Massively complex systems, such as social networks (Camacho, Panizo-LLedot, Bello-Orgaz, Gonzalez-Pardo, & Cambria, 2020; Lara-Cabrera et al., 2017), renewable energy problems (Twidell & Weir, 2015), or Internet-of-Things problems (Lin et al., 2017), generate massive amounts of data. These massively complex systems have attracted the attention of both industrial and research communities, because the analysis of data can generate valuable knowledge about the specific domain. But at the same time, the amount of data generated and the complexity of the problems mean that classical algorithms and approaches do not provide suitable solutions. In this case, it is quite common for computational intelligence (CI) techniques to extract the knowledge. CI can be defined as a set of bio-inspired research areas focused on the study of adaptive mechanisms to enable, or facilitate, intelligent behaviour in complex and changing environments. There are several research fields that compose CI, including swarm intelligence (Gonzalez-Pardo, Jung, & Camacho, 2017), and evolutionary computation (Salcedo-Sanz, Ortiz-Garcýa, Ángel M. Pérez-Bellido, Portilla-Figueras, & Prieto, 2011). This special issue is focused on the application of bio-inspired algorithms to massively complex systems, ranging from concepts and theoretical developments to advances technologies and innovative applications. This special issue welcomed submissions of original papers introducing research results on all the aspects covering the application of CI algorithms to massively complex systems, ranging from concepts and theoretical developments to advanced technologies and innovative applications. This issue presents expanded versions of the best papers presented at the 19th International Conference on Intelligent Data Engineering and Automated Learning (IDEAL 2018), which was held in Madrid (Spain). As the special issue editors, we would like to take this opportunity to thank the various authors for their papers and the reviewers for their work. We are also grateful to Jon Hall, Editor-in-Chief of the Wiley journal Expert Systems. We would like to particularly thank the IDEAL'18 programme committee members for their hard work and dedication.

Abstract This paper empirically analyses the price of diamonds from different perspectives. The sample data contains detailed information on more than 165,000 diamonds certified by Gemological Institute of America, which can be purchased since July 2016 from a large online diamond supplier. Our empirical analysis allows to extend the classic 4Cs model in several directions as follows: (a) the classical 4Cs model is insufficient in order to explain the price, so that other attributes, such as polishing, symmetry, and fluorescence, must be incorporated to accurately estimate the price of a particular piece; (b) the large sample size allows us to analyse specific price ranges characterized by high market activity; (3) a very detailed analysis has been conducted for round diamonds, incorporating interactions between attributes within the regression model and studying the marginal rates of substitution between diamond weight and alternative characteristics given a certain price. Our model is able to detect diamonds that could constitute a clear market opportunity for buyers. This model can help to select efficient demand options taking advantage of the information available on the website, improving the overall efficiency of exchange in this sector.

Abstract This paper develops three frameworks based on a metaheuristic algorithm to train neural network classifiers. The architecture is a single‐hidden‐layer feedforward network. The first methodology spreads a base configuration over the nodes of a computing cluster; each of them executes the same algorithm to train the neural network with a different parameter setting. The second approach does a refined training via a biphase metaheuristic algorithm to maintain the diversity a period longer than the usual; it may be run in a sequential or distributed way. The third framework performs a data preparation phase by means of feature subset selection to reduce the number of inputs to the biphase metaheuristic algorithm. The two first methodologies have been tested using a complete test bed with product and unipolar sigmoid units in the hidden layer, and the statistical tests reveal that product nodes are significantly the most accurate. The third framework has included four feature subset selectors with different properties to reduce the number of inputs to the product unit artificial neural network, and the nonstatistical test shed light on that the results with a preprocessing phase are significantly more accurate than the results with the raw data.

This paper presents a quality enhancement of the selected features by a hybrid filter-based jointly on feature ranking and feature subset selection (FR-FSS) using a consistency-based measure via merging new features which are obtained applying other FR-FSS evaluated with a correlation metric. The goal is to overcome the accuracy of a neural network classifier containing product units as hidden nodes combined with a feature selection pre-processing step by means of a single consistency-based FR-FSS filter. Neural models are trained with a refined evolutionary programming approach called two-stage evolutionary algorithm. The experimentation has been carried out in eight complex classification problems, seven out of them from UCI (University of California at Irvine) repository and one real-world problem, with high test error rates (around 20%) with powerful classifiers such as 1-nearest neighbour or C4.5. Non-parametric statistical tests revealed that the new proposal significantly improves the accuracy of the neural models.