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 97

which a value of 0 . 4 <P f < 0 . 5 was reported as the most appropriate. f(G i ) is the
fitness value of the island G i and Φ(G i ) its constraints violation degree, such that

p

max 0 ,ψ j ( G i ) 2

Φ( G i ) = (5.39)

j = 1

where ψ j denotes the constraint violation for the j th constraint.

5.4.3.6 Population Update Strategy

It has already been mentioned that the proposed algorithms adopt different mecha-
nisms for updating the population. The operating principles of the CBBO, CBBO-
DE, and 2-Stage-CBBO-DE updating strategies are described as follows:

1. CBBO : In the CBBO algorithm, the population is updated by successively apply-
ing the migration procedure followed by the mutation procedure in an iterative
fashion, similar to the philosophy employed in original BBO (see Algorithm 1 ).

2. CBBO-DE : This variant incorporates the mutation procedure inherited from DE
algorithm [ 19 , 22 ], to replace the existing mutation procedure in BBO. Unlike
CBBO, CBBO-DE first generates new parameter vectors, by using the DE mu-
tation operation, and then the BBO-based migration operator is applied for the
resultant mutated vectors [ 6 ].

(a) DE Mutation
The mutation is performed by calculating weighted vector differences be-
tween other randomly selected individuals of the same population. A muta-
tion scale factor F is used to control the amplification of the differential vari-
ation. The mutation operation constructs, for each population vector G i,g ,a
mutant vector V i,g .
Different mutation schemes are suggested by Price et al. [ 19 ]. The gen-
eral convention used to name the different DE variants is DE/x/y/z .Here DE
stands for differential evolution, x represents a string that denotes the base
vector, i.e., the vector being perturbed (whether it is randomly selected or it
is the best vector in the population with respect to fitness value and constraint
violation), y is the number of difference vectors, considered for perturbation
of x , and z denotes the crossover scheme which may be binomial or expo-
nential . The mutation is performed following the DE/rand/1/bin -variant, also
known as the classical version of DE, which is the most frequently used mu-
tation strategy. This mutation scheme uses a randomly selected base vector
G r 1 ,g and only one weighted difference vector F( G r 2 ,g −

G r 3 ,g ) is used to

perturb it:

V i,g = G r 1 ,g + F( G r 2 ,g − G r 3 ,g ), (5.40)