A Comparative Study of Modified BBO Variants and Other Metaheuristics for Optimal Power Allocation in Wireless Sensor Networks - Advances in Heuristic Signal Processing and Applications - page 99

proposed algorithm, the mutation is performed using the DE/rand/1 mutation
strategy as follows:

G r 3 ,g )
where G r 1 ,g , G r 2 ,g , and G r 3 ,g are three individual vectors chosen at random
and mutually different.
After the mutation phase, a crossover operation is applied to each pair of
the target vector G i,g and its corresponding mutant vector V i,g to generate a
trial vector M i,g :

V i,g = G r 1 ,g + F( G r 2 ,g −

V i,j,g if rand ( 0 , 1 ) ≤

CR or j = j rand ,

M i,j,g = (5.44)

G i,j,g otherwise,

1 , 2 ,...,L.
The crossover factor CR is randomly taken from the interval

i = 1 , 2 ,...,NP and j =

and
presents the probability of creating parameters for trial vector from a mutant
vector. Index j rand is a randomly chosen integer within the range

[ 0 , 1 ]

.It
is responsible for the trial vector containing at least one parameter from the
mutant vector. rand ( 0 , 1 ) is a uniform random number in the range

[ 1 ,NP ]

[ 0 , 1 ] .

5.4.3.7 Selection

We adopt the binary tournament selection, described in [ 9 ]. Hence, the island G i,g
will be replaced by its newly mutated and migrant island M i,g , to survive as a mem-
ber for the next generation g + 1, under any of the following conditions:

•

G i,g is infeasible, but M i,g is feasible,

• Both G i,g and M i,g are feasible, but f( M i,g )<f( G i,g ) ,

• Both G i,g and M i,g are infeasible, but Viol ( M i,g )< Viol ( G i,g ) (the island having

smaller constraint violation is preferred).
In order to impose the same degree of importance to all constraints, the maximum
violation value for each constraint in the whole population is used to normalize each
violated constraint calculated in ( 5.45 ):

p

ψ j ( G i,g )
ψ max (j)

Viol ( G i,g ) = (5.45)

j = 1

where ψ max (j) is the greatest violation value for the constraint j .
The selection procedure is shown in Algorithm 3 .

5.4.3.8 Elitism

To prevent the loss of the best islands, elitism is implemented as follows: the n elit
worst islands of the current generation are replaced by the n elit elite islands from the
previous generation ( n elit is the elitism parameter).