Given the global situation caused by the worldwide COVID-19 pandemic, most academic events worldwide were held completely online in 2021. These difficult circumstances, faced by many researchers and students, did not limit the quality of the submissions received at most events. It was particularly true for two of the most prestigious events in genetic programming (GP): EuroGP 2021 and the GECCO 2021 GP Track. This special issue presents works that are considered to be highlights of both events, serving as a testament of the high quality work done by the GP community in 2021.

The european conference on genetic programming (EuroGP) is the only conference devoted entirely to GP. In 2021 it was chaired by Nuno Lourenço and Ting Hu. There were 17 papers (11 oral presentations and 6 poster presentations), from a total of 27 submissions. The genetic and evolutionary computation conference (GECCO), the flagship event of the Association for Computing Machinery (ACM) Special Interest Group on Genetic and Evolutionary Computation (SIGEVO), it is yearly one of the largest and most prestigious events in Evolutionary Computation and Artificial Intelligence. The GP track is one of the largest, and in 2021 it was chaired by Mengjie Zhang and Leonardo Trujillo. From a total of 32 submissions, 11 papers were accepted for oral presentation and 11 posters.

This special issue presents a collection of works that were selected for their quality and overall scientific contribution, highlighting the work done in our field, in an attempt to reach a broader audience through the Genetic Programming and Evolvable Machines journal. From each event several papers were selected, based on the reviews and analysis by the event chairs, a total of three papers from EuroGP and two from GECCO are presented here. The authors expanded their original contribution, to present novel and interesting ideas stemming from their conference publications. These works then went through the regular and rigorous review process of this journal.

In the extended EuroGP paper by Lima et al., titled A Grammar-based GP approach applied to the design of deep neural networks, an evolutionary grammar-based GP algorithm was designed as a unified approach to the design of deep neural networks. The proposed approach was validated in three applications: the design of convolutional neural networks (CNNs) for image classification, graph neural networks (GNNs) for text classification, and U-Net for image segmentation. The results show that the evolutionary grammar-based GP can efficiently generate different deep learning architectures, adapted to each problem, employing choices that differ from what is usually seen in networks designed by hand.

Pinos et al. proposed a multi-objective neural architecture search (NAS) method based on Cartesian GP in the second extended EuroGP paper, titled EvoApproxNAS: Evolutionary Approximation and Neural Architecture Search. The method allowed approximate operations to be used in convolutional neural networks (CNNs) to reduce the power consumption of a target hardware implementation. Evolved CNNs are compared with CNNs developed by other NAS methods on the CIFAR-10 and SVHN benchmark problems.

In the paper by Horibe et al. titled Severe Damage Recovery in Evolving Soft Robots through Differentiable Programming, the authors propose a system based on neural cellular automata to give locomoting robots the ability to regenerate themselves when they suffer damage, akin to what happens in some biological organisms such as salamanders. The proposed approach is based on two steps. In the first step, an evolutionary approach is used to evolve a neural cellular automata that can grow the control and morphology of the robot. Then, the model is further trained to grow a particular robot with the ability of recovering from multiple forms of damage.

Both of the GECCO 2021 GP Track papers highlight the fact that the GP community needs challenging and informative benchmarks, to develop, improve and tune the wide variety of methods studied in our field. The first paper is by Helmuth and Kelly titled Applying Genetic Programming to PSB2: The Next Generation Program Synthesis Benchmark Suite. In 2015 the General Program Synthesis Benchmark Suite (PSB1) was proposed by Helmuth and Spector, which impacted both the GP and program synthesis communities in important ways. However, given the advances made in these areas in recent years, in many ways spurred on by the PSB1 suite, the community needed a new challenge, and Helmuth and Kelly present an outstanding one. The PSB2 suite will surely push research in program synthesis further, providing an important stepping stone to push towards real-world programming by artificial means. The work also presents novel results by applying PushGP to tackle this intriguing new benchmark.

The second paper from GECCO is by Aldeia and de Franca titled Interpretability in Symbolic Regression: a benchmark of Explanatory Methods using the Feynman data set. This paper presents a benchmark to evaluate the interpretability of symbolic regression models, the iirsBenchmark. Most readers will know that GP has always offered the potential for highly interpretable solutions, while many other machine learning methods struggle to provide this feature to the end user. However, the ability to always achieve, in a measurable way at least, true interpretability for the domain expert is in no way guaranteed. Through this unique benchmark, Aldeia and de Franca show that symbolic regression models are able to identify the correct explanation for a variety of datasets, even when the symbolic expression was not a perfect match, the models still exploited, and therefore detected, the main relationships between the problem inputs and the output, outperforming other regressors. Hopefully this benchmark will motivate GP researchers to integrate and prioritize measures of interpretability in their evolved solutions.

To finalize, all the editors of this special issue extend our heartfelt gratitude to all those that helped make the special issue a reality. The Editor-In-Chief, Lee Spector, of this fantastic publication for leading the way and entrusting this project to us, and the wonderful editorial team at Springer. The reviewers, for their hard work and care in reviewing the papers, your comments were invaluable. Last, but not least, we thank the authors of each paper, your excellent and hard work during trying times made this special issue possible, your works are without a doubt highlights of GP in 2021.