A Study of Adaptive Penalty Functions for Constrained Genetic Algorithm- Based Optimization

Constrained optimization via the Genetic Algorithm (GA) is often a challenging endeavor, as the GA is most directly suited to unconstrained optimization. Traditionally, external penalty functions have been used to convert a constrained optimization problem into an unconstrained problem for GA-based optimization. This approach requires the somewhat arbitrary selection of penalty draw-down coefficients. In this paper, several potential approaches are presented that utilize adaptive penalty functions that change the value of the draw-down coefficients during a run of the genetic algorithm. A simple one-dimensional constrained problem and a more complex twodimensional constrained problem were solved using the adaptive penalty strategies. Then, a stiffened composite panel was optimized for minimum weight, subject to several constraints using the adaptive penalty methods to provide insight to how the approaches perform on an engineering problem. Based on these problem solutions, conclusions were drawn regarding the efficacy of adaptive penalty functions for constrained optimization.