Crossover effect over penalty methods in function optimization with constraints

One of the most common and versatile techniques for coping with constraints consists of the penalty of the solutions whose variables do not fulfill the constraints. The genetic algorithm (GA) is one of the main tools used for the optimization of functions with constraints. In this context the crossover operator must tend to generate individuals within or near the feasible region in order to converge to useful solutions. In this work we make an analysis of the influence of the crossover operator in this kind of problems. We have used a test set that includes functions with linear and nonlinear constraints. The results confirm the importance of the crossover operator.