Estadística e Investigación Operativa

URI permanente para esta comunidadhttps://hdl.handle.net/11441/10843

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A Better Approach for Solving a Fuzzy Multiobjective Programming Problem by Level Sets
(MDPI, 2021-04-28) Hernández Jiménez, Beatriz; Ruiz Garzón, Gabriel; Beato Moreno, Antonio; Osuna Gómez, Rafaela; Estadística e Investigación Operativa; Universidad de Sevilla. FQM153: Estadística e Investigación Operativa
In this paper, we deal with the resolution of a fuzzy multiobjective programming problem using the level sets optimization. We compare it to other optimization strategies studied until now and we propose an algorithm to identify possible Pareto efficient optimal solutions.
A biobjective approach to recoverable robustness based on location planning
(ELSEVIER SCIENCE BV, 2017-02-16) Carrizosa Priego, Emilio José; Goerigk, Marc; Schöbel, Anita; Universidad de Sevilla. Departamento de Estadística e Investigación Operativa; Universidad de Sevilla. FQM329: Optimización
Finding robust solutions of an optimization problem is an important issue in practice, and various con- cepts on how to define the robustness of a solution have been suggested. The idea of recoverable robust- ness requires that a solution can be recovered to a feasible one as soon as the realized scenario becomes known. The usual approach in the literature is to minimize the objective function value of the recovered solution in the nominal or in the worst case. As the recovery itself is also costly, there is a trade-offbetween the recovery costs and the solution value obtained; we study both, the recovery costs and the solution value in the worst case in a biobjective setting. To this end, we assume that the recovery costs can be described by a metric. We show that in this case the recovery robust problem can be reduced to a location problem. We show how weakly Pareto efficient solutions to this biobjective problem can be computed by minimiz- ing the recovery costs for a fixed worst-case objective function value and present approaches for the case of linear and quasiconvex problems for finite uncertainty sets. We furthermore derive cases in which the size of the uncertainty set can be reduced without changing the set of Pareto efficient solutions.
A biobjective method for sample allocation in stratified sampling
(Elsevier, 2007-03-01) Carrizosa Priego, Emilio José; Romero Morales, María Dolores; Universidad de Sevilla. Departamento de Estadística e Investigación Operativa; Ministerio de Ciencia y Tecnología (MCYT). España; Universidad de Sevilla. FQM329: Optimizacion
The two main and contradicting criteria guiding sampling design are accuracy of estimators and sampling costs. In stratified random sampling, the sample size must be allocated to strata in order to optimize both objectives. In this note we address, following a biobjective methodology, this allocation problem. A two-phase method is proposed to describe the set of Pareto-optimal solutions of this nonlinear integer biobjective problem. In the first phase, all supported Pareto-optimal solutions are described via a closed formula, which enables quick computation. Moreover, for the common case in which sampling costs are independent of the strata, all Pareto-optimal solutions are shown to be supported. For more general cost structures, the non-supported Pareto-optimal solutions are found by solving a parametric knapsack problem. Bounds on the criteria can also be imposed, directing the search towards implementable sampling plans. Our method provides a deeper insight into the problem than simply solving a scalarized version, whereas the computational burden is reasonable.
A biobjective method for sample allocation in stratified sampling
(ELSEVIER SCIENCE BV, 2006-02-16) Carrizosa Priego, Emilio José; Romero Morales, María Dolores; Universidad de Sevilla. Departamento de Estadística e Investigación Operativa
The two main and contradicting criteria guiding sampling design are accuracy of estimators and sampling costs. In stratified random sampling, the sample size must be allocated to strata in order to optimize both objectives. In this note we address, following a biobjective methodology, this allocation problem. A two-phase method is proposed to describe the set of Pareto-optimal solutions of this nonlinear integer biobjective problem. In the first phase, all supported Pareto-optimal solutions are described via a closed formula, which enables quick computation. Moreover, for the common case in which sampling costs are independent of the strata, all Pareto-optimal solutions are shown to be supported. For more general cost structures, the non-supported Pareto-optimal solutions are found by solving a parametric knapsack problem. Bounds on the criteria can also be imposed, directing the search towards implementable sampling plans. Our method provides a deeper insight into the problem than simply solving a scalarized version, whereas the computational burden is reasonable.
A Branch-Price-and-Cut Procedure for the Discrete Ordered Median Problem
(informs, 2020-01-07) Deleplanque, Samuel; Labbé, Martine; Ponce López, Diego; Puerto Albandoz, Justo; Universidad de Sevilla. Departamento de Estadística e Investigación Operativa; Universidad de Sevilla. FQM331: Metodos y Modelos de la Estadistica y la Investigacion Operativa
The discrete ordered median problem (DOMP) is formulated as a set-partitioning problem using an exponential number of variables. Each variable corresponds to a set of demand points allocated to the same facility with the information of the sorting position of their corresponding costs. We develop a column generation approach to solve the continuous relaxation of this model. Then we apply a branch-price-and-cut algorithm to solve small- to large-sized instances of DOMP in competitive computational time.
A characterization of distributions based on linear regression of order statistics and record values
(Indian Statistical Institute, 1997) López Blázquez, José Fernando; Moreno Rebollo, Juan Luis; Universidad de Sevilla. Departamento de Estadística e Investigación Operativa; Universidad de Sevilla. FQM331: Métodos y Modelos de la Estadística y la Investigación Operativa; Universidad de Sevilla. FQM153: Estadística e Investigación Operativa
We obtain the family of distributions for which the regression of one order statistic on another, not necessarily adjacent, is linear. As a consequence, we present a characterization of uniform distributions on an interval. We also characterize the distributions that appear when we impose the condition of linearity of regression for record values.
A characterization of efficient points in constrained location problems with regional demand
(ELSEVIER SCIENCE BV, 1996-02-01) Carrizosa Priego, Emilio José; Plastria, Frank; Universidad de Sevilla. Departamento de Estadística e Investigación Operativa; Universidad de Sevilla. FQM329: Optimización
In this paper we characterize the set of efficient points in the planar point-objective location problem under a convex locational constraint, when distances are measured by a strictly convex norm in ~2 and the set of demand points is a compact set. It is shown that, under these assumptions, the efficient set coincides with the closest-point projection of the convex hull of the demand points onto the feasible set.
A characterization of halfspace depth
(Elsevier, 1996-07-01) Carrizosa Priego, Emilio José; Universidad de Sevilla. Departamento de Estadística e Investigación Operativa; Universidad de Sevilla. FQM329: Optimizacion
In this note we present a characterization of halfspace depth which relates it with well-known concepts of Locational Analysis. This characterization also leads to a natural extension of the concept of depth to noneuclidean location estimation as well as other settings like regression.
A characterization of the multivariate excess wealth ordering
(Elsevier, 2011-11) Fernández Ponce, José María; Pellerey, Franco; Rodríguez Griñolo, María del Rosario; Universidad de Sevilla. Departamento de Estadística e Investigación Operativa; Universidad de Sevilla. FQM328: Metodos Cuantitativos en Evaluacion
In this paper, some new properties of the upper-corrected orthant of a random vector are proved. The univariate rightspread or excess wealth function, introduced by Fernández-Ponce et al. (1996), is extended to multivariate random vectors, and some properties of this multivariate function are studied. Later, this function was used to define the excess wealth ordering by Shaked and Shanthikumar (1998) and Fernández-Ponce et al. (1998). The multivariate excess wealth function enable us to define a new stochastic comparison which is weaker than the multivariate dispersion orderings. Also, some properties relating the multivariate excess wealth order with stochastic dependence are described.
A class of goodness-of-fit tests for circular distributions based on trigonometric moments
(Statistical Institute of Catalonia, 2019) Rao Jammalamadaka, Sreenivasa; Jiménez Gamero, María Dolores; Meintanis, Simos G.; Universidad de Sevilla. Departamento de Estadística e Investigación Operativa
We propose a class of goodness–of–fit test procedures for arbitrary parametric families of circular distributions with unknown parameters. The tests make use of the specific form of the characteristic function of the family being tested, and are shown to be consistent. We derive the asymptotic null distribution and suggest that the new method be implemented using a bootstrap resampling technique that approximates this distribution consistently. As an illustration, we then specialize this method to testing whether a given data set is from the von Mises distribution, a model that is commonly used and for which considerable theory has been developed. An extensive Monte Carlo study is carried out to compare the new tests with other existing omnibus tests for this model. An application involving five real data sets is provided in order to illustrate the new procedure.
A combinatorial optimization approach to scenario filtering in portfolio selection
(Elsevier, 2022-02-05) Puerto Albandoz, Justo; Ricca, Federica; Rodríguez Madrena, Moisés; Scozzari, Andrea; Universidad de Sevilla. Departamento de Estadística e investigación operativa; Universidad de Sevilla. FQM331: Metodos y Modelos de la Estadistica y la Investigacion Operativa
Recent studies stressed the fact that covariance matrices computed from empirical financial time series appear to contain a high amount of noise. This makes the classical Markowitz Mean–Variance Optimization model unable to correctly evaluate the performance associated to selected portfolios. Since the Markowitz model is still one of the most used practitioner-oriented tool, several filtering methods have been proposed in the literature to overcome the problem. Among them, the two most promising ones refer to the Random Matrix Theory and to the Power Mapping strategy. The basic idea of these methods is to transform the estimated correlation matrix before applying the Mean–Variance Optimization model. However, experimental analysis shows that these two strategies are not always effective when applied to real financial datasets. In this paper we propose a new filtering method based on Quadratic Programming. We develop a Mixed Integer Quadratic Programming model, which is able to filter those observations that may affect the performance of the selected portfolio. We discuss the properties of this new model and test it on some real financial datasets. We compare the out-of-sample performance of our portfolios with the one of the portfolios provided by the two above mentioned alternative filtering methods giving evidence that our method outperforms them. Although our model can be solved efficiently with standard optimization solvers, the computational burden increases for large datasets. To solve also these problems, we propose a heuristic procedure, which, on the basis of our empirical results, shows to be both efficient and effective.
A comparative study of formulations and solution methods for the discrete ordered p-median problem
(Elsevier, 2016-06-06) Labbé, Martine; Ponce López, Diego; Puerto Albandoz, Justo; Universidad de Sevilla. Departamento de Estadística e Investigación Operativa; Universidad de Sevilla. FQM331: Métodos y Modelos de la Estadística y la Investigación Operativa
This paper presents several new formulations for the Discrete Ordered Median Problem (DOMP) based on its similarity with some scheduling problems. Some of the new formulations present a considerably smaller number of constraints to define the problem with respect to some previously known formulations. Furthermore, the lower bounds provided by their linear relaxations improve the ones obtained with previous formulations in the literature even when strengthening is not applied. We also present a polyhedral study of the assignment polytope of our tightest formulation showing its proximity to the convex hull of the integer solutions of the problem. Several resolution approaches, among which we mention a branch and cut algorithm, are compared. Extensive computational results on two families of instances, namely randomly generated and from Beasley's OR-library, show the power of our methods for solving DOMP.
A comparison of formulations and solution methods for the minimum-envy location problem. Additional results
(2008) Espejo Miranda, María Inmaculada; Marín Pérez, Alfredo; Puerto Albandoz, Justo; Rodríguez Chía, Antonio Manuel; Universidad de Sevilla. Departamento de Estadística e Investigación Operativa; Universidad de Sevilla. FQM331: Metodos y Modelos de la Estadistica y la Investigacion Operativa
We consider a discrete facility location problem with a new form of equity criterion. The model discussed in the paper analyzes the case where demand points only have strict preference order on the sites where the plants can be located. The goal is to find the location of the facilities minimizing the total envy felt by the entire set of demand points. We define this new total envy criterion and provide several integer linear programming formulations that reflect and model this approach. Extensive computational tests are reported, showing the potentials and limits of each formulation on several types of instances.
A computational study of a nonlinear minsum facility location problem
(PERGAMON-ELSEVIER SCIENCE LTD, 2012-01-31) Carrizosa Priego, Emilio José; Ushakov, Anton; Vasilyev, Igor; Universidad de Sevilla. Departamento de Estadística e Investigación Operativa; Universidad de Sevilla. FQM329: Optimización
A discrete location problem with nonlinear objective is addressed. A set of p plants is to be open to serve a given set of clients. Together with the locations, the number p of facilities is also a decision variable. The objective is to minimize the total cost, represented as the transportation cost between clients and plants, plus an increasing nonlinear function of p. Two Lagrangean relaxations are considered to derive lower bounds. Dual information is also used to design acore heuristic. Computational results are given, showing that nearly optimal solutions are obtained in short running times.
A cooperative location game based on the 1-center location problem
(Elsevier, 2011-10-16) Puerto Albandoz, Justo; Tamir, Arie; Perea Rojas-Marcos, Federico; Universidad de Sevilla. Departamento de Estadística e Investigación Operativa; Universidad de Sevilla. FQM331: Metodos y Modelos de la Estadistica y la Investigacion Operativa
In this paper we introduce and analyze new classes of cooperative games related to facility location models defined on general metric spaces. The players are the customers (demand points) in the location problem and the characteristic value of a coalition is the cost of serving its members. Specifically, the cost in our games is the service radius of the coalition. We study the existence of core allocations and the existence of polynomial representations of the cores of these games, focusing on network spaces, i.e., finite metric spaces induced by undirected graphs and positive edge lengths, and on the ℓp metric spaces defined over Rd.
A cost-sensitive constrained Lasso
(Springer, 2020-03-02) Blanquero Bravo, Rafael; Carrizosa Priego, Emilio José; Ramírez Cobo, Josefa; Sillero Denamiel, María Remedios; Universidad de Sevilla. Departamento de Estadística e Investigación Operativa; Universidad de Sevilla. FQM329: Optimización
The Lasso has become a benchmark data analysis procedure, and numerous variants have been proposed in the literature. Although the Lasso formulations are stated so that overall prediction error is optimized, no full control over the accuracy prediction on certain individuals of interest is allowed. In this work we propose a novel version of the Lasso in which quadratic performance constraints are added to Lasso-based objective functions, in such a way that threshold values are set to bound the prediction errors in the different groups of interest (not necessarily disjoint). As a result, a constrained sparse regression model is defined by a nonlinear optimization problem. This cost-sensitive constrained Lasso has a direct application in heterogeneous samples where data are collected from distinct sources, as it is standard in many biomedical contexts. Both theoretical properties and empirical studies concerning the new method are explored in this paper. In addition, two illustrations of the method on biomedical and sociological contexts are considered.
A data science approach for spatiotemporal modelling of low and resident air pollution in Madrid (Spain): Implications for epidemiological studies
(Elsevier, 2019) Gómez Losada, Álvaro; Santos, Francisca M.; Gibert, Karina; Pires, José Carlos M.; Universidad de Sevilla. Departamento de Estadística e Investigación Operativa
Model developments to assess different air pollution exposures within cities are still a key challenge in environmental epidemiology. Background air pollution is a long-term resident and low-level concentration pollution difficult to quantify, and to which population is chronically exposed. In this study, hourly time series of four key air pollutants were analysed using Hidden Markov Models to estimate the exposure to background pollution in Madrid, from 2001 to 2017. Using these estimates, its spatial distribution was later analysed after combining the interpolation results of ordinary kriging and inverse distance weighting. The ratio of ambient to background pollution differs according to the pollutant studied but is estimated to be on average about six to one. This methodology is proposed not only to describe the temporal and spatial variability of this complex exposure, but also to be used as input in new modelling approaches of air pollution in urban areas.
A DC biobjective location model
(Springer, 2002) Blanquero Bravo, Rafael; Carrizosa Priego, Emilio José; Universidad de Sevilla. Departamento de Estadística e Investigación Operativa; Universidad de Sevilla. FQM329: Optimización
In this paper we address the biobjective problem of locating a semiobnoxious facility, that must provide service to a given set of demand points and, at the same time, has some negative effect on given regions in the plane. In the model considered, the location of the new facility is selected in such a way that it gives answer to these contradicting aims: minimize the service cost (given by a quite general function of the distances to the demand points) and maximize the distance to the nearest affected region, in order to reduce the negative impact. Instead of addressing the problem following the traditional trend in the literature (i.e., by aggregation of the two objectives into a single one), we will focus our attention in the construction of a finite ε-dominating set, that is, a finite feasible subset that approximates the Pareto-optimal outcome for the biobjective problem. This approach involves the resolution of univariate d.c. optimization problems, for each of which we show that a d.c. decomposition of its objective can be obtained, allowing us to use standard d.c. optimization techniques.
A discretization result for some optimization problems in framework spaces with polyhedral obstacles and the Manhattan metric
(Elsevier, 2018-07) Puerto Albandoz, Justo; Rodríguez Madrena, Moisés; Universidad de Sevilla. Departamento de Estadística e Investigación Operativa; Ministerio de Economía y Competitividad (MINECO). España; European Commission (EC). Fondo Europeo de Desarrollo Regional (FEDER); Universidad de Sevilla. FQM331: Métodos y Modelos de la Estadística y la Investigación Operativa
In this work we consider the shortest path problem and the single facility Weber location problem in any real space of finite dimension where there exist different types of polyhedral obstacles or forbidden regions. These regions are polyhedral sets and the metric considered in the space is the Manhattan metric. We present a result that reduce these continuous problems into problems in a “add hoc” graph, where the original problems can be solved using elementary techniques of Graph Theory. We show that, fixed the dimension of the space, both the reduction and the resolution can be done in polynomial time.
A discretizing algorithm for location problems
(ELSEVIER SCIENCE BV, 1995) Carrizosa Priego, Emilio José; Puerto Gómez, Justo; Universidad de Sevilla. Departamento de Estadística e Investigación Operativa; Universidad de Sevilla. FQM329: Optimización
A new and simple methodology is proposed to solve both constrained and unconstrained planar continuous single-facility location problems. As particular instances, the classical location problems with mixed gauges can be solved. Theoretical convergence is proved, and numerical examples are given, showing a fast convergence in a small number of steps.

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