Since its introduction, Geometric Semantic Genetic Programming (GSGP) has aroused the interest of numerous researchers and several studies have demonstrated that GSGP is able to effectively optimize training data by means of small variation steps, that also have the effect of limiting overfitting. In order to speed up the search process, in this paper we propose a system that integrates a local search strategy into GSGP (called GSGP-LS). Furthermore, we present a hybrid approach, that combines GSGP and GSGP-LS, aimed at exploiting both the optimization speed of GSGP-LS and the ability to limit overfitting of GSGP. The experimental results we present, performed on a set of complex real-life applications, show that GSGP-LS achieves the best training fitness while converging very quickly, but severely overfits. On the other hand, GSGP converges slowly relative to the other methods, but is basically not affected by overfitting. The best overall results were achieved with the hybrid approach, allowing the search to converge quickly, while also exhibiting a noteworthy ability to limit overfitting. These results are encouraging, and suggest that future GSGP algorithms should focus on finding the correct balance between the greedy optimization of a local search strategy and the more robust geometric semantic operators.

In standard genetic programming (GP), a search is performed over a syntax space defined by the set of primitives, looking for the best expressions that minimize a cost function based on a training set. However, most GP systems lack a numerical optimization method to fine tune the implicit parameters of each candidate solution. Instead, GP relies on more exploratory search operators at the syntax level. This work proposes a memetic GP, tailored for binary classification problems. In the proposed method, each node in a GP tree is weighted by a real-valued parameter, which is then numerically optimized using a continuous transfer function and the Trust Region algorithm is used as a local search method. Experimental results show that potential classifiers produced by GP are improved by the local searcher, and hence the overall search is improved achieving significant performance gains, that are competitive with state-of-the-art methods on well-known benchmarks.