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 98

where the indices r 1 ,r 2 ,r 3 are randomly chosen over the interval ]

and should be mutually different from the running index i and F is a real
constant scaling factor within the range

[ 1 ,NP

[ 0 , 2 ] , usually chosen less than 1.

(b) Migration
The DE mutation produces new vectors V i,g ( i 1 ,...,NP ), which are up-

dated by the BBO-based migration operator. The migration operator is the
same as what was employed in original BBO, except that it is applied to the
newly modified individuals V i,g . This operation produces new population
vectors M i,g as follows:

=

V k,j,g if rand ( 0 , 1 )<λ i ,
V i,j,g otherwise,

M i,j,g = (5.41)

1 ,...,D and V k,j,g is the j th decision variable
of a randomly selected individual V k,g among the transformed population in
generation g . V k,g is selected with a probability based on its emigration rate
μ k and λ i is the immigration rate of the individual M i,g .
3. 2-Stage-CBBO-DE
The population update strategy of the 2-Stage-CBBO-DE algorithm is similar to
the one described in [ 5 ]. The population is updated by applying, alternately from
one iteration of the algorithm to the next, the BBO and DE updating methods, as
described bellow.

where i = 1 , 2 ,...,N , j =

• BBO updating method

The BBO updating method consists of applying the migration and the mutation
operators. The migration operator reproduces a new population vector M i,g as
follows:

G k,j,g if rand ( 0 , 1 )<λ i ,
G i,j,g otherwise,

M i,j,g = (5.42)

where i 1 ,...,L and G k,j,g is the j th decision variable of

a randomly selected individual G k,g . G k,g is selected with a probability based
on μ k .
The mutation is performed for the whole population by perturbing the
newly migrant individuals M i,g as follows:

= 1 , 2 ,...,NP , j =

rand (l j ,u j ) if rand ( 0 , 1 )<m(i) ,
M i,j,g

M i,j,g = (5.43)

otherwise,

where i 1 ,...,L , m(i) is the mutation rate given by

Eq. ( 5.34 ) and rand (l j ,u j ) is a random number (uniformly distributed) be-
tween lower and upper bounds l j and u j .

= 1 , 2 ,...,NP , j =

• DE updating method

DE employs the mutation operation to produce a mutant vector with respect to
each individual, the so-called target vector, in the current population. For the