Bio-inspired Evolutionary Computing with Context-Awareness and Collective-Effect - Technologies and Applications of Artificial Intelligence - page 102

experimental results show that the proposed HBA can significantly improve the per-
formance of the original bat algorithm, which can be very useful for the future.
The original bat algorithm was hybridized by the differential evolutions (DE). DE
is a typical evolutionary algorithm with differential mutation, crossover and selection
that was successfully applied to continuous function optimization, proposed by Storn
and Price [11-13]. HBA differs from the original BA in local search step. A random
solution is selected and modified by “DE/rand/1/bin” strategy of DE. The differential
mutation randomly selects two solutions and adds a scaled difference between them to
produce the third solution. This mutation can be expressed as follows:

, for i=1,…, PS (3)

where is the candidate solution presented by the i th bat at iteration t, generated by
mutation and PS is the population size. ∈0.1,1.0 is the mutation rate as a scaling
factor to scale the adjustment. The variables, r 0 , r 1 and r 2 , are random integers from 1
to PS. w is the bat in a population. This intention of HBA is to produce a position of
bat different from the position of all bats in a population.
Uniform crossover is employed as a differential crossover by the DE. The trial vec-
tor is built out of parameter values that have been copied from two different solutions.
This crossover can be expressed as follows:

0,1
,

.

. (4)

where j is the j th dimension in bat i . z is a new solution generated by crossover of the
original position and the solution generated by mutation. ∈0.0,1.0 is the cros-
sover rate and controls the fraction of parameters that are copied to the trial solution.
Note, the relation assures that the trial vector is different from the original
solution . In [10], the strategy “DE/rand/1/bin” is applied to produce the variety
of trial position and denotes that the base vector is randomly selected, 1 vector differ-
ence is added to it, and the number of modified parameters in mutation vector follows
binomial distribution. This operation in HBA benefits the information gathering for
population to produce a better position of bats. Then, differential selection can be
expressed as follows:

(5)

where f is the fitness function used to evaluate the quality of position for each bat in
HBA. If the quality of new position generated by crossover is better than the quality
of the original position, the bat will move to the new position. Otherwise, the bats stay
in the current position. In HBA, an operator of DE is applied in local search to gather
the information. The various positions of bats are produced by information gathering
to improve the solving efficiency in BA.