Deep Ordinal Classification in Forest Areas Using Light Detection and Ranging Point Clouds.

Recent advances in Deep Learning and aerial Light Detection And Ranging (LiDAR) have offered the possibility of refining the classification and segmentation of 3D point clouds to contribute to the monitoring of complex environments. In this context, the present study focuses on developing an ordinal classification model in forest areas where LiDAR point clouds can be classified into four distinct ordinal classes: ground, low vegetation, medium vegetation, and high vegetation. To do so, an effective soft labeling technique based on a novel proposed generalized exponential function (CE-GE) is applied to the PointNet network architecture. Statistical analyses based on Kolmogorov-Smirnov and Student's t-test reveal that the CE-GE method achieves the best results for all the evaluation metrics compared to other methodologies. Regarding the confusion matrices of the best alternative conceived and the standard categorical cross-entropy method, the smoothed ordinal classification obtains a more consistent classification compared to the nominal approach. Thus, the proposed methodology significantly improves the point-by-point classification of PointNet, reducing the errors in distinguishing between the middle classes (low vegetation and medium vegetation).

Cluster analysis and forecasting of viruses incidence growth curves: Application to SARS-CoV-2.

The sanitary emergency caused by COVID-19 has compromised countries and generated a worldwide health and economic crisis. To provide support to the countries' responses, numerous lines of research have been developed. The spotlight was put on effectively and rapidly diagnosing and predicting the evolution of the pandemic, one of the most challenging problems of the past months. This work contributes to the existing literature by developing a two-step methodology to analyze the transmission rate, designing models applied to territories with similar pandemic behavior characteristics. Virus transmission is considered as bacterial growth curves to understand the spread of the virus and to make predictions about its future evolution. Hence, an analytical clustering procedure is first applied to create groups of locations where the virus transmission rate behaved similarly in the different outbreaks. A curve decomposition process based on an iterative polynomial process is then applied, obtaining meaningful forecasting features. Information of the territories belonging to the same cluster is merged to build models capable of simultaneously predicting the 14-day incidence in several locations using Evolutionary Artificial Neural Networks. The methodology is applied to Andalusia (Spain), although it is applicable to any region across the world. Individual models trained for a specific territory are carried out for comparison purposes. The results demonstrate that this methodology achieves statistically similar, or even better, performance for most of the locations. In addition to being extremely competitive, the main advantage of the proposal lies in its complexity cost reduction. The total number of parameters to be estimated is reduced up to 93.51% for the short term and 93.31% for the mid-term forecasting, respectively. Moreover, the number of required models is reduced by 73.53% and 58.82% for the short- and mid-term forecasting horizons.

COVID-19 contagion forecasting framework based on curve decomposition and evolutionary artificial neural networks: A case study in Andalusia, Spain.

Many types of research have been carried out with the aim of combating the COVID-19 pandemic since the first outbreak was detected in Wuhan, China. Anticipating the evolution of an outbreak helps to devise suitable economic, social and health care strategies to mitigate the effects of the virus. For this reason, predicting the SARS-CoV-2 transmission rate has become one of the most important and challenging problems of the past months. In this paper, we apply a two-stage mid and long-term forecasting framework to the epidemic situation in eight districts of Andalusia, Spain. First, an analytical procedure is performed iteratively to fit polynomial curves to the cumulative curve of contagions. Then, the extracted information is used for estimating the parameters and structure of an evolutionary artificial neural network with hybrid architectures (i.e., with different basis functions for the hidden nodes) while considering single and simultaneous time horizon estimations. The results obtained demonstrate that including polynomial information extracted during the training stage significantly improves the mid- and long-term estimations in seven of the eight considered districts. The increase in average accuracy (for the joint mid- and long-term horizon forecasts) is 37.61% and 35.53% when considering the single and simultaneous forecast approaches, respectively.

Crossroads in Liver Transplantation: Is Artificial Intelligence the Key to Donor-Recipient Matching?

Liver transplantation outcomes have improved in recent years. However, with the emergence of expanded donor criteria, tools to better assist donor-recipient matching have become necessary. Most of the currently proposed scores based on conventional biostatistics are not good classifiers of a problem that is considered "unbalanced." In recent years, the implementation of artificial intelligence in medicine has experienced exponential growth. Deep learning, a branch of artificial intelligence, may be the answer to this classification problem. The ability to handle a large number of variables with speed, objectivity, and multi-objective analysis is one of its advantages. Artificial neural networks and random forests have been the most widely used deep classifiers in this field. This review aims to give a brief overview of D-R matching and its evolution in recent years and how artificial intelligence may be able to provide a solution.

Machine learning methods in organ transplantation.

PURPOSE OF REVIEW: Machine learning techniques play an important role in organ transplantation. Analysing the main tasks for which they are being applied, together with the advantages and disadvantages of their use, can be of crucial interest for clinical practitioners. RECENT FINDINGS: In the last 10 years, there has been an explosion of interest in the application of machine-learning techniques to organ transplantation. Several approaches have been proposed in the literature aiming to find universal models by considering multicenter cohorts or from different countries. Moreover, recently, deep learning has also been applied demonstrating a notable ability when dealing with a vast amount of information. SUMMARY: Organ transplantation can benefit from machine learning in such a way to improve the current procedures for donor--recipient matching or to improve standard scores. However, a correct preprocessing is needed to provide consistent and high quality databases for machine-learning algorithms, aiming to robust and fair approaches to support expert decision-making systems.

Validation of artificial neural networks as a methodology for donor-recipient matching for liver transplantation.

In 2014, we reported a model for donor-recipient (D-R) matching in liver transplantation (LT) based on artificial neural networks (ANNs) from a Spanish multicenter study (Model for Allocation of Donor and Recipient in España [MADR-E]). The aim is to test the ANN-based methodology in a different European health care system in order to validate it. An ANN model was designed using a cohort of patients from King's College Hospital (KCH; n = 822). The ANN was trained and tested using KCH pairs for both 3- and 12-month survival models. End points were probability of graft survival (correct classification rate [CCR]) and nonsurvival (minimum sensitivity [MS]). The final model is a rule-based system for facilitating the decision about the most appropriate D-R matching. Models designed for KCH had excellent prediction capabilities for both 3 months (CCR-area under the curve [AUC] = 0.94; MS-AUC = 0.94) and 12 months (CCR-AUC = 0.78; MS-AUC = 0.82), almost 15% higher than the best obtained by other known scores such as Model for End-Stage Liver Disease and balance of risk. Moreover, these results improve the previously reported ones in the multicentric MADR-E database. In conclusion, the use of ANN for D-R matching in LT in other health care systems achieved excellent prediction capabilities supporting the validation of these tools. It should be considered as the most advanced, objective, and useful tool to date for the management of waiting lists. Liver Transplantation 24 192-203 2018 AASLD.

Use of artificial intelligence as an innovative donor-recipient matching model for liver transplantation: results from a multicenter Spanish study.

BACKGROUND & AIMS: There is an increasing discrepancy between the number of potential liver graft recipients and the number of organs available. Organ allocation should follow the concept of benefit of survival, avoiding human-innate subjectivity. The aim of this study is to use artificial-neural-networks (ANNs) for donor-recipient (D-R) matching in liver transplantation (LT) and to compare its accuracy with validated scores (MELD, D-MELD, DRI, P-SOFT, SOFT, and BAR) of graft survival. METHODS: 64 donor and recipient variables from a set of 1003 LTs from a multicenter study including 11 Spanish centres were included. For each D-R pair, common statistics (simple and multiple regression models) and ANN formulae for two non-complementary probability-models of 3-month graft-survival and -loss were calculated: a positive-survival (NN-CCR) and a negative-loss (NN-MS) model. The NN models were obtained by using the Neural Net Evolutionary Programming (NNEP) algorithm. Additionally, receiver-operating-curves (ROC) were performed to validate ANNs against other scores. RESULTS: Optimal results for NN-CCR and NN-MS models were obtained, with the best performance in predicting the probability of graft-survival (90.79%) and -loss (71.42%) for each D-R pair, significantly improving results from multiple regressions. ROC curves for 3-months graft-survival and -loss predictions were significantly more accurate for ANN than for other scores in both NN-CCR (AUROC-ANN=0.80 vs. -MELD=0.50; -D-MELD=0.54; -P-SOFT=0.54; -SOFT=0.55; -BAR=0.67 and -DRI=0.42) and NN-MS (AUROC-ANN=0.82 vs. -MELD=0.41; -D-MELD=0.47; -P-SOFT=0.43; -SOFT=0.57, -BAR=0.61 and -DRI=0.48). CONCLUSIONS: ANNs may be considered a powerful decision-making technology for this dataset, optimizing the principles of justice, efficiency and equity. This may be a useful tool for predicting the 3-month outcome and a potential research area for future D-R matching models.

Learning Ordinal-Hierarchical Constraints for Deep Learning Classifiers.

Real-world classification problems may disclose different hierarchical levels where the categories are displayed in an ordinal structure. However, no specific deep learning (DL) models simultaneously learn hierarchical and ordinal constraints while improving generalization performance. To fill this gap, we propose the introduction of two novel ordinal-hierarchical DL methodologies, namely, the hierarchical cumulative link model (HCLM) and hierarchical-ordinal binary decomposition (HOBD), which are able to model the ordinal structure within different hierarchical levels of the labels. In particular, we decompose the hierarchical-ordinal problem into local and global graph paths that may encode an ordinal constraint for each hierarchical level. Thus, we frame this problem as simultaneously minimizing global and local losses. Furthermore, the ordinal constraints are set by two approaches ordinal binary decomposition (OBD) and cumulative link model (CLM) within each global and local function. The effectiveness of the proposed approach is measured on four real-use case datasets concerning industrial, biomedical, computer vision, and financial domains. The extracted results demonstrate a statistically significant improvement to state-of-the-art nominal, ordinal, and hierarchical approaches.

A memetic dynamic coral reef optimisation algorithm for simultaneous training, design, and optimisation of artificial neural networks.

Artificial Neural Networks (ANNs) have been used in a multitude of real-world applications given their predictive capabilities, and algorithms based on gradient descent, such as Backpropagation (BP) and variants, are usually considered for their optimisation. However, these algorithms have been shown to get stuck at local optima, and they require a cautious design of the architecture of the model. This paper proposes a novel memetic training method for simultaneously learning the ANNs structure and weights based on the Coral Reef Optimisation algorithms (CROs), a global-search metaheuristic based on corals' biology and coral reef formation. Three versions based on the original CRO combined with a Local Search procedure are developed: (1) the basic one, called Memetic CRO; (2) a statistically guided version called Memetic SCRO (M-SCRO) that adjusts the algorithm parameters based on the population fitness; (3) and, finally, an improved Dynamic Statistically-driven version called Memetic Dynamic SCRO (M-DSCRO). M-DSCRO is designed with the idea of improving the M-SCRO version in the evolutionary process, evaluating whether the fitness distribution of the population of ANNs is normal to automatically decide the statistic to be used for assigning the algorithm parameters. Furthermore, all algorithms are adapted to the design of ANNs by means of the most suitable operators. The performance of the different algorithms is evaluated with 40 classification datasets, showing that the proposed M-DSCRO algorithm outperforms the other two versions on most of the datasets. In the final analysis, M-DSCRO is compared against four state-of-the-art methods, demonstrating its superior efficacy in terms of overall accuracy and minority class performance.

Activation Functions for Convolutional Neural Networks: Proposals and Experimental Study.

Activation functions lie at the core of every neural network model from shallow to deep convolutional neural networks. Their properties and characteristics shape the output range of each layer and, thus, their capabilities. Modern approaches rely mostly on a single function choice for the whole network, usually ReLU or other similar alternatives. In this work, we propose two new activation functions and analyze their properties and compare them with 17 different function proposals from recent literature on six distinct problems with different characteristics. The objective is to shed some light on their comparative performance. The results show that the proposed functions achieved better performance than the most commonly used ones.

Development and validation of the Gender-Equity Model for Liver Allocation (GEMA) to prioritise candidates for liver transplantation: a cohort study.

BACKGROUND: The Model for End-stage Liver Disease (MELD) and its sodium-corrected variant (MELD-Na) have created gender disparities in accessing liver transplantation. We aimed to derive and validate the Gender-Equity Model for liver Allocation (GEMA) and its sodium-corrected variant (GEMA-Na) to amend such inequities. METHODS: In this cohort study, the GEMA models were derived by replacing creatinine with the Royal Free Hospital glomerular filtration rate (RFH-GFR) within the MELD and MELD-Na formulas, with re-fitting and re-weighting of each component. The new models were trained and internally validated in adults listed for liver transplantation in the UK (2010-20; UK Transplant Registry) using generalised additive multivariable Cox regression, and externally validated in an Australian cohort (1998-2020; Royal Prince Alfred Hospital [Australian National Liver Transplant Unit] and Austin Hospital [Victorian Liver Transplant Unit]). The study comprised 9320 patients: 5762 patients for model training, 1920 patients for internal validation, and 1638 patients for external validation. The primary outcome was mortality or delisting due to clinical deterioration within the first 90 days from listing. Discrimination was assessed by Harrell's concordance statistic. FINDINGS: 449 (5·8%) of 7682 patients in the UK cohort and 87 (5·3%) of 1638 patients in the Australian cohort died or were delisted because of clinical deterioration within 90 days. GEMA showed improved discrimination in predicting mortality or delisting due to clinical deterioration within the first 90 days after waiting list inclusion compared with MELD (Harrell's concordance statistic 0·752 [95% CI 0·700-0·804] vs 0·712 [0·656-0·769]; p=0·001 in the internal validation group and 0·761 [0·703-0·819] vs 0·739 [0·682-0·796]; p=0·036 in the external validation group), and GEMA-Na showed improved discrimination compared with MELD-Na (0·766 [0·715-0·818] vs 0·742 [0·686-0·797]; p=0·0058 in the internal validation group and 0·774 [0·720-0·827] vs 0·745 [0·690-0·800]; p=0·014 in the external validation group). The discrimination capacity of GEMA-Na was higher in women than in the overall population, both in the internal (0·802 [0·716-0·888]) and external validation cohorts (0·796 [0·698-0·895]). In the pooled validation cohorts, GEMA resulted in a score change of at least 2 points compared with MELD in 1878 (52·8%) of 3558 patients (25·0% upgraded and 27·8% downgraded). GEMA-Na resulted in a score change of at least 2 points compared with MELD-Na in 1836 (51·6%) of 3558 patients (32·3% upgraded and 19·3% downgraded). In the whole cohort, 3725 patients received a transplant within 90 days of being listed. Of these patients, 586 (15·7%) would have been differently prioritised by GEMA compared with MELD; 468 (12·6%) patients would have been differently prioritised by GEMA-Na compared with MELD-Na. One in 15 deaths could potentially be avoided by using GEMA instead of MELD and one in 21 deaths could potentially be avoided by using GEMA-Na instead of MELD-Na. INTERPRETATION: GEMA and GEMA-Na showed improved discrimination and a significant re-classification benefit compared with existing scores, with consistent results in an external validation cohort. Their implementation could save a clinically meaningful number of lives, particularly among women, and could amend current gender inequities in accessing liver transplantation. FUNDING: Junta de Andalucía and EDRF.

A mixed distribution to fix the threshold for Peak-Over-Threshold wave height estimation.

Modelling extreme values distributions, such as wave height time series where the higher waves are much less frequent than the lower ones, has been tackled from the point of view of the Peak-Over-Threshold (POT) methodologies, where modelling is based on those values higher than a threshold. This threshold is usually predefined by the user, while the rest of values are ignored. In this paper, we propose a new method to estimate the distribution of the complete time series, including both extreme and regular values. This methodology assumes that extreme values time series can be modelled by a normal distribution in a combination of a uniform one. The resulting theoretical distribution is then used to fix the threshold for the POT methodology. The methodology is tested in nine real-world time series collected in the Gulf of Alaska, Puerto Rico and Gibraltar (Spain), which are provided by the National Data Buoy Center (USA) and Puertos del Estado (Spain). By using the Kolmogorov-Smirnov statistical test, the results confirm that the time series can be modelled with this type of mixed distribution. Based on this, the return values and the confidence intervals for wave height in different periods of time are also calculated.

The Role of Intraperitoneal Intraoperative Chemotherapy with Paclitaxel in the Surgical Treatment of Peritoneal Carcinomatosis from Ovarian Cancer-Hyperthermia versus Normothermia: A Randomized Controlled Trial.

BACKGROUND: The treatment of ovarian carcinomatosis with cytoreductive surgery and HIPEC is still controversial. The effect and pharmacokinetics of the chemotherapeutics used (especially taxanes) are currently under consideration. METHODS: A phase II, simple blind and randomized controlled trial (NTC02739698) was performed. The trial included 32 patients with primary or recurrent ovarian carcinomatosis undergoing cytoreductive surgery (CRS) and intraoperative intraperitoneal chemotherapy with paclitaxel (PTX): 16 in hyperthermic (42-43 °C) and 16 in normothermic (37 °C) conditions. Tissue, serum and plasma samples were taken in every patient before and after intraperitoneal chemotherapy to measure the concentration of PTX. To analyze the immunohistochemical profile of p53, p27, p21, ki67, PCNA and caspase-3 and the pathological response, a scale of intensity and percentage of expression and a grouped Miller and Payne system were used, respectively. Perioperative characteristics and morbi-mortality were also analyzed. RESULTS: The main characteristics of patients, surgical morbidity, hemotoxicity and nephrotoxicity were similar in both groups. The concentration of paclitaxel in the tissue was higher than that observed in plasma and serum, although no statistically significant differences were found between the two groups. No statistically significant association regarding pathological response and apoptosis (caspase-3) between both groups was proved. There were no statistically significant differences between the normothermic and the hyperthermic group for pathological response and apoptosis. CONCLUSIONS: The use of intraperitoneal PTX has proven adequate pharmacokinetics with reduction of cell cycle and proliferation markers globally without finding statistically significant differences between its administration under hyperthermia versus normothermia conditions.

Time-Series Clustering Based on the Characterization of Segment Typologies.

Time-series clustering is the process of grouping time series with respect to their similarity or characteristics. Previous approaches usually combine a specific distance measure for time series and a standard clustering method. However, these approaches do not take the similarity of the different subsequences of each time series into account, which can be used to better compare the time-series objects of the dataset. In this article, we propose a novel technique of time-series clustering consisting of two clustering stages. In a first step, a least-squares polynomial segmentation procedure is applied to each time series, which is based on a growing window technique that returns different-length segments. Then, all of the segments are projected into the same dimensional space, based on the coefficients of the model that approximates the segment and a set of statistical features. After mapping, a first hierarchical clustering phase is applied to all mapped segments, returning groups of segments for each time series. These clusters are used to represent all time series in the same dimensional space, after defining another specific mapping process. In a second and final clustering stage, all the time-series objects are grouped. We consider internal clustering quality to automatically adjust the main parameter of the algorithm, which is an error threshold for the segmentation. The results obtained on 84 datasets from the UCR Time Series Classification Archive have been compared against three state-of-the-art methods, showing that the performance of this methodology is very promising, especially on larger datasets.

Statistical methods versus machine learning techniques for donor-recipient matching in liver transplantation.

Donor-Recipient (D-R) matching is one of the main challenges to be fulfilled nowadays. Due to the increasing number of recipients and the small amount of donors in liver transplantation, the allocation method is crucial. In this paper, to establish a fair comparison, the United Network for Organ Sharing database was used with 4 different end-points (3 months, and 1, 2 and 5 years), with a total of 39, 189 D-R pairs and 28 donor and recipient variables. Modelling techniques were divided into two groups: 1) classical statistical methods, including Logistic Regression (LR) and Naïve Bayes (NB), and 2) standard machine learning techniques, including Multilayer Perceptron (MLP), Random Forest (RF), Gradient Boosting (GB) or Support Vector Machines (SVM), among others. The methods were compared with standard scores, MELD, SOFT and BAR. For the 5-years end-point, LR (AUC = 0.654) outperformed several machine learning techniques, such as MLP (AUC = 0.599), GB (AUC = 0.600), SVM (AUC = 0.624) or RF (AUC = 0.644), among others. Moreover, LR also outperformed standard scores. The same pattern was reproduced for the others 3 end-points. Complex machine learning methods were not able to improve the performance of liver allocation, probably due to the implicit limitations associated to the collection process of the database.

Ordinal classification of the affectation level of 3D-images in Parkinson diseases.

Parkinson's disease is characterised by a decrease in the density of presynaptic dopamine transporters in the striatum. Frequently, the corresponding diagnosis is performed using a qualitative analysis of the 3D-images obtained after the administration of [Formula: see text]I-ioflupane, considering a binary classification problem (absence or existence of Parkinson's disease). In this work, we propose a new methodology for classifying this kind of images in three classes depending on the level of severity of the disease in the image. To tackle this problem, we use an ordinal classifier given the natural order of the class labels. A novel strategy to perform feature selection is developed because of the large number of voxels in the image, and a method for generating synthetic images is proposed to improve the quality of the classifier. The methodology is tested on 434 studies conducted between September 2015 and January 2019, divided into three groups: 271 without alteration of the presynaptic nigrostriatal pathway, 73 with a slight alteration and 90 with severe alteration. Results confirm that the methodology improves the state-of-the-art algorithms, and that it is able to find informative voxels outside the standard regions of interest used for this problem. The differences are assessed by statistical tests which show that the proposed image ordinal classification could be considered as a decision support system in medicine.

Using machine learning methods to determine a typology of patients with HIV-HCV infection to be treated with antivirals.

Several European countries have established criteria for prioritising initiation of treatment in patients infected with the hepatitis C virus (HCV) by grouping patients according to clinical characteristics. Based on neural network techniques, our objective was to identify those factors for HIV/HCV co-infected patients (to which clinicians have given careful consideration before treatment uptake) that have not being included among the prioritisation criteria. This study was based on the Spanish HERACLES cohort (NCT02511496) (April-September 2015, 2940 patients) and involved application of different neural network models with different basis functions (product-unit, sigmoid unit and radial basis function neural networks) for automatic classification of patients for treatment. An evolutionary algorithm was used to determine the architecture and estimate the coefficients of the model. This machine learning methodology found that radial basis neural networks provided a very simple model in terms of the number of patient characteristics to be considered by the classifier (in this case, six), returning a good overall classification accuracy of 0.767 and a minimum sensitivity (for the classification of the minority class, untreated patients) of 0.550. Finally, the area under the ROC curve was 0.802, which proved to be exceptional. The parsimony of the model makes it especially attractive, using just eight connections. The independent variable "recent PWID" is compulsory due to its importance. The simplicity of the model means that it is possible to analyse the relationship between patient characteristics and the probability of belonging to the treated group.

Dynamically weighted evolutionary ordinal neural network for solving an imbalanced liver transplantation problem.

OBJECTIVE: Create an efficient decision-support model to assist medical experts in the process of organ allocation in liver transplantation. The mathematical model proposed here uses different sources of information to predict the probability of organ survival at different thresholds for each donor-recipient pair considered. Currently, this decision is mainly based on the Model for End-stage Liver Disease, which depends only on the severity of the recipient and obviates donor-recipient compatibility. We therefore propose to use information concerning the donor, the recipient and the surgery, with the objective of allocating the organ correctly. METHODS AND MATERIALS: The database consists of information concerning transplants conducted in 7 different Spanish hospitals and the King's College Hospital (United Kingdom). The state of the patients is followed up for 12 months. We propose to treat the problem as an ordinal classification one, where we predict the organ survival at different thresholds: less than 15 days, between 15 and 90 days, between 90 and 365 days and more than 365 days. This discretization is intended to produce finer-grain survival information (compared with the common binary approach). However, it results in a highly imbalanced dataset in which more than 85% of cases belong to the last class. To solve this, we combine two approaches, a cost-sensitive evolutionary ordinal artificial neural network (ANN) (in which we propose to incorporate dynamic weights to make more emphasis on the worst classified classes) and an ordinal over-sampling technique (which adds virtual patterns to the minority classes and thus alleviates the imbalanced nature of the dataset). RESULTS: The results obtained by our proposal are promising and satisfactory, considering the overall accuracy, the ordering of the classes and the sensitivity of minority classes. In this sense, both the dynamic costs and the over-sampling technique improve the base results of the considered ANN-based method. Comparing our model with other state-of-the-art techniques in ordinal classification, competitive results can also be appreciated. The results achieved with this proposal improve the ones obtained by other state-of-the-art models: we were able to correctly predict more than 73% of the transplantation results, with a geometric mean of the sensitivities of 31.46%, which is much higher than the one obtained by other models. CONCLUSIONS: The combination of the proposed cost-sensitive evolutionary algorithm together with the application of an over-sampling technique improves the predictive capability of our model in a significant way (especially for minority classes), which can help the surgeons make more informed decisions about the most appropriate recipient for an specific donor organ, in order to maximize the probability of survival after the transplantation and therefore the fairness principle.

An alternative approach for neural network evolution with a genetic algorithm: crossover by combinatorial optimization.

In this work we present a new approach to crossover operator in the genetic evolution of neural networks. The most widely used evolutionary computation paradigm for neural network evolution is evolutionary programming. This paradigm is usually preferred due to the problems caused by the application of crossover to neural network evolution. However, crossover is the most innovative operator within the field of evolutionary computation. One of the most notorious problems with the application of crossover to neural networks is known as the permutation problem. This problem occurs due to the fact that the same network can be represented in a genetic coding by many different codifications. Our approach modifies the standard crossover operator taking into account the special features of the individuals to be mated. We present a new model for mating individuals that considers the structure of the hidden layer and redefines the crossover operator. As each hidden node represents a non-linear projection of the input variables, we approach the crossover as a problem on combinatorial optimization. We can formulate the problem as the extraction of a subset of near-optimal projections to create the hidden layer of the new network. This new approach is compared to a classical crossover in 25 real-world problems with an excellent performance. Moreover, the networks obtained are much smaller than those obtained with classical crossover operator.