Partition-based distributionally robust optimization via optimal transport with order cone constraints

In this paper we wish to tackle stochastic programs affected by ambiguity about the probability law that governs their uncertain parameters. Using optimal transport theory, we construct an ambiguity set that exploits the knowledge about the distribution of the uncertain parameters, which is provided by: (1) sample data and (2) a-priori information on the order among the probabilities that the true data-generating distribution assigns to some regions of its support set. This type of order is enforced by means of order cone constraints and can encode a wide range of information on the shape of the probability distribution of the uncertain parameters such as information related to monotonicity or multi-modality. We seek decisions that are distributionally robust. In a number of practical cases, the resulting distributionally robust optimization (DRO) problem can be reformulated as a finite convex problem where the a-priori information translates into linear constraints. In addition, our method inherits the finite-sample performance guarantees of the Wasserstein-metric-based DRO approach proposed by Mohajerin Esfahani and Kuhn (Math Program 171(1–2):115–166. https://doi.org/10.1007/s10107-017-1172-1, 2018), while generalizing this and other popular DRO approaches. Finally, we have designed numerical experiments to analyze the performance of our approach with the newsvendor problem and the problem of a strategic firm competing à la Cournot in a market.This research has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant Agreement No. 755705). This work was also supported in part by the Spanish Ministry of Economy, Industry and Competitiveness and the European Regional Development Fund (ERDF) through Project ENE2017-83775-P

Data-driven distributionally robust optimization with Wasserstein metric, moment conditions and robust constraints

We consider optimization problems where the information on the uncertain parameters reduces to a finite data sample. Using the Wasserstein metric, a ball in the space of probability distributions centered at the empirical distribution is constructed. The goal is to solve a minimization problem subject to the worst-case distribution within this Wasserstein ball. Moreover, we consider moment constraints in order to add a priori information about the random phenomena. In addition, we not only consider moment constraints but also take into account robust classical constraints. These constraints serve to hedge decisions against realizations of random variables for which we do not have distributional information other than their support set. With these assumptions we need to solve a data-driven distributionally robust optimization problem with several types of constraints. We show that strong duality holds under mild assumptions, and the distributionally robust optimization problems overWasserstein balls with moment constraints and robust classical constraints can in fact be reformulated as tractable finite programs. Finally, a taxonomy of the tractable finite programs is shown under di erent assumptions about the objective function, the constraints and the support set of the random variables.European Research Council University of Málaga. Campus de Excelencia Internacional Andalucía Tech

Distributionally robust stochastic programs with side information based on trimmings

We consider stochastic programs conditional on some covariate information, where the only knowledge of the possible relationship between the uncertain parameters and the covariates is reduced to a finite data sample of their joint distribution. By exploiting the close link between the notion of trimmings of a probability measure and the partial mass transportation problem, we construct a data-driven Distributionally Robust Optimization (DRO) framework to hedge the decision against the intrinsic error in the process of inferring conditional information from limited joint data. We show that our approach is computationally as tractable as the standard (without side information) Wasserstein-metric-based DRO and enjoys performance guarantees. Furthermore, our DRO framework can be conveniently used to address data-driven decision-making problems under contaminated samples. Finally, the theoretical results are illustrated using a single-item newsvendor problem and a portfolio allocation problem with side information.Open Access funding provided by Universidad de Málaga / CBUA thanks to the CRUE-CSIC agreement with Springer Nature. This research has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant agreement No. 755705). This work was also supported in part by the Spanish Ministry of Science and Innovation (AEI/10.13039/501100011033) through project PID2020-115460GB-I00 and in part by the Junta de Andalucía through the research project P20_00153. Finally, the authors thankfully acknowledge the computer resources, technical expertise, and assistance provided by the SCBI (Supercomputing and Bioinformatics) center of the University of Málaga

Relajación Lagrangiana, métodos heurísticos y metaheurísticos en algunos modelos de Localización e Inventarios

En la actualidad, nos encontramos con numerosas situaciones en las que se requiere la mejor ubicación espacial de un cierto objeto que cumpla con una serie de necesidades, donde este proceso implica una toma de decisión. Ejemplos de ello aparecen en la cadena de suministro, donde el objetivo es optimizar tanto las decisiones de tipo estratégico (Localización) como las de tipo táctico (Inventario) o en problemas de localización de servicios tanto públicos como privados. En este trabajo, se formulan con detalle algunos ejemplos de los problemas anteriores, tales como un modelo integrado de Localización-Inventario, el problema de la p-mediana con restricciones de distancia máxima y un problema bi-objetivo. Finalmente, se resuelven los mismos a través de métodos como relajación Lagrangiana, métodos heurísticos o metaheurísticos tales como GRASP y se han obtenido resultados novedosos, proporcionando diferentes procedimientos de resolución que mejoran los existentes en la literatura.Departamento de Estadística e Investigación OperativaMáster en Investigación en Matemática

Estudio de propiedades retrohereditarias en algunos problemas secuenciales de Optimización Estocástica

De un modo muy general, puede decirse que el objetivo de la Optimización Estocástica es encontrar soluciones óptimas en problemas de optimización que involucran incertidumbre en los datos. Un problema que con cierta frecuencia aparece en el mundo empresarial es el que se presenta al gestor de un sistema en el cual se deben tomar decisiones de un modo secuencial de forma que entre cada dos decisiones consecutivas tiene lugar un fenómeno aleatorio. En este trabajo se formula con detalle el problema anterior y se analizan propiedades retrohereditarias que nos facilitan la obtención de soluciones óptimas. Se han obtenido resultados novedosos, proporcionando teoremas bajo hipótesis más débiles que los existentes en la literatura. Además, para el cálculo explícito de las políticas (s,S) y analizar las soluciones óptimas hemos desarrollado programas en AMPL, así como un análisis de la sensibilidad.Grado en Matemática

Distributionally Robust Optimal Power Flow with Contextual Information

Adrián Esteban-Pérez, Juan M. Morales, Distributionally Robust Optimal Power Flow with Contextual Information, European Journal of Operational Research (2022), doi: https://doi.org/10.1016/j.ejor.2022.10.024In this paper, we develop a distributionally robust chance-constrained formulation of the Optimal Power Flow problem (OPF) whereby the system operator can leverage contextual information. For this purpose, we exploit an ambiguity set based on probability trimmings and optimal transport through which the dispatch solution is protected against the incomplete knowledge of the relationship between the OPF uncertainties and the context that is conveyed by a sample of their joint probability distribution. We provide a tractable reformulation of the proposed distributionally robust chance-constrained OPF problem under the popular conditional-value-at-risk approximation. By way of numerical experiments run on a modified IEEE-118 bus network with wind uncertainty, we show how the power system can substantially benefit from taking into account the well-known statistical dependence between the point forecast of wind power outputs and its associated prediction error. Furthermore, the experiments conducted also reveal that the distributional robustness conferred on the OPF solution by our probability-trimmings-based approach is superior to that bestowed by alternative approaches in terms of expected cost and system reliability.European Research Council (755705); Ministerio de Ciencia e Innovación del Gobierno de España (PID2020- 115460GB-I00/AEI/10.13039/501100011033); Junta de Andalucía y fondos FEDER (P20 00153); Universidad de Málag

Influence of temperature and salinity on hydrodynamic forces

Sobre el diagrama de fuerzas de inercia y de arrastre en un pilote empleado en energía eólica marina se analiza el efecto de la temperatura y la salinidad y, por ello, la relevancia en la turbulencia, Reynolds, CD y CM respectivamente. The purpose of this study is to introduce an innovative approach to offshore engineering so as to take variations in sea temperature and salinity into account in the calculation of hydrodynamic forces. With this in mind, a thorough critical analysis of the influence of sea temperature and salinity on hydrodynamic forces on piles like those used nowadays in offshore wind farms will be carried out. This influence on hydrodynamic forces occurs through a change in water density and viscosity due to temperature and salinity variation. Therefore, the aim here is to observe whether models currently used to estimate wave forces on piles are valid for different ranges of sea temperature and salinity apart from observing the limit when diffraction or nonlinear effects arise combining both effects with the magnitude of the pile diameter. Hence, specific software has been developed to simulate equations in fluid mechanics taking into account nonlinear and diffraction effects. This software enables wave produced forces on a cylinder supported on the sea bed to be calculated. The study includes observations on the calculation model’s sensitivity as to a variation in the cylinder’s diameter, on the one hand and, on the other, as to temperature and salinity variation. This software will enable an iterative calculation to be made for finding out the shape the pressure wave caused when a wave passes over will have for different pile diameters and water with different temperature and salinity

Comportamiento hidrodinámico y sensibilidad de los esquemas de diseño en estructuras de gravedad aplicadas a energías eólicas marinas

Las distintas tipologías estructurales empleadas en energías eólicas marinas dependen básicamente de la capacidad portante del terreno, las profundidades del emplazamiento, las características del parque y las afecciones a la costa, tanto a nivel línea de orilla, como de percepción visual y paisajística. El empleo de estructuras, tanto de gravedad (GBS), como pilotadas, trípodes, flotantes o de tecnología offshore, queda condicionada por los datos de partida descritos anteriormente. Además, podría añadirse que el cálculo de las fuerzas hidrodinámicas en las estructuras offshore, es uno de los problemas clave, para los ingenieros de diseño de hoy en día, que participan en la ingeniería marítima, como sugiere Negro et al. (2014)

A New Optical Density Granulometry-Based Descriptor for the Classification of Prostate Histological Images Using Shallow and Deep Gaussian Processes

[EN] Background and objective Prostate cancer is one of the most common male tumors. The increasing use of whole slide digital scanners has led to an enormous interest in the application of machine learning techniques to histopathological image classification. Here we introduce a novel family of morphological descriptors which, extracted in the appropriate image space and combined with shallow and deep Gaussian process based classifiers, improves early prostate cancer diagnosis. Method We decompose the acquired RGB image in its RGB and optical density hematoxylin and eosin components. Then, we define two novel granulometry-based descriptors which work in both, RGB and optical density, spaces but perform better when used on the latter. In this space they clearly encapsulate knowledge used by pathologists to identify cancer lesions. The obtained features become the inputs to shallow and deep Gaussian process classifiers which achieve an accurate prediction of cancer. Results We have used a real and unique dataset. The dataset is composed of 60 Whole Slide Images. For a five fold cross validation, shallow and deep Gaussian Processes obtain area under ROC curve values higher than 0.98. They outperform current state of the art patch based shallow classifiers and are very competitive to the best performing deep learning method. Models were also compared on 17 Whole Slide test Images using the FROC curve. With the cost of one false positive, the best performing method, the one layer Gaussian process, identifies 83.87% (sensitivity) of all annotated cancer in the Whole Slide Image. This result corroborates the quality of the extracted features, no more than a layer is needed to achieve excellent generalization results. Conclusion Two new descriptors to extract morphological features from histological images have been proposed. They collect very relevant information for cancer detection. From these descriptors, shallow and deep Gaussian Processes are capable of extracting the complex structure of prostate histological images. The new space/descriptor/classifier paradigm outperforms state-of-art shallow classifiers. Furthermore, despite being much simpler, it is competitive to state-of-art CNN architectures both on the proposed SICAPv1 database and on an external databaseThis work was supported by the Ministerio de Economia y Competitividad through project DPI2016-77869. The Titan V used for this research was donated by the NVIDIA CorporationEsteban, AE.; López-Pérez, M.; Colomer, A.; Sales, MA.; Molina, R.; Naranjo Ornedo, V. (2019). A New Optical Density Granulometry-Based Descriptor for the Classification of Prostate Histological Images Using Shallow and Deep Gaussian Processes. Computer Methods and Programs in Biomedicine. 178:303-317. https://doi.org/10.1016/j.cmpb.2019.07.003S30331717

COLECCIÓN JOSEFINA DE LA TORRE MILLARES [Material gráfico]

FORMA PARTE DE LA COLECCIÓN FOTOGRÁFICA DE JOSEFINA DE LA TORRE, CUYOS ARTEFACTOS FOTO-QUÍMICOS ESTÁN CUSTODIADOS EN LA CASA MUSEO DE PÉREZ GALDÓS.Copia digital. Madrid : Ministerio de Educación, Cultura y Deporte. Subdirección General de Coordinación Bibliotecaria, 201