8. How to Exploit Alignment in the Error Space: Two Different GP Models

From a recent study, we know that if we are able to find two optimally aligned individuals, then we can reconstruct a globally optimal solution analytically for any regression problem. With this knowledge in mind, the objective of this chapter is to discuss two Genetic Programming (GP) models aimed at finding pairs of optimally aligned individuals. The first one of these models, already introduced in a previous publication, is ESAGP-1. The second model, discussed for the first time here, is called Pair Optimization GP (POGP). The main difference between these two models is that, while ESAGP-1 represents solutions in a traditional way, as single expressions (as in standard GP), in POGP individuals are pairs of expressions, that evolution should “push” towards the optimal alignment. The results we report for both these models are extremely encouraging. In particular, ESAGP-1 outperforms standard GP and geometric semantic GP on two complex real-life applications. At the same time, a preliminary set of results obtained on a set of symbolic regression benchmarks indicate that POGP, although rather new and still in need of improvement, is a very promising model, that deserves future developments and investigation.