| Abstract: | 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. |