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Discovering knowledge from data is a quantum jump from quantity to quality, which is the characteristic and the spirit of the development of science. Symbolic regression (SR) is playing a greater role in the discovery of knowledge from data, specifically in this era of exponential data growth, because SRs are able to discover mathematical formulas from data. These formulas may provide scientifically meaningful models, especially when combined with domain knowledge. This article provides an overview of SR applications in the field of materials science and engineering. Integrating domain knowledge with SR is the key and a crucial approach, which allows gaining knowledge from data quickly, accurately, and scientifically. In the data-driven paradigm, SR allows for uncovering the underlying mechanisms of materials behavior, properties, and functions, in a wide range of areas from basic academic research to industrial applications, including experiments and computations, by providing explicit interpretable models from data, in comparison with other machine-learning “black-box” models. SR will be a powerful tool for rational and automatic materials development.

Effective blood glucose management is crucial for people with diabetes to avoid acute complications. Predicting extreme values accurately and in a timely manner is of vital importance to them. People with diabetes are particularly concerned about suffering a hypoglycemia (low value) event and, moreover, that the event will be prolonged in time. It is crucial to predict hyperglycemia (high value) and hypoglycemia events that may cause health damages in the short term and potential permanent damages in the long term. This paper describes our research on predicting hypoglycemia events at 30, 60, 90, and 120 minutes using machine learning methods. We propose using structured Grammatical Evolution and dynamic structured Grammatical Evolution to produce interpretable mathematical expressions that predict a hypoglycemia event. Our proposal generates white-box models induced by a grammar based on if-then-else conditions using blood glucose, heart rate, number of steps, and burned calories as the inputs for the machine learning technique. We apply these techniques to create three types of models: individualized, cluster, and population-based. They all are then compared with the predictions of eleven machine learning techniques. We apply these techniques to a dataset of 24 real patients of the Hospital Universitario Principe de Asturias, Madrid, Spain. The resulting models, presented as if-then-else statements that incorporate numeric, relational, and logical operations between variables and constants, are inherently interpretable. The True Positive Rate and True Negative Rate metrics are above 0.90 for 30-minute predictions, 0.80 for 60 min, and 0.70 for 90 min and 120 min for the three types of models. Individualized models exhibit the best metrics, while cluster and population-based models perform similarly. Structured and dynamic structured grammatical evolution techniques perform similarly for all forecasting horizons. Regarding the comparison of different machine learning techniques, on the shorter forecasting horizons, our proposals have a high probability of winning, a probability that diminishes on the longer time horizons. Structured grammatical evolution provides advanced forecasting models that facilitate model explanation, modification, and retesting, offering flexibility for refining solutions post-creation and a deeper understanding of blood glucose behavior. These models have been integrated into the glUCModel application, designed to serve people with diabetes.

GRAPE is an implementation of Grammatical Evolution (GE) in DEAP, an Evolutionary Computation framework in Python, which consists of the necessary classes and functions to evolve a population of grammar-based solutions, while reporting essential measures. This tool was developed at the Bio-computing and Developmental Systems (BDS) Research Group, the birthplace of GE, as an easy to use (compared to the canonical C++ implementation, libGE) tool that inherits all the advantages of DEAP, such as selection methods, parallelism and multiple search techniques, all of which can be used with GRAPE. In this paper, we address some problems to exemplify the use of GRAPE and to perform a comparison with PonyGE2, an existing implementation of GE in Python. The results show that GRAPE has a similar performance, but is able to avail of all the extra facilities and functionality found in the DEAP framework. We further show that GRAPE enables GE to be applied to systems identification problems and we demonstrate this on two benchmark problems.

Generative art is a domain in which artistic output is created via a procedure or heuristic that may result in digital and/or physical results. A generative artist will typically act as a domain expert by specifying the algorithms that will form the basis of the piece as well as defining and refining parameters that can impact the results, however such efforts can require a significant amount of time to generate the final output. This article presents and extends GenerativeGI , an evolutionary computation-based technique for creating generative art by automatically searching through combinations of artistic techniques and their accompanying parameters to produce outputs desirable by the designer. Generative art techniques and their respective parameters are encoded within a grammar that is then the target for genetic improvement. This grammar-based approach, combined with a many-objective evolutionary algorithm, enables the designer to efficiently search through a massive number of possible outputs that reflect their aesthetic preferences. We included a total of 15 generative art techniques and performed three separate empirical evaluations, each of which targets different aesthetic preferences and varying aspects of the search heuristic. Experimental results suggest that GenerativeGI can produce outputs that are significantly more novel than those generated by random or single objective search. Furthermore,  GenerativeGI produces individuals with a larger number of relevant techniques used to generate their overall composition.

The presented work outlines a new genetic crossover operator, which can be used to solve problems by the Grammatical Evolution technique. This new operator intensively applies the one-point crossover procedure to randomly selected chromosomes with the aim of drastically reducing their fitness value. The new operator is applied to chromosomes selected randomly from the genetic population. This new operator was applied to two techniques from the recent literature that exploit Grammatical Evolution: artificial neural network construction and rule construction. In both case studies, an extensive set of classification problems and data-fitting problems were incorporated to estimate the effectiveness of the proposed genetic operator. The proposed operator significantly reduced both the classification error on the classification datasets and the feature learning error on the fitting datasets compared to other machine learning techniques and also to the original models before applying the new operator.

A multitude of problems in the contemporary literature are addressed using machine learning models, the most widespread of which are artificial neural networks. Furthermore, in recent years, evolutionary techniques have emerged that identify both the architecture of artificial neural networks and their corresponding parameters. Among these techniques, one can also identify the artificial neural networks being constructed, in which the structure and parameters of the neural network are effectively identified using Grammatical Evolution. In this work, a pre-training stage is introduced in which an artificial neural network with a fixed number of parameters is trained using some optimization technique such as the genetic algorithms used here. The final result of this additional phase is a trained artificial neural network, which is introduced into the genetic population used by Grammatical Evolution in the second phase. In this way, finding the overall minimum of the error function will be significantly accelerated, making the second phase method more efficient. The current work was applied to many classification and regression problems found in the related literature, and it was compared against other methods used for neural network training as well as against the original method used to construct neural networks.

Today, face recognition research is popular owing to its potential applications, especially where privacy and security are involved. Many methods of deep learning can extract many complicated face features. Convolutional Neural Network (CNN) is normally used for face and image recognition. The CNN is a type of Artificial Neural Network (ANN) employing a convolution methodology that extracts features from input data for increasing the actual number of features. In this work, a Region-based Fully CNN (R-FCN) based framework for face detection is proposed. The R-FCN refers to a completely convolutional structure using a new position-sensitive pooling layer that extracts a score for the prediction of each such region. This helps in speeding up the network and sharing the computation of Region of Interests (RoIs), thus preventing the loss of information by the feature map in RoI-pooling. In this work, a hybrid Grammatical Evolution (GE) with a Grey Wolf Optimizer (GWO) (GE-GWO) algorithm has been proposed for optimizing the R-FCN structure to enhance face detection. The WIDER face dataset with a Face Detection Dataset and Benchmark (FDDB) was employed to evaluate techniques. The results have proved that the proposed technique achieves better performance (precision, recall, and ROC curve) than other existing methods in the range of 1.5–4.2%.

Earthquake predictability remains a central challenge in seismology. Are earthquakes inherently unpredictable phenomena, or can they be forecasted through advances in technology? Contemporary seismological research continues to pursue this scientific milestone, often referred to as the ‘Holy Grail’ of earthquake prediction. In the direction of earthquake prediction based on historical data, the Grammatical Evolution technique of GenClass demonstrated high predictive accuracy for earthquake magnitude. Similarly, our research team follows this line of reasoning, operating under the belief that nature provides a pattern that, with the appropriate tools, can be decoded. What is certain is that, over the past 30 years, scientists and researchers have made significant strides in the field of seismology, largely aided by the development and application of artificial intelligence techniques. Artificial Neural Networks (ANNs) were first applied in the domain of seismology in 1994. The introduction of deep neural networks (DNNs), characterized by architectures incorporating two hidden layers, followed in 2002. Subsequently, recurrent neural networks (RNNs) were implemented within seismological studies as early as 2007. Most recently, grammatical evolution (GE) has been introduced in seismological studies (2025). Despite continuous progress in the field, achieving the so-called “triple prediction”—the precise estimation of the time, location, and magnitude of an earthquake—remains elusive. Nevertheless, machine learning and soft computing approaches have long played a significant role in seismological research. Concerning these approaches, significant advancements have been achieved, both in mapping seismic patterns and in predicting seismic characteristics on a smaller geographical scale. In this way, our research analyzes historical seismic events from 2004 to 2011 within the latitude range of 21°–79° longitude range of 33°–176°. The data is categorized and classified, with the aim of employing grammatical evolution techniques to achieve more accurate and timely predictions of earthquake magnitudes. This paper presents a systematic effort to enhance magnitude prediction accuracy using GE, contributing to the broader goal of reliable earthquake forecasting. Subsequently, this paper presents the superiority of GenClass, a key element of the grammatical evolution techniques, with an average error of 19%, indicating an overall accuracy of 81%.

Transistor-level Integrated Circuit (IC) design is fundamental to modern electronics, yet it remains one of the most expertise-intensive and time-consuming stages of chip development. As circuit complexity continues to rise, the need to automate this low-level design process has become critical to sustaining innovation and productivity across the semiconductor industry. This study presents a fully automated methodology for transistor-level IC design using a novel framework that integrates Grammatical Evolution (GE) with Cadence SKILL code. Beyond automation, the framework explicitly examines how symmetry and asymmetry shape the evolutionary search space and resulting circuit structures. To address the time-consuming and expertise-intensive nature of conventional integrated circuit design, the framework automates the synthesis of both digital and analogue circuits without requiring prior domain knowledge. A specialised attribute grammar (AG) evolves circuit topology and sizing, with performance assessed by a multi-objective fitness function. Symmetry is analysed at three levels: (i) domain-level structural dualities (e.g., NAND/NOR mirror topologies and PMOS/NMOS exchanges), (ii) objective-level symmetries created by logic threshold settings, and (iii) representational symmetries managed through grammatical constraints that preserve valid connectivity while avoiding redundant isomorphs. Validation was carried out on universal logic gates (NAND and NOR) at multiple logic thresholds, as well as on a temperature sensor. Under stricter thresholds, the evolved logic gates display emergent duality, converging to mirror-image transistor configurations; relaxed thresholds increase symmetric plateaus and slow convergence. The evolved logic gates achieve superior performance over conventional Complementary Metal–Oxide–Semiconductor (CMOS), Transmission Gate Logic (TGL), and Gate Diffusion Input (GDI) implementations, demonstrating lower power consumption, a reduced Power–Delay Product (PDP), and fewer transistors. Similarly, the evolved temperature sensor exhibits improved sensitivity, reduced power, and Integral Nonlinearity (INL), and a smaller area compared to the conventional Proportional to Absolute Temperature (PTAT) or “gold” circuit, without requiring resistors. The analogue design further demonstrates beneficial asymmetry in device roles, breaking canonical structures to achieve higher performance. Across all case studies, the evolved designs matched or outperformed their manually designed counterparts, demonstrating that this GE-based approach provides a scalable and effective path toward fully automated, symmetry-aware integrated circuit synthesis.

This study presents a novel hybrid approach combining grammatical evolution with constrained genetic algorithms to overcome key limitations in automated neural network design. The proposed method addresses two critical challenges: the tendency of grammatical evolution to converge to suboptimal architectures due to local optima, and the common overfitting problems in evolved networks. Our solution employs grammatical evolution for initial architecture generation while implementing a specialized genetic algorithm that simultaneously optimizes network parameters within dynamically adjusted bounds. The genetic component incorporates innovative penalty mechanisms in its fitness function to control neuron activation patterns and prevent overfitting. Comprehensive testing across 53 diverse datasets shows our method achieves superior performance compared to traditional optimization techniques, with an average classification error of 21.18% vs. 36.45% for ADAM, while maintaining better generalization capabilities. The constrained optimization approach proves particularly effective in preventing premature convergence, and the penalty system successfully mitigates overfitting even in complex, high-dimensional problems. Statistical validation confirms these improvements are significant (p < 1.1×10−8) and consistent across multiple domains, including medical diagnosis, financial prediction, and physical system modeling. This work provides a robust framework for automated neural network construction that balances architectural innovation with parameter optimization while addressing fundamental challenges in evolutionary machine learning.