A survey and numerical comparison of factor-free penalty function constraint-handling techniques in genetic algorithms

Numerous techniques have been proposed for handling almost all kinds of constraints in searching for solutions to constrained optimization problems. Among these methods, penalty function has been the most commonly used approach. However, a drawback of the penalty function method lies in the difficulty of setting adequate penalty factors. Thus, due to the unavailability of appropriate penalty factors, the factor-free penalty function is created to decide penalties directly by the severities of constraint violations, and is expected to capture the distance to feasibility without any user-defined factors. However, although various factor-free penalty functions have been developed, a formal comparison of these functions is short. Therefore, in order to have a clearer picture of the factor-free penalty functions and their performances, this article surveys and compares the factor-free penalty functions proposed in prior literature, and performs a numerical comparison of these (nine) functions by applying the genetic algorithm on a collection of 37 popular test problems.