d	the current transverse local displacement of the blade
$d_{tip}$	the current transverse displacement of the tip blade
$d_{per}$	the permissible transverse local displacement of the blade
$d_{tip\_per}$	the permissible displacement of the tip blade
${\epsilon }_{per}$	the current the blade deformation
${\epsilon }_{per}$	the allowable the blade deformation
$f_h$	the frequency of harmonic vibration
$f_{nl}$	the l-th natural frequencies of the blade
m	the current mass of the blade
$m_{per}$	the permissible mass of the blade
${\sigma }_{}$	the current stress in the blade
${\sigma }_{per}$	the permissible stress in the blade
w	column array weights of the respective objective functions
Ω	the domain of possible solutions
X	column matrix of design variables
$X_j^L$	the lower bound of the design variables
$X_j^U$	the upper bound of the design variables