Solving constrained optimization problems with new penalty function approach using genetic algorithms

In this paper a novel penalty function is proposed for constrained optimization problems with linear and nonlinear constraints using a genetic algorithm. We show that by using a mapping function to "wrap" up the constraints, a constrained optimization problem can be converted to an unconstrained optimization problem, and we prove mathematically that the best solution of the converted unconstrained optimization problem approaches the best solution of the constrained optimization problem if a tuning parameter for the wrapping function approaches zero. A genetic algorithm is then used to search for the optimal solutions of the converted unconstrained optimization problems. Two test examples were used to show the effectiveness of the approach.