Bio-inspired Evolutionary Computing with Context-Awareness and Collective-Effect - Technologies and Applications of Artificial Intelligence - page 111

function and Ackley function in this study are the same as [10]. Therefore, these two
functions are adopted to the comparison of solving efficiency for GBA, HBA and BA in
these three kinds of dimensions. The simulation results of compared three algorithms are
shown in Table 2.
The purpose is to compare the quality of global optimal solution between GBA,
HBA and BA in an iteration limitation. For BA, there are severe average errors of
global optimal solution in these three kinds of dimensions for these two examined
functions. Therefore, these iteration limitations are insufficient to discover the eligible
global optimal solution. Furthermore, the HBA is proposed to improve the quality of
global optimal solution in an iteration limitation. The strategies of differential evolu-
tion are applied to reform the local search in BA to design HBA. The average error of
global optimal solution is decreased so that it is noticeably improved in HBA, particu-
larly for Griewangk function shown in Table 2. These simulation results prove that
HBA based on DE applied in local search benefits the improvement of quality with
global optimal solution.

Table 2. The statistics comparison of BA, HBA, and GBA in benchmark functions with various
dimensions

Algorithm Function Statistics d=10 d=20 d=30

Min. 3.29E+01 8.77E+01 1.58E+02

Max. 1.73E+02 1.43E+02 4.18E+02

Griewangk

Avg. 8.30E+01 1.46E+00 1.51E+02

Std. 6.94E+01 1.64E+01 1.52E+01

BA

Min. 1.37E+01 2.15E+02 3.39E+02

Max. 2.00E+01 5.87E+02 7.82E+02

Ackley

Avg. 1.75E+01 3.38E+02 4.67E+02

Std. 1.73E+01 1.80E+01 1.76E+01

Min. 2.25E-09 1.01E-07 6.38E-06

Max. 3.97E-05 2.96E+01 3.57E+01

Griewangk

Avg. 3.18E-06 8.56E-07 6.42E-05

Std. 1.14E-07 2.17E+00 3.12E+00

HBA

Min. 6.31E-04 3.70E-05 5.43E-04

Max. 2.00E+01 5.48E+01 9.85E+01

Ackley

Avg. 1.16E+01 3.82E-05 2.53E-03

Std. 1.78E+01 1.95E+01 1.94E+01

Min. 0.00E+00 0.00E+00 0.00E+00

Max. 0.00E+00 0.00E+00 0.00E+00

Griewangk

Avg. 0.00E+00 0.00E+00 0.00E+00

GBA

Std. 0.00E+00 0.00E+00 0.00E+00

Min. 1.45E-16 1.45E-16 1.45E-16

Max. 1.12E-14 1.86E-14 2.97E-14

Ackley

Avg. 1.24E-15 3.36E-15 6.04E-15

Std. 0.00E+00 0.00E+00 0.00E+00