Crossover Operator Effect in Function Optimization with Constraints

Most real-world optimization problems consist of linear cost functions subject to a set of constraints. In genetic algorithms the techniques for coping with such constraints are manifold: penalty functions, keeping the population in the feasible region, etc. Mutation and crossover operators must take into account the specific features of this kind of problems, as they are the responsible of the generation of new individuals. In this work, we make an analysis of the influence of the selection of the crossover operator in the problem of function optimization with constraints. We focus our work on the crossover operator because this operator is the most characteristic of genetic algorithms. We have used a test set that includes functions with linear and non-linear constraints. The results confirm the importance of crossover operator, as great differences are observed in the performance of the studied operators. The crossover based on confidence intervals shows the most robust behavior.