The interpretability of classification systems refers to the ability of these to express their behaviour in a way that is easily understandable by a user. Interpretable classification models allow for external validation by an expert and, in certain disciplines such as medicine or business, providing information about decision making is essential for ethical and human reasons. Fuzzy rule-based classification systems are consolidated powerful classification tools based on fuzzy logic and designed to produce interpretable models; however, in presence of a large number of attributes, even rule-based models tend to be too complex to be easily interpreted. In this work, we propose a novel multivariate feature selection method in which both search strategy and classifier are based on multi-objective evolutionary computation. We designed a set of experiments to establish an acceptable setting with respect to the number of evaluations required by the search strategy and by the classifier, and we tested our strategy on a real-life dataset. Then, we compared our results against a wide range of feature selection methods that includes filter, wrapper, multivariate and univariate methods, with deterministic and probabilistic search strategies, and with evaluators of diverse nature. Finally, the fuzzy rule based classification model obtained with the proposed method has been evaluated with standard performance metrics and compared with other well-known fuzzy rule-based classifiers. We have used two real-life datasets extracted from a contact center; in one case, with the proposed method we obtained an accuracy of 0.7857 with 8 rules, while the best fuzzy classifier compared obtained 0.7679 with 8 rules, and in the second case, we obtained an accuracy of 0.7403 with 5 rules, while the best fuzzy classifier compared obtained 0.6364 with 4 rules.

Feature selection (FS) for deep learning prediction models is a difficult topic for researchers to tackle. Most of the approaches proposed in the literature consist of embedded methods through the use of hidden layers added to the neural network architecture that modify the weights of the units associated with each input attribute so that the worst attributes have less weight in the learning process. Other approaches used for deep learning are filter methods, which are independent of the learning algorithm, which can limit the precision of the prediction model. Wrapper methods are impractical with deep learning due to their high computational cost. In this article, we propose new attribute subset evaluation FS methods for deep learning of the wrapper, filter and wrapper-filter hybrid types, where multiobjective and many-objective evolutionary algorithms are used as search strategies. A novel surrogate-assisted approach is used to reduce the high computational cost of the wrapper-type objective function, while the filter-type objective functions are based on correlation and an adaptation of the reliefF algorithm. The proposed techniques have been applied in a time series forecasting problem of air quality in the Spanish south-east and an indoor temperature forecasting problem in a domotic house, with promising results compared to other FS techniques used in the literature.

Whenever countries are threatened by a pandemic, as is the case with the COVID-19 virus, governments need help to take the right actions to safeguard public health as well as to mitigate the negative effects on the economy. A restrictive approach can seriously damage the economy. Conversely, a relaxed one may put at risk a high percentage of the population. Other investigations in this area are focused on modelling the spread of the virus or estimating the impact of the different measures on its propagation. However, in this paper, we propose a new methodology for helping governments in planning the phases to combat the pandemic based on their priorities. To this end, we implement the SEIR epidemiological model to represent the evolution of the COVID-19 virus on the population. To optimize the best sequences of actions governments can take, we propose a methodology with two approaches, one based on Deep Q-Learning and another one based on Genetic Algorithms. The sequences of actions (confinement, self-isolation, two-meter distance or not taking restrictions) are evaluated according to a reward system focused on meeting two objectives: firstly, getting few people infected so that hospitals are not overwhelmed, and secondly, avoiding taking drastic measures which could cause serious damage to the economy. The conducted experiments evaluate our methodology based on the accumulated rewards during the established period. The experiments also prove that it is a valid tool for governments to reduce the negative effects of a pandemic by optimizing the planning of the phases. According to our results, the approach based on Deep Q-Learning outperforms the one based on Genetic Algorithms.

In this paper we will discuss some new developments in the design of numerical methods for optimal control problems of Lagrangian systems on Lie groups. We will construct these geometric integrators using discrete variational calculus on Lie groups, deriving a discrete version of the second-order Euler–Lagrange equations. Interesting applications as, for instance, a discrete derivation of the Euler–Poincaré equations for second-order Lagrangians and its application to optimal control of a rigid body, and of a Cosserat rod are shown at the end of the paper.