Comparative study of four penalty-free constraint-handling techniques in structural optimization using harmony search

This study investigates the search capability, stability, and computational efficiency of four improved penalty-free constraint-handling techniques (CHTs), including the death penalty, the Deb rule, the filter method, and the mapping strategy, in structural optimization using harmony search (HS). The first three general-purpose CHTs have been improved by hybridizing with a structural analysis filter strategy to enhance their computational efficiency based on the characteristics of structural optimization and the solution updating rule of the HS. This study also has modified the mapping operator of the mapping strategy to handle size and shape optimization with Euler buckling constraints. Four numerical examples examine the performances of these CHTs. The comparative results show that the mapping strategy exhibits apparent superiority both in search capability and stability among the four. However, it also demands the most computational cost, and the improved Deb rule becomes the most competitive method while considering computational efficiency. The difference between the death penalty and the Deb rule method is that the feasible solution initialization process required by the death penalty method will deteriorate its computational efficiency in problems with small feasible space. The filter method always reserves some infeasible solutions to guide the search in the iteration process. However, its performances are inferior to the other three approaches in four benchmark problems.