Moraglio et al. have recently introduced new genetic operators for genetic programming, called geometric semantic operators. It is possible to prove that these operators induce a unimodal ﬁtness landscape for all the problems consisting in matching input data with known target outputs (like regression and classiﬁcation). This feature facilitates genetic programming evolvability, which makes these operators extremely promising. Nevertheless, Moraglio et al. leave one big open problem: these operators, by construction, always produce offspring that are larger than their parents, causing an exponential growth in the size of the individuals, which actually renders them useless in practice.
In this seminar, a general introduction to optimization, to fitness landscapes and to evolutionary computation, with particular focus on genetic programming, is offered. After that, geometric semantic operators are presented and the fact that they induce a unimodal fitness landscape on every possible instance of regression and classification is informally shown. Finally, after discussing the limitation of geometric semantic operators, a new efﬁcient implementation of them is presented.
This new implementation allows us, for the ﬁrst time, to use these operators on complex real-life applications, like the two complex problems in pharmacokinetics that are discussed in the seminar. The presented experiments conﬁrm the excellent evolvability of geometric semantic operators, demonstrated by the good results reported on training data. Furthermore, a surprisingly good generalization ability was achieved, testified by the excellent results obtained on test data.
This fact can be explained considering some particular properties of geometric semantic operators, which makes them even more appealing than before.