Lexicase parent selection considers training cases separately, postulating that aggregated fitness reduces the information about the behavior of individuals. Originally lexicase was proposed in the context of program synthesis, characterized by uncompromising problems that require qualitatively different actions for different inputs, but it has since been extended to regression problems. To facilitate valley-crossing a relaxation parameter ϵ was added broadening the pass condition at a given training case. Although ϵ-lexicase has demonstrated superior effectiveness, it was compared against selection methods that aggregated squared (or absolute) errors. Recent contributions, however, demonstrate that correlation fitness functions can lead to significant performance gains over the root mean square error (RMSE) in tournament-guided evolution for symbolic regression. Here we compare ϵ-lexicase (with and without down-sampling) against tournament selection using both error- and correlation-based fitness to guide Genetic Programming (GP). We also assess batch ϵ-lexicase selection as an intermediate condition. Finally, we explore different selection pressures to assess the exploration-exploitation trade-off. We analyze the experimental results using different metrics, including code redundancy, sharpness-awareness and selection impact. Our results demonstrate that tournament selection with correlation fitness function significantly outperforms ϵ-lexicase on regression problems and that its batch variant also benefits from correlation-based aggregation.

This manuscript presents an improved version of the Inclusive Genetic Programming (IGP) algorithm. The IGP was developed to promote and maintain the population's genotypic diversity and showed superior performance compared to standard Genetic Programming (GP). In this work, two modifications to the IGP are proposed: first, the diversity promotion and maintenance mechanism is enhanced with information from the phenotype of the individuals rather than only the genotype; second, the Evolutionary Demes Despeciation Algorithm - V2 (EDDA-V2) is used to initialize the population. The phenotype is considered to differentiate the individuals also according to their behaviour rather than only their structure, while EDDA-V2 is employed to start the evolution with a simultaneously diverse and fit population, contrary to traditional initialization techniques. The algorithms incorporating these improvements are called Full Inclusive Genetic Programming (FIGP) and FIGP _E, respectively with and without the EDDA-V2 initialization. The experimental results, performed over eight benchmarks and considering six algorithms, demonstrate the superior performance of FIGP and FIGP _E in comparison to other GP formulations. Moreover, the EDDA-V2 initialization allows for a significant reduction of the computational time.

In this contribution, we discuss the basic concepts of genotypes and phenotypes in tree-based GP (TGP), and then analyze their behavior using five real-world datasets. We show that TGP exhibits the same behavior that we can observe in other GP representations: At the genotypic level trees show frequently unchecked growth with seemingly ineffective code, but on the phenotypic level, much smaller trees can be observed. To generate phenotypes, we provide a unique technique for removing semantically ineffective code from GP trees. The approach extracts considerably simpler phenotypes while not being limited to local operations in the genotype. We generalize this transformation based on a problem-independent parameter that enables a further simplification of the exact phenotype by coarse-graining to produce approximate phenotypes. The concept of these phenotypes (exact and approximate) allows us to clarify what evolved solutions truly predict, making GP models considered at the phenotypic level much better interpretable.

Allowing the population size to variate during the evolution can bring advantages to evolutionary algorithms (EAs), retaining computational effort during the evolution process. Dynamic populations use computational resources wisely in several types of EAs, including genetic programming. However, so far, a thorough study on the use of dynamic populations in Geometric Semantic Genetic Programming (GSGP) is missing. Still, GSGP is a resource-greedy algorithm, and the use of dynamic populations seems appropriate. This paper adapts algorithms to GSGP to manage dynamic populations that were successful for other types of EAs and introduces two novel algorithms. The novel algorithms exploit the concept of semantic neighbourhood. These methods are assessed and compared through a set of eight regression problems. The results indicate that the algorithms outperform standard GSGP, confirming the suitability of dynamic populations for GSGP. Interestingly, the novel algorithms that use semantic neighbourhood to manage variation in population size are particularly effective in generating robust models even for the most difficult of the studied test problems.

Full-reference image quality measures are a fundamental tool to approximate the human visual system in various applications for digital data management: from retrieval to compression to detection of unauthorized uses. Inspired by both the effectiveness and the simplicity of hand-crafted Structural Similarity Index Measure (SSIM), in this work, we present a framework for the formulation of SSIM-like image quality measures through genetic programming. We explore different terminal sets, defined from the building blocks of structural similarity at different levels of abstraction, and we propose a two-stage genetic optimization that exploits hoist mutation to constrain the complexity of the solutions. Our optimized measures are selected through a cross-dataset validation procedure, which results in superior performance against different versions of structural similarity, measured as correlation with human mean opinion scores. We also demonstrate how, by tuning on specific datasets, it is possible to obtain solutions that are competitive with (or even outperform) more complex image quality measures.

The growing production of digital content and its dissemination across the worldwide web require eficient and precise management. In this context, image quality assessment measures (IQAMs) play a pivotal role in guiding the development of numerous image processing systems for compression, enhancement, and restoration. The structural similarity index (SSIM) is one of the most common IQAMs for estimating the similarity between a pristine reference image and its corrupted variant. The multi-scale SSIM is one of its most popular variants that allows assessing image quality at multiple spatial scales. This paper proposes a two-stage genetic programming (GP) approach to evolve novel multi-scale IQAMs, that are simultaneously more effective and efficient. We use GP to perform feature selection in the first stage, while the second stage generates the final solutions. The experimental results show that the proposed approach outperforms the existing MS-SSIM. A comprehensive analysis of the feature selection indicates that, for extracting multi-scale similarities, spatially-varying convolutions are more effective than dilated convolutions. Moreover, we provide evidence that the IQAMs learned for one database can be successfully transferred to previously unseen databases. We conclude the paper by presenting a set of evolved multi-scale IQAMs and providing their interpretation.

Bakurov, I., Castelli, M., Fontanella, F., & Vanneschi, L. (2019). A regression-like classification system for geometric semantic genetic programming. In J. J. Merelo, J. Garibaldi, A. Linares-Barranco, K. Madani, K. Warwick, & K. Warwick (Eds.), Proceedings of the 11th International Joint Conference on Computational Intelligence (IJCCI 2019) (Vol. 1, pp. 40-48). (IJCCI 2019 - Proceedings of the 11th International Joint Conference on Computational Intelligence). SciTePress.

Initializing the population is a crucial step for genetic programming, and several strategies have been proposed so far. The issue is particularly important for geometric semantic genetic programming, where initialization is known to play a very important role. In this paper, we propose an initialization technique inspired by the biological phenomenon of demes despeciation, i.e. the combination of demes of previously distinct species into a new population. In synthesis, the initial population of geometric semantic genetic programming is created using the best individuals of a set of separate subpopulations, or demes, some of which run standard genetic programming and the others geometric semantic genetic programming for few generations. Geometric semantic genetic programming with this novel initialization technique is shown to outperform geometric semantic genetic programming using the traditional ramped half-and-half algorithm on six complex symbolic regression applications. More specifically, on the studied problems, the proposed initialization technique allows us to generate solutions with comparable or even better generalization ability, and of significantly smaller size than the ramped half-and-half algorithm.