An adaptive penalty function in genetic algorithms for structural design optimization

In genetic algorithms, constraints are mostly handled by using the concept of penalty functions, which penalize infeasible solutions by reducing their fitness values in proportion to the degrees of constraint violation. In most penalty schemes, some coefficients or constants have to be specified at the beginning of the calculation. Since these coefficients usually have no clear physical meanings, it is nearly impossible to estimate appropriate values of these coefficients even by experience. Moreover, most schemes employ constant coefficients throughout the entire calculation. This may result in too weak or too strong a penalty during different phases of the evolution. In this study, a new penalty scheme that is free from the aforementioned disadvantages is developed. The proposed penalty function will be able to adjust itself during the evolution in such a way that the desired degree of penalty is always obtained. The coefficient used in the proposed scheme will have a clear physical meaning. Thus, it will not be difficult to set the value of the coefficient by using experience.