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Advances in Geometric Semantic Genetic Programming (GSGP) have shown that this variant of Genetic Programming (GP) reaches better results than its predecessor for supervised machine learning problems, particularly in the task of symbolic regression. However, by construction, the geometric semantic crossover operator generates individuals that grow exponentially with the number of generations, resulting in solutions with limited use. This paper presents a new method for individual simplification named GSGP with Reduced trees (GSGP-Red). GSGP-Red works by expanding the functions generated by the geometric semantic operators. The resulting expanded function is guaranteed to be a linear combination that, in a second step, has its repeated structures and respective coefficients aggregated. Experiments in 12 real-world datasets show that it is not only possible to create smaller and completely equivalent individuals in competitive computational time, but also to reduce the number of nodes composing them by 58 orders of magnitude, on average., 8 pages, In proceedings of Genetic and Evolutionary Computation Conference (GECCO 2018), Kyoto, Japan

Automatic Machine Learning is a growing area of machine learning that has a similar objective to the area of hyper-heuristics: to automatically recommend optimized pipelines, algorithms or appropriate parameters to specific tasks without much dependency on user knowledge. The background knowledge required to solve the task at hand is actually embedded into a search mechanism that builds personalized solutions to the task. Following this idea, this paper proposes RECIPE (REsilient ClassifIcation Pipeline Evolution), a framework based on grammar-based genetic programming that builds customized classification pipelines. The framework is flexible enough to receive different grammars and can be easily extended to other machine learning tasks. RECIPE overcomes the drawbacks of previous evolutionary-based frameworks, such as generating invalid individuals, and organizes a high number of possible suitable data pre-processing and classification methods into a grammar. Results of f-measure obtained by RECIPE are compared to those two state-of-the-art methods, and shown to be as good as or better than those previously reported in the literature. RECIPE represents a first step towards a complete framework for dealing with different machine learning tasks with the minimum required human intervention.

Recent advances in geometric semantic genetic programming (GSGP) have shown that the results obtained by these methods can outperform those obtained by classical genetic programming algorithms, in particular in the context of symbolic regression. However, there are still many open issues on how to improve their search mechanism. One of these issues is how to get around the fact that the GSGP crossover operator cannot generate solutions that are placed outside the convex hull formed by the individuals of the current population. Although the mutation operator alleviates this problem, we cannot guarantee it will find promising regions of the search space within feasible computational time. In this direction, this paper proposes a new geometric dispersion operator that uses multiplicative factors to move individuals to less dense areas of the search space around the target solution before applying semantic genetic operators. Experiments in sixteen datasets show that the results obtained by the proposed operator are statistically significantly better than those produced by GSGP and that the operator does indeed spread the solutions around the target solution.

This paper investigates the impact of geometric semantic crossover operators in a wide range of symbolic regression problems. First, it analyses the impact of using Manhattan and Euclidean distance geometric semantic crossovers in the learning process. Then, it proposes two strategies to numerically optimize the crossover mask based on mathematical properties of these operators, instead of simply generating them randomly. An experimental analysis comparing geometric semantic crossovers using Euclidean and Manhattan distances and the proposed strategies is performed in a test bed of twenty datasets. The results show that the use of different distance functions in the semantic geometric crossover has little impact on the test error, and that our optimized crossover masks yield slightly better results. For SGP practitioners, we suggest the use of the semantic crossover based on the Euclidean distance, as it achieved similar results to those obtained by more complex operators.

This chapter describes the Sequential Symbolic Regression (SSR) method, a new strategy for function approximation in symbolic regression. The SSR method is inspired by the sequential covering strategy from machine learning, but instead of sequentially reducing the size of the problem being solved, it sequentially transforms the original problem into potentially simpler problems. This transformation is performed according to the semantic distances between the desired and obtained outputs and a geometric semantic operator. The rationale behind SSR is that, after generating a suboptimal function f via symbolic regression, the output errors can be approximated by another function, in a subsequent iteration. The method was tested in eight polynomial functions, and compared with canonical genetic programming (GP) and geometric semantic genetic programming (SGP). Results showed that SSR significantly outperforms SGP and presents no statistical difference from GP. More importantly, they show the potential of the proposed approach: an effective way of applying geometric semantic operators to combine different (partial) solutions, and at the same time, avoiding the exponential growth problem arising from the use of semantic operators.