Gpax: Genetic Parabolic Adaptive Crossover Operator

In this paper we propose a new crossover operator for real coded evolutionary algorithms that is based on a parabolic probability density function. This density function depends on two real parameters α and β which have the capacity to achieve exploration and exploitation dynamically during the evolutionary process in relation to the best individuals. In other words, the proposed crossover operator is able to handle the generational diversity of the population in such a way that it can either generate additional population diversity, therefore allowing exploration to take effect, or use the diversity previously generated to exploit the better solutions. In order to test the performance of this crossover, we have used a set of test functions and have made a comparative study of the proposed crossover against other classic crossover operators. The analysis of the results allows us to affirm that the proposed operator displays a very suitable behavior, although, it should be noted that it offers a better behavior applied to complex search spaces than simple ones.