This paper presents a multiobjective evolutionary algorithm to optimize radial basis function neural networks (RBFNNs) in order to approach target functions from a set of input-output pairs. The procedure allows the application of heuristics to improve the solution of the problem at hand by including some new genetic operators in the evolutionary process. These new operators are based on two well-known matrix transformations: singular value decomposition (SVD) and orthogonal least squares (OLS), which have been used to define new mutation operators that produce local or global modifications in the radial basis functions (RBFs) of the networks (the individuals in the population in the evolutionary procedure). After analyzing the efficiency of the different operators, we have shown that the global mutation operators yield an improved procedure to adjust the parameters of the RBFNNs.

To date, clustering techniques have always been oriented to solve classification and pattern recognition problems. However, some authors have applied them unchanged to construct initial models for function approximators. Nevertheless, classification and function approximation problems present quite different objectives. Therefore it is necessary to design new clustering algorithms specialized in the problem of function approximation. This paper presents a new clustering technique, specially designed for function. approximation problems, which improves the performance of the approximator system obtained, compared with other models derived from traditional classification oriented clustering algorithms and input-output clustering techniques.

Most genetic algorithm (GA) users adjust the main parameters of the design of a GA (crossover and mutation probability, population size, number of generations, crossover, mutation, and selection operators) manually. Nevertheless, when GA applications are being developed it is very important to know which parameters have the greatest influence on the behavior and performance of a GA. The purpose of this study was to analyze the dynamics of GAs when confronted with modifications to the principal parameters that define them, taking into account the two main characteristics of GAs; their capacity for exploration and exploitation. Therefore, the dynamics of GAs have been analyzed from two viewpoints. The first is to study the best solution found by the system, i.e., to observe its capacity to obtain a local or global optimum. The second viewpoint is the diversity within the population of GAs; to examine this, the average fitness was calculated. The relevancy and relative importance of the parameters involved in GA design are investigated by using a powerful statistical tool, the analysis of the variance (ANOVA).

Electroencephalography (EEG) datasets are often small and high dimensional, owing to cumbersome recording processes. In these conditions, powerful machine learning techniques are essential to deal with the large amount of information and overcome the curse of dimensionality. Artificial Neural Networks (ANNs) have achieved promising performance in EEG-based Brain-Computer Interface (BCI) applications, but they involve computationally intensive training algorithms and hyperparameter optimization methods. Thus, an awareness of the quality-cost trade-off, although usually overlooked, is highly beneficial. In this paper, we apply a hyperparameter optimization procedure based on Genetic Algorithms to Convolutional Neural Networks (CNNs), Feed-Forward Neural Networks (FFNNs), and Recurrent Neural Networks (RNNs), all of them purposely shallow. We compare their relative quality and energy-time cost, but we also analyze the variability in the structural complexity of networks of the same type with similar accuracies. The experimental results show that the optimization procedure improves accuracy in all models, and that CNN models with only one hidden convolutional layer can equal or slightly outperform a 6-layer Deep Belief Network. FFNN and RNN were not able to reach the same quality, although the cost was significantly lower. The results also highlight the fact that size within the same type of network is not necessarily correlated with accuracy, as smaller models can and do match, or even surpass, bigger ones in performance. In this regard, overfitting is likely a contributing factor since deep learning approaches struggle with limited training examples.

The identification of a model is one of the key issues in the field of fuzzy system modeling and function approximation theory. There are numerous approaches to the issue of parameter optimization within a fixed fuzzy system structure but no reliable method to obtain the optimal topology of the fuzzy system from a set of input-output data. This paper presents a reliable method to obtain the structure of a complete rule-based fuzzy system for a specific approximation accuracy of the training data, i.e., it can decide which input variables must be taken into account in the fuzzy system and how many membership functions (MFs) are needed in every selected input variable in order to reach the approximation target with the minimum number of parameters.