parasitic
behaviour of some cuckoo species in combination with the Lévy flight
behaviour of some birds and fruit flies [18]. This algorithm uses
three idealized rules: (i) Each cuckoo lays one egg at a time and dumps
it in a randomly chosen nest; (ii) The best nests with high quality of
eggs (fitness) will carry over to the next generations; (iii) The number
of available host nests is fixed, and the egg laid by a cuckoo is
discovered by the host bird with a probability pa[0, 1]. In this case, the host bird can either throw the egg away or
abandon the nest, and build a completely new nest.
A new cuckoo (solution) by Lévy flights is generated as follows:
(42)
where α > 0 is the step size which should be related
to the scales of the problem of interest. The Lévy flight essentially
provides a random walk while the random step length is drawn from a Lévy
distribution which has an infinite variance with an infinite mean. Here
the steps essentially form a random walk process with a powerlaw
step-length distribution with a heavy tail. Some of the new solutions
should be generated by Lévy walk around the best solution obtained so
far, this will speed up the local search. However, a substantial
fraction of the new solutions should be generated by far field
randomization and whose locations should be far enough from the current
best solution, this will make sure the system will not be trapped in a
local optimum [18].