Research Article

A Novel Quantum-Behaved Bat Algorithm with Mean Best Position Directed for Numerical Optimization

Table 1

Benchmark function.

CategoryNumberFunctionRange

IF1305.12, 5.12]0
F23010, 10]0
F330100, 100]0
F430100, 100]0
F53030, 30]0
F6301.28, 1.28]0

IIF7305.12, 5.12]0
F83032, 32]0
F930600, 600]0
F103050, 50]0
F113050, 50]0
F123010, 10]−1

IIIF1330100, 100]0
F1430100, 100]0
F15305, 5]0
F1630100, 100]0
F17300, 600]0
F183032, 32]0

IVF19 (CF1)Hybrid Composition Function
, = Rastrigin’s Function
, = Weierstrass Function
, = Griewank’s Function
, = Ackley’s Function
, = Sphere Function

305, 5]0
F20 (CF2)Rotated version of Hybrid Composition Function F19
Except which are different linear transformation matrixes with condition number of 2, all other settings are the same as F19
305, 5]0
F21 (CF3)F20 with noise in fitness
Let F20 be ; then
All settings are the same as F20
305, 5]0
F22 (CF4)Rotated Hybrid Composition Function
, = Ackley’s Function 
, = Rastrigin’s Function 
, = Sphere Function 
, = Weierstrass Function 
, ,
, = Griewank’s Function 


are all rotation matrixes. Condition numbers are
305, 5]0
F23 (CF5)Rotated Hybrid Composition Function with narrow basin global optimum
All settings are the same as F22 except


305, 5]0
F24 (CF6)Rotated Hybrid Composition Function with global optimum on the bounds
All settings are the same as F23 except, after loading the data file,
set , for
305, 5]0