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. |