Most of the penalty function methods require pre-defined or
static penalty function coefficients at the beginning of the calculations.
These coefficients are generally determined by trial and error
methods. If the penalty function coefficients are too low, the optimized
design converges to an unfeasible solution without satisfying
the constraints. On the other hand, if the penalty function coefficients
are too high, the optimized design will not have a satisfactory
objective function value. In order to overcome this drawback of the
static penalty function method, various types of penalty functions
have been proposed and studied [38,17]. Adaptive penalty is one
of the methods, in which a penalty function coefficient is adapted
according to feedback received from the search process. Different
versions of the adaptive penalty function techniques have been
proposed by various researchers including Hadj-Alouane and Bean
[39], Nanakorn and Meesomklik [40], Hasancebi [18], and Togan
and Daloglu [11].