An Analysis of Geometric Semantic Crossover: A Computational Geometry Approach

Geometric semantic operators have recently shown their ability to outperform standard genetic operators on different complex real world problems. Nonetheless, they are affected by drawbacks. In this paper, we focus on one of these drawbacks, i.e. the fact that geometric semantic crossover has often a poor impact on the evolution. Geometric semantic crossover creates an offspring whose semantics stands in the segment joining the parents (in the semantic space). So, it is intuitive that it is not able to find, nor reasonably approximate, a globally optimal solution, unless the semantics of the individuals in the population “contains” the target. In this paper, we introduce the concept of convex hull of a genetic programming population and we present a method to calculate the distance from the target point to the convex hull. Then, we give experimental evidence of the fact that, in four different real-life test cases, the target is always outside the convex hull. As a consequence, we show that geometric semantic crossover is not helpful in those cases, and it is not even able to approximate the population to the target. Finally, in the last part of the paper, we propose ideas for future work on how to improve geometric semantic crossover.