Artículos (Estadística e Investigación Operativa)

URI permanente para esta colecciónhttps://hdl.handle.net/11441/10844

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A mathematical programming approach to hierarchical clustering
(Springer, 2026) Amorosi, Lavinia; Puerto Albandoz, Justo; Valverde Martín, Carlos; Organización Industrial y Gestión de Empresas I; Estadística e Investigación Operativa; Ministerio de Ciencia, Innovación y Universidades (MICIU). España; Junta de Andalucía; European Union; Sapienza University of Rome
Hierarchical clustering is a statistical technique for analyzing the existing groups (clusters) within a dataset and constructing a hierarchy of clusters. This is represented by a rooted tree (dendrogram) whose leaves correspond to the data points, and each internal node represents the cluster containing its descendant leaves. Among the methods for performing hierarchical clustering, the agglomerative methods are based on greedy procedures that yield a sequence of nested partitions, where each level of the hierarchy joins two clusters from the lower partition according to a local criterion. In this work, motivated by the lack of exact approaches that guarantee global optimality, we present the first unified mathematical programming formalization of agglomerative approaches for hierarchical clustering. Through computational experiments, we validate the proposed formulations and evaluate, according to different measures commonly used in this context, the dendrograms obtained from the exact solution of the formulations and those produced by the greedy approach. Furthermore, by exploiting the mathematical formulation, we also present a scalable matheuristic algorithm capable of dealing with large-sized datasets.
El espejismo de lo suficientemente bueno
(Universidad Complutense de Madrid, 2025-12-18) Torrejón Valenzuela, Alberto; Estadística e Investigación Operativa
The biobjective minimum-cost perfect matching problem and Chinese postman problem
(Wiley, 2023-07-21) Pozo Montaño, Miguel Ángel; Puerto Albandoz, Justo; Roldán Bocanegra, Ignacio; Ecuaciones Diferenciales y Análisis Numérico; FQM331: Métodos y Modelos de la Estadística y la Investigación Operativa
In this paper, we address the biobjective versions of the perfect matching problem (PMP) and the Chinese postman problem (CPP). Both problems are solved by means of integer formulations or separating blossom inequalities, exploiting the PMP relationship with the CPP. In both cases, we first find the set of supported nondominated solutions and then we use them to obtain the nonsupported ones. The set of supported nondominated solutions are obtained solving scalarized integer formulations. To obtain the sets of nonsupported solutions, we resort to solving lexicographic problems based on adding additional linear constraints to the original problems. For this reason, we also characterize the combinatorial structure of the PMP vertices with one or two additional constraints. We also investigate when it is possible to use the PMP to solve CPP in the biobjective case.We report computational experiments comparing the different approaches and formulations based on different types of graphs with up to 700 nodes.
Time-Weighted Result-Based Strength Indicators from Head-to-Head Outcomes: An Application to Trotter (Harness) Racing
(MDPI, 2026) Ligero Acosta, Manuel; Muñoz Pichardo, Juan Manuel; Gómez, María Dolores; Ripollés Lobo, María; Valera Córdoba, María Mercedes; Agronomía; Estadística e Investigación Operativa; AGR273: Nuevas Tecnologías de Mejora Animal y de Sus Sistemas Productivos; FQM153: Estadística e Investigación Operativa
We propose a general methodology for constructing dynamic performance indicators (or strength metrics) in any sport that relies on comparative outcomes among competitors, using chronological positional data. Specifically, we develop a family of strength indicators for harness trotting races based on time-weighted, head-to-head results. Using the official Balearic trotting records (1990–2023), we construct win, draw, and confrontation matrices up to each event and apply a triweight kernel to reduce the influence of older results. From these matrices, we derive a family of five bounded, interpretable indicators on the interval: an overall average win rate, a category-adjusted version, and three distance-specific versions (short, medium, and long). Indicator validation is performed via predictive validation, employing regularized logistic regression models (Elastic Net) based on indicator differences between horse pairs. Standard metrics (accuracy, calibration, discrimination, and Brier score) are used for the validation analysis. The results confirm that the indicators are coherent, stable, and interpretable, demonstrating that the generic construction procedure yields robust outcomes. We conclude that these indicators establish a solid and easily updatable foundation for developing dynamic ranking systems and practical selection/handicap procedures in trotting.
Diario de un investigador de IO
(Sociedad Española de Estadística e Investigación Operativa, 2026-03-15) Carrizosa Priego, Emilio José; Estadística e Investigación Operativa; FQM329: Optimización
Repasando páginas de mi (nunca escrito) diario, encuentro mi visión personal sobre el mundo académico y el área de Estadística e Investigación Operativa en dos momentos bien diferentes: principios de los años 90 del siglo pasado y ahora.
Almost Uniform Vs. Pointwise Convergence from a Linear Point of View
(Springer, 2026-04-06) Bernal González, Luis; Calderón Moreno, María del Carmen; Gerlach Mena, Pablo José; Prado Bassas, José Antonio; Análisis Matemático; FQM127: Análisis Funcional no Lineal
A review of the state of the art of the comparison between any two different modes of convergence of sequences of measurable functions is carried out with focus on the algebraic structure of the families under analysis. As a complement of the amount of results obtained by several authors, it is proved, among other assertions and under natural assumptions, the existence of large vector subspaces as well as of large algebras contained in the family of the sequences of measurable functions converging to zero pointwise almost everywhere but not almost uniformly, and in the family of the sequences of measurable functions converging to zero almost uniformly but not uniformly almost everywhere.
Inter‐platform ecosystems
(Wiley, 2026-01-22) Carballa-Smichowsk, Bruno; Duch Brown, Néstor; Martens, Bertin; Gómez Losada, Álvaro; Estadística e Investigación Operativa; FQM153: Estadística e Investigación Operativa
We extend ecosystem theory to cases in which platforms are complementors to each other: inter-platform ecosystems. Analyzing web traffic data on 241 European platforms, we identify and characterize demand-side inter-platform ecosystems, and propose a theory of why they emerge. We posit that demandside inter-platform ecosystems solve matching problems generated by externalities platforms impose on each other. We describe four strategies platforms implement to solve these problems: network fusion (hosting competitor content), user-community-driven interactions (facilitating cross-posting), meta-platform (aggregating another platform), and platform concatenation (referring users to another platform for customized complementary services). We link these strategies to the nature of the externalities, the types of platforms involved and their competitive relationship. We conclude with implications for theory and suggestions for further research.
Evaluación de la exactitud posicional de las cuencas hidrográficas derivadas de un modelo digital de elevaciones (MDE)
(Colegio Oficial de Ingeniería Geomática y Topográfica, 2022) Reinoso Gordo, Juan Francisco; Ariza López, Francisco Javier; Ureña Cámara, Manuel Antonio; Barrera, D.; Eddargani, Salah; Estadística e Investigación Operativa; Agencia Estatal de Investigación
El presente trabajo se centra en evaluar la exactitud posicional planimétrica esperable para las cuencas hidrográfica extraídas de un MDE con un determinado algoritmo. Para ello, se partirá de un MDE de referencia (MDEref) del que, tras aplicar el algoritmo A, se obtienen algunas de sus cuencas hidrográficas (CHref) que se utilizarán como verdad terreno. El MDE del que se quiere conocer su calidad funcional se denomina MDEpro, y sus cuencas hidrográficas de las que se evaluarán su exactitud planimétrica se denominan (CHpro). En este trabajo se ha ideado un método que permite comparar planimétricamente CHpro con CHref, y dar una estimación de su exactitud.
Estimation of background PM2.5 concentrations for an air-polluted environment
(Elsevier, 2019-08-24) Wang, Sheng-Hsiang; Hung, Ruo-Ya; Lin, Neng-Huei; Gómez Losada, Álvaro; Pires, José C.M.; Shimada, Kojiro; Hatakeyama, Shiro; Takami, Akinori; Estadística e Investigación Operativa; FQM153: Estadística e Investigación Operativa
The background PM2.5 concentration represents the combined emissions from natural domestic and foreign sources, which has implications for the maximum effect, in terms of air-quality control, that can be achieved by reducing emissions. However, estimating the background PM2.5 concentration via background monitoring sites for a densely populated region (e.g., Taiwan) has been a challenge. In this study, we compared two statistical methods of estimating the background concentration using an 11-year time series (2005–2016) of data from three air-quality stations in Taiwan. The results of two methods showed good agreement for the background PM2.5 concentration estimation, which was about 4.4 μg m−3 and comparable to literature reports. According to the trend analysis, the concentration has decreased at a rate of 1–2 μg m−3 decade−1 as a result of better emissions control in East Asia in recent years. Furthermore, the local concentration can exceed the regional background value by up to 5 times due to local emissions, topographic effects, and weather regimes. When considering the cross-county transport of PM2.5, a difference as high as 5 μg m−3 exists between two prevailing-wind scenarios. This study provides crucial information to policy-makers on setting an achievable and reasonable goal for PM2.5 reduction.
Optimal randomized classification trees
(Elsevier, 2021-03-08) Blanquero Bravo, Rafael; Carrizosa Priego, Emilio José; Molero del Río, María Cristina; Romero Morales, Dolores; Estadística e Investigación Operativa; FQM329: Optimización
Classification and Regression Trees (CARTs) are off-the-shelf techniques in modern Statistics and Machine Learning. CARTs are traditionally built by means of a greedy procedure, sequentially deciding the splitting predictor variable(s) and the associated threshold. This greedy approach trains trees very fast, but, by its nature, their classification accuracy may not be competitive against other state-of-the-art procedures. Moreover, controlling critical issues, such as the misclassification rates in each of the classes, is difficult. To address these shortcomings, optimal decision trees have been recently proposed in the literature, which use discrete decision variables to model the path each observation will follow in the tree. Instead, we propose a new approach based on continuous optimization. Our classifier can be seen as a randomized tree, since at each node of the decision tree a random decision is made. The computational experience reported demonstrates the good performance of our procedure.
Mathematical optimization in classification and regression trees
(Springer, 2021-03-17) Carrizosa Priego, Emilio José; Molero del Río, María Cristina; Romero Morales, Dolores; Estadística e Investigación Operativa; FQM329: Optimización
Classification and regression trees, as well as their variants, are off-the-shelf methods in Machine Learning. In this paper, we review recent contributions within the Continuous Optimization and the Mixed-Integer Linear Optimization paradigms to develop novel formulations in this research area. We compare those in terms of the nature of the decision variables and the constraints required, as well as the optimization algorithms proposed. We illustrate how these powerful formulations enhance the flexibility of tree models, being better suited to incorporate desirable properties such as cost-sensitivity, explainability, and fairness, and to deal with complex data, such as functional data.
Interval order relationships based on automorphisms and their application to interval optimization
(Elsevier, 2022-10-03) Costa, T. M.; Chalco Cano, Y.; Osuna Gómez, Rafaela; Lodwick, W. A.; Estadística e Investigación Operativa
This paper presents a method to generate preference ordering relations on interval space based on a family of automorphisms on the bidimensional Euclidean space. This method generates a family of order relation with which many order relations presented in the literature can be obtained as particular cases. This family of preference order relations is used to provide a formulation for a family of interval optimization problems that unifies those formulations whose solution concepts are a Pareto-type. The elements belonging to this family are called -interval optimization problems. An advantage of the proposed method is that decision makers can consider a suitable interval optimization problem, choosing an appropriate order relation, which is obtained by choosing an automorphism. Moreover, this paper shows that each -interval optimization problem is equivalent to a biobjective optimization problem. Some optimality conditions for the -interval optimization problems are obtained. The method, concepts and results presented herein are illustrated by several examples.
New preference order relationships and their application to multiobjective interval and fuzzy interval optimization problems
(Elsevier, 2022-12-20) Costa, T. M.; Osuna Gómez, Rafaela; Chalco Cano, Y.; Estadística e Investigación Operativa
Recently, a method to generate preference ordering relationships in interval space, which is based on a family of automorphisms in bidimensional Euclidean space, and the family of φ-interval optimization problems were introduced in the literature. In this article both the method to generate preference ordering relationships in interval space and the family of φ-interval optimization problems are generalized, providing frameworks for dealing with families of multiobjective interval and multiobjective fuzzy interval optimization problems called the family of φ-multiobjective interval optimization problems and the family of φ-multiobjective fuzzy interval optimization problems, respectively. It is shown that those multiobjective interval and multiobjective fuzzy interval optimization problems presented in the literature, whose formulations are based on a given preference order relationship, can be seen as particular cases of a φ-multiobjective interval optimization problem and of a φ-multiobjective fuzzy interval optimization problems, respectively. Some optimality conditions for both these two families of optimization problems are provided and the methods, concepts and results presented herein are illustrated by several examples.
Thresholds Value of Soil Trace Elements for the Suitability of Eucalyptus (The Case Study of Guadiamar Green Corridor)
(Elsevier, 2022-12-16) Blanco Velázquez, Francisco José; Anaya Romero, María; Pinos Mejías, Rafael; Estadística e Investigación Operativa; FQM153: Estadística e Investigación Operativa
A maximal point of a polynomial on a Banach space is a point in the unit ball at which the polynomial attains its norm. Lower bounds are given for the distances between zeros and maximal points.
New optimality conditions for multiobjective fuzzy programming problems
(University of Sistan and Baluchestan, 2020-06) Osuna Gómez, Rafaela; Hernández Jiménez, Beatriz; Chalco Cano, Y.; Ruiz Garzón, Gabriel; Estadística e Investigación Operativa
In this paper we study fuzzy multiobjective optimization problems defined for n variables. Based on a new p-dimensional fuzzy stationary-point definition, necessary efficiency conditions are obtained. And we prove that these conditions are also sufficient under new fuzzy generalized convexity notions. Furthermore, the results are obtained under general differentiability hypothesis.
Necessary and sufficient conditions for interval-valued differentiability
(Wiley, 2022-07-26) Osuna Gómez, Rafaela; Mendonca da Costa, Tiago; Hernández Jiménez, Beatriz; Ruiz Garzón, Gabriel; Estadística e Investigación Operativa
This paper presents necessary and sufficient conditions for generalized Hukuhara differentiability of interval-valued functions and counterexamples of some equivalences previously presented in the literature, for which important results are based on. Moreover, applications of interval generalized Hukuhara differentiability are presented.
Characterization of background particulate matter concentrations using the combination of two clustering techniques in zones with heterogeneous emission sources
(Elsevier, 2020-07-29) Martín Cruz, Yumara; Vera Castellano, Antonio; Gómez Losada, Álvaro; Estadística e Investigación Operativa; FQM153: Estadística e Investigación Operativa
The estimation of the background atmospheric concentration allows to assess local contributions and helping to the design of air quality improvement policies. Using clustering techniques and bivariate analysis, this study aims to characterize the background concentration of PM10 (particulate matter with an aerodynamic diameter less than or equal to 10 μm) and PM2.5 (particulate matter with an aerodynamic diameter less than or equal to 2.5 μm) in environments with heterogeneous emission sources. Background PM10 and PM2.5 pollution was characterized using Hidden Markov and Finite Mixture Models in four air quality monitoring stations, from 2011 to 2017. Average background concentrations in all stations were of 12.7 2.2 μg m-3 for PM10 and 4.6 0.4 μg m-3 for PM2.5. The contribution of background concentration to ambient pollution (both PM10 and PM2.5) was high (more than 40%) in all studied stations, being a 10% higher in background stations (Camping Temisas and Parque de San Juan) compared with stations influenced by an anthropogenic source (Castillo Romeral and San Agustín). Estimated background concentration showed significant differences among studied areas according to Kruskal-Wallis test (p 0.001) and coefficients of divergence, which were greater than 0.2. PM10 and PM2.5 monthly profiles (concentration level) showed that the traffic urban station presented seasonality, probably due to the summer tourism, and daily profiles exhibited a differentiated bimodal distribution. The estimation of background concentrations in this study will allow to quantify local contributions from Saharan outbreaks and to study its possible effects on human health and marine biota.
Inflammation-adjusted optimal serum cut-off alpha-1 antitrypsin values for detecting deficient patients: a cross-sectional analysis of the AVATAR cohort
(European Respiratory Society, 2025) López-Campos Bodineau, José Luis; Muñoz Sánchez, Belén; Quintana-Gallego, Esther; Muñoz Pichardo, Juan Manuel; Medicina; Estadística e Investigación Operativa; FQM153: Estadística e Investigación Operativa; CTS274: Esfuerzo y Rehabilitación Respiratoria
Currently, most diagnostic algorithms for alpha-1 antitrypsin deficiency (AATD) commence with the measurement of serum alpha-1 antitrypsin (AAT) levels, followed by genotyping or phenotyping to confirm the deficiency. However, there is no consensus on the threshold level at which further diagnostic procedures should be pursued. To make matters more complicated, it has been shown that elevated acute phase reactants, such as C-reactive protein (CRP), can modify AAT values, further complicating diagnosis. Of note, there no agreement on the AAT threshold levels when a pro-inflammatory situation with increased CRP is present. By examining a real-life prospective cohort encompassing a variety of mutations, the current analysis seeks to establish the optimal cut-off value for serum AAT levels in diagnosing AATD adjusting the estimation with the value of CRP.
A relative robust approach on expected returns with bounded CVaR for portfolio selection
(Elsevier, 2021-04-21) Benati, Stefano; Conde Sánchez, Eduardo; Estadística e Investigación Operativa
A robust optimization model to find a stable investment portfolio is proposed under twofold uncertainty sources: the random nature of returns for a given economic scenario which is in itself unknown. Our model combines expected returns together with risk and regret measures in order to find a solution ensuring acceptable returns while the investor is protected from the market volatility. More formally, we formulate a model that minimizes the maximum regret on the expected returns while the conditional value-at-risk is upper bounded under different scenario settings. Several mathematical formulations are analyzed. Duality relations drive us to obtaining bounds on the optimal objective value of the problem in order to develop a cutting plane approach. We show experimentally that, despite the large number (hundreds of thousands) of constraints and variables of the resulting problem, an optimal portfolio can be found in a few seconds. Finally, our model is tested in a financial decision making environment by simulating its application in different markets indexes and under different underlying economic conditions. It will be seen that using scenarios usually improves the realized portfolio returns.
An orness based decision support model to aggregate ordered costs
(Elsevier, 2023-02-15) Conde Sánchez, Eduardo; Estadística e Investigación Operativa; FQM329: Optimización
In this paper each possible decision in a given economic context is assessed according to a weighted aggregation of its ordered costs, what is known in the literature as an Ordered Weighted Averaging, or OWA, measure. We assume these weights are uncertain and belong to a given set through which different decision attitudes toward risk are modeled. A compromise (minmax regret) solution is proposed in order to conciliate these admissible decision scenarios. In particular, the choice of a set of weights with bounded orness, a measure of the aversion to the risk, is analyzed. A Linear Programming problem is proposed in order to find a consensus solution under such a set of bounded orness OWA operators. Later, this model is generalized by adding bounds on the difference of consecutive individual weights for the ordered costs and a Benders decomposition scheme is analyzed in order to solve the corresponding optimization problem. It is shown how this model can support decisions about the location of a new facility under a set of different OWA operators and its relation with the efficiency (Pareto optimality) from a multicriteria decision making viewpoint.

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