Regularized model learning in EDAs for continuous and multi-objective optimization

Probabilistic modeling is the de�ning characteristic of estimation of distribution algorithms (EDAs) which determines their behavior and performance in optimization. Regularization is a well-known statistical technique used for obtaining an improved model by reducing the generalization error of estimation, especially in high-dimensional problems. `1-regularization is a type of this technique with the appealing variable selection property which results in sparse model estimations. In this thesis, we study the use of regularization techniques for model learning in EDAs. Several methods for regularized model estimation in continuous domains based on a Gaussian distribution assumption are presented, and analyzed from di�erent aspects when used for optimization in a high-dimensional setting, where the population size of EDA has a logarithmic scale with respect to the number of variables. The optimization results obtained for a number of continuous problems with an increasing number of variables show that the proposed EDA based on regularized model estimation performs a more robust optimization, and is able to achieve signi�cantly better results for larger dimensions than other Gaussian-based EDAs. We also propose a method for learning a marginally factorized Gaussian Markov random �eld model using regularization techniques and a clustering algorithm. The experimental results show notable optimization performance on continuous additively decomposable problems when using this model estimation method. Our study also covers multi-objective optimization and we propose joint probabilistic modeling of variables and objectives in EDAs based on Bayesian networks, speci�cally models inspired from multi-dimensional Bayesian network classi�ers. It is shown that with this approach to modeling, two new types of relationships are encoded in the estimated models in addition to the variable relationships captured in other EDAs: objectivevariable and objective-objective relationships. An extensive experimental study shows the e�ectiveness of this approach for multi- and many-objective optimization. With the proposed joint variable-objective modeling, in addition to the Pareto set approximation, the algorithm is also able to obtain an estimation of the multi-objective problem structure. Finally, the study of multi-objective optimization based on joint probabilistic modeling is extended to noisy domains, where the noise in objective values is represented by intervals. A new version of the Pareto dominance relation for ordering the solutions in these problems, namely �-degree Pareto dominance, is introduced and its properties are analyzed. We show that the ranking methods based on this dominance relation can result in competitive performance of EDAs with respect to the quality of the approximated Pareto sets. This dominance relation is then used together with a method for joint probabilistic modeling based on `1-regularization for multi-objective feature subset selection in classi�cation, where six di�erent measures of accuracy are considered as objectives with interval values. The individual assessment of the proposed joint probabilistic modeling and solution ranking methods on datasets with small-medium dimensionality, when using two di�erent Bayesian classi�ers, shows that comparable or better Pareto sets of feature subsets are approximated in comparison to standard methods.

MBIS: Multivariate Bayesian Image Segmentation Tool

We present MBIS (Multivariate Bayesian Image Segmentation tool), a clustering tool based on the mixture of multivariate normal distributions model. MBIS supports multi-channel bias field correction based on a B-spline model. A second methodological novelty is the inclusion of graph-cuts optimization for the stationary anisotropic hidden Markov random field model. Along with MBIS, we release an evaluation framework that contains three different experiments on multi-site data. We first validate the accuracy of segmentation and the estimated bias field for each channel. MBIS outperforms a widely used segmentation tool in a cross-comparison evaluation. The second experiment demonstrates the robustness of results on atlas-free segmentation of two image sets from scan-rescan protocols on 21 healthy subjects. Multivariate segmentation is more replicable than the monospectral counterpart on T1-weighted images. Finally, we provide a third experiment to illustrate how MBIS can be used in a large-scale study of tissue volume change with increasing age in 584 healthy subjects. This last result is meaningful as multivariate segmentation performs robustly without the need for prior knowledge.

Diversidad funcional y diversidad filogenética en los bosques secos del sur del Ecuador

El concepto tradicional de reglas de ensamblaje refleja la idea de que las especies no co-ocurren al azar sino que están restringidos en su co-ocurrencia por la competencia interespecífica o por un filtrado ambiental. En está tesis abordé la importancia de los procesos que determinan el ensamble de la comunidad en la estructuración de los Bosques Secos en el Sur del Ecuador. Este estudio se realizó en la región biogeográfica Tumbesina, donde se encuentra la mayor concentración de bosques secos tropicales bien conservados del sur de Ecuador, y que constituyen una de las áreas de endemismo más importantes del mundo. El clima se caracteriza por una estación seca que va desde mayo a diciembre y una estación lluviosa de enero a abril, su temperatura anual varía entre 20°C y 26°C y una precipitación promedio anual entre 300 y 700 mm. Mi primer tema fue orientado a evaluar si la distribución de los rasgos funcionales a nivel comunitario es compatible con la existencia de un filtro ambiental (filtrado del hábitat) o con la existencia de un proceso de limitación de la semejanza funcional impuesta por la competencia inter-específica entre 58 especies de plantas leñosas repartidas en 109 parcelas (10x50m). Para ello, se analizó la distribución de los valores de cinco rasgos funcionales (altura máxima, densidad de la madera, área foliar específica, tamaño de la hoja y de masa de la semilla), resumida mediante varios estadísticos (rango, varianza, kurtosis y la desviación estándar de la distribución de distancias funcionales a la especies más próxima) y se comparó con la distribución esperada bajo un modelo nulo con ausencia de competencia. Los resultados obtenidos apoyan que tanto el filtrado ambiental como la limitación a la semejanza afectan el ensamble de las comunidades vegetales de los bosques secos Tumbesinos. Un segundo tema fue identificar si la diversidad funcional está condicionada por los gradientes ambientales, y en concreto si disminuye en los ambientes más estresantes a causa del filtrado ambiental, y si por el contrario aumenta en los ambientes más benignos donde la competencia se vuelve más importante, teniendo en cuenta las posibles modificaciones a este patrón general a causa de las interacciones de facilitación. Para abordar este estudio analizamos tanto las variaciones en la diversidad funcional (respecto a los de los cinco rasgos funcionales empleados en el primer capítulo de la tesis) como las variaciones de diversidad filogenética a lo largo de un gradiente de estrés climático en los bosques tumbesinos, y se contrastaron frente a las diversidades esperadas bajo un modelo de ensamblaje completamente aleatorio de la comunidad. Los análisis mostraron que tan sólo la diversidad de tamaños foliares siguió el patrón de variación esperado, disminuyendo a medida que aumentó el estrés abiótico mientras que ni el resto de rasgos funcionales ni la diversidad funcional multivariada ni la diversidad filogenética mostraron una variación significativa a lo largo del gradiente ambiental. Un tercer tema fue evaluar si los procesos que organizan la estructura funcional de la comunidad operan a diferentes escalas espaciales. Para ello cartografié todos los árboles y arbustos de más de 5 cm de diámetro en una parcela de 9 Ha de bosque seco y caractericé funcionalmente todas las especies. Dicha parcela fue dividida en subparcelas de diferente tamaño, obteniéndose subparcelas a seis escalas espaciales distintas. Los resultados muestran agregación de estrategias funcionales semejantes a escalas pequeñas, lo que sugiere la existencia bien de filtros ambientales actuando a escala fina o bien de procesos competitivos que igualan la estrategia óptima a dichas escalas. Finalmente con la misma información de la parcela permanente de 9 Ha. Nos propusimos evaluar el efecto y comportamiento de las especies respecto a la organización de la diversidad taxonómica, funcional y filogenética. Para ello utilicé tres funciones sumario espaciales: ISAR- para el nivel taxonómico, IFDAR para el nivel funcional y IPSVAR para el nivel filogenética y las contrastamos frente a modelos nulos que describen la distribución espacial de las especies individuales. Los resultados mostraron que en todas las escalas espaciales consideradas para ISAR, IFDAR y IPSVAR, la mayoría de las especies se comportaron como neutras, es decir, que están rodeados por la riqueza de diversidad semejante a la esperada. Sin embargo, algunas especies aparecieron como acumuladoras de diversidad funcional y filogenética, lo que sugiere su implicación en procesos competitivos de limitación de la semejanza. Una pequeña proporción de las especies apareció como repelente de la diversidad funcional y filogenética, lo que sugiere su implicación en un proceso de filtrado de hábitat. En este estudio pone de relieve cómo el análisis de las dimensiones alternativas de la biodiversidad, como la diversidad funcional y filogenética, puede ayudarnos a entender la co-ocurrencia de especies en diversos ensambles de comunidad. Todos los resultados de este estudio aportan nuevas evidencias de los procesos de ensamblaje de la comunidad de los Bosques Estacionalmente secos y como las variables ambientales y la competencia juegan un papel importante en la estructuración de la comunidad. ABSTRACT The traditional concept of the rules assembly for species communities reflects the idea that species do not co-occur at random but are restricted in their co-occurrence by interspecific competition or an environmental filter. In this thesis, I addressed the importance of the se processes in the assembly of plant communities in the dry forests of southern Ecuador. This study was conducted in the biogeographic region of Tumbesina has the largest concentration of well-conserved tropical dry forests of southern Ecuador, and is recognized as one of the most important areas of endemism in the world. The climate is characterized by a dry season from May to December and a rainy season from January to April. The annual temperature varies between 20 ° C and 26 ° C and an average annual rainfall between 300 and 700 mm. I first assessed whether the distribution of functional traits at the level of the community is compatible with the existence of an environmental filter (imposed by habitat) or the existence of a limitation on functional similarity imposed by interspecific competition. This analysis was conducted for 58 species of woody plants spread over 109 plots of 10 x 50 m. Specifically, I compared the distribution of values of five functional traits (maximum height, wood density, specific leaf area, leaf size and mass of the seed), via selected statistical properties (range, variance, kurtosis and analyzed the standard deviation of the distribution of the closest functional species) distances and compared with a expected distribution under a null model of no competition. The results support that both environmental filtering and a limitation on trait similarity affect the assembly of plant communities in dry forests Tumbesina. My second chapter evaluated whether variation in functional diversity is conditioned by environmental gradients. In particular, I tested whether it decreases in the most stressful environments because of environmental filters, or if, on the contrary, functional diversity is greater in more benign environments where competition becomes more important (notwithstanding possible changes to this general pattern due to facilitation). To address this theme I analyzed changes in both the functional diversity (maximum height, wood density, specific leaf area, leaf size and mass of the seed) and the phylogenetic diversity, along a gradient of climatic stress in Tumbes forests. The observed patterns of variation were contrasted against the diversity expected under a completely random null model of community assembly. Only the diversity of leaf sizes followed the hypothesis decreasing in as trait variation abiotic stress increased, while the other functional traits multivariate functional diversity and phylogenetic diversity no showed significant variation along the environmental gradient. The third theme assess whether the processes that organize the functional structure of the community operate at different spatial scales. To do this I mapped all the trees and shrubs of more than 5 cm in diameter within a plot of 9 hectares of dry forest and functionally classified each species. The plot was divided into subplots of different sizes, obtaining subplots of six different spatial scales. I found aggregation of similar functional strategies at small scales, which may indicate the existence of environmental filters or competitive processes that correspond to the optimal strategy for these fine scales. Finally, with the same information from the permanent plot of 9 ha, I evaluated the effect and behavior of individual species on the organization of the taxonomic, functional and phylogenetic diversity. The analysis comprised three spatial summary functions: ISAR- for taxonomic level analysis, IFDAR for functional level analysis, and IPSVAR for phylogenetic level analysis, in each case the pattern of diversity was contrasted against null models that randomly reallocate describe the spatial distribution of individual species and their traits. For all spatial scales considering ISAR, IFDAR and IPSVAR, most species behaved as neutral, i.e. they are surrounded by the diversity of other traits similar to that expected under a null model. However, some species appeared as accumulator of functional and phylogenetic diversity, suggesting that they may play a role in competitive processes that limiting similarity. A small proportion of the species appeared as repellent of functional and phylogenetic diversity, suggesting their involvement in a process of habitat filtering. These analysis highlights that the analysis of alternative dimensions of biodiversity, such as functional and phylogenetic diversity, can help us understand the co-occurrence of species in the assembly of biotic communities. All results of this study provide further evidence of the processes of assembly of the community of the seasonally dry forests as environmental variables and competition play an important role in structuring the community.

Methodology for assessing regional economic impacts of charging HGVs in Spain: an integrated approach through a random utility based multiregional input-output and a road transportation network model

An integrated approach composed of a random utility-based multiregional input-output model and a road transport network model was developed for evaluating the application of a fee to heavy-goods vehicles (HGVs) in Spain. For this purpose, a distance-based charge scenario (in euros per vehicle kilometer) for HGVs was evaluated for a selected motorway network in Spain. Although the aim of this charging policy was to increase the efficiency of transport, the approach strongly identified direct and indirect impacts on the regional economy. Estimates of the magnitude and extent of indirect effects on aggregated macroeconomic indicators (employment and gross domestic product) are provided. The macroeconomic effects of the charging policy were found to be positive for some regions and negative for other regions.