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312

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## Publications

Publications (312)

In this paper, a model that combines the movement of a multivisit drone with a limited endurance and a base vehicle that can move freely in the continuous space is considered. The mothership is used to charge the battery of the drone, whereas the drone performs the task of visiting multiple targets of distinct shapes: points and polygonal chains. F...

Opinion surveys can contain closed questions to which respondents can give multiple answers. We propose to model these data as networks in which vertices are eligible items and arcs are respondents. This representation opens up the possibility of using complex networks methodologies to retrieve information and most prominently, the possibility of u...

We propose a new optimization model to detect overlapping communities in networks. The model elaborates suggestions contained in Zhang et al. (2007), in which overlapping communities were identified through the use of a fuzzy membership function, calculated as the outcome of a mathematical programming problem. In our approach, we retain the idea of...

In this paper we propose a general methodology for the optimal automatic routing of spatial pipelines motivated by a recent collaboration with Ghenova, a leading Naval Engineering company. We provide a minimum cost multicommodity network flow based model for the problem incorporating all the technical requirements for a feasible pipeline routing. A...

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...

This paper presents a new two‐phase algorithm for the bi‐objective minimum spanning tree (BMST) problem. In the first phase, it computes the extreme supported efficient solutions resorting to both mathematical programming and algorithmic approaches, while the second phase is devoted to obtaining the remaining efficient solutions (non‐extreme suppor...

This paper presents new models for segmentation of 2D and 3D Scanning-Transmission Electron Microscope images based on the ordered median function. The main advantage of using this function is its good adaptability to the different types of images to be studied due to the wide range of weight vectors that can be cast. Classical segmentation models...

In this paper we present a novel mathematical optimization-based methodology to construct tree-shaped classification rules for multiclass instances. Our approach consists of building Classification Trees in which, except for the leaf nodes, the labels are temporarily left out and grouped into two classes by means of a SVM separating hyperplane. We...

This paper deals with a cost sensitive extension of the standard Support Vector Machine (SVM) using an ordered weighted sum of the deviations of misclassified individuals with respect to their corresponding supporting hyperplanes. In contrast with previous heuristic approaches, an exact method that applies the ordered weighted average operator in t...

In this paper we address two different related problems. We first study the problem of finding a simple shortest path in a $d$-dimensional real space subdivided in several polyhedra endowed with different $\ell_p$-norms. This problem is a variant of the weighted region problem, a classical path problem in computational geometry introduced in Mitche...

In this paper we propose a novel methodology to construct Optimal Classification Trees that takes into account that noisy labels may occur in the training sample. The motivation of this new methodology is based on the superaditive effect of combining together margin based classifiers and outlier detection techniques. Our approach rests on two main...

The concept of Owen point, introduced in Guardiola et al. (2009), is an appealing solution concept that for Production-Inventory games (PI-games) always belongs to their core. The Owen point allows all the players in the game to operate at minimum cost but it does not take into account the cost reduction induced by essential players over their foll...

This paper considers the optimization problems that arise to coordinate a tandem between a mothership vehicle and a fleet of drones. %more than one drone. Each drone can be launched from the mothership to perform an operation. After completing the operations the drones return to the mothership to recharge batteries and to be ready for a new operati...

In this paper, we address the Continuous Multifacility Monotone Ordered Median Problem. This problem minimizes a monotone ordered weighted median function of the distances between given demand points in $\mathbb{R}^d$ and its closest facility among the $p$ selected, also in a continuous space. We propose a new branch-and-price procedure for this pr...

In this paper we propose a general methodology for the optimal automatic routing of spatial pipelines motivated by a recent collaboration with Ghenova, a leading Naval Engineering company. We provide a minimum cost multicommodity network flow based model for the problem incorporating all the technical requirements for a feasible pipeline routing. A...

This paper deals with an extension of the Support Vector Machine (SVM) for classification problems where, in addition to maximize the margin, i.e., the width of strip defined by the two supporting hyperplanes, the minimum of the ordered weighted sum of the deviations of miclassified individuals is considered. Since the ordered weighted sum includes...

In this paper we deal with an extension of the crossing postman problem to design routes that have to visit different shapes of dimensional elements rather than edges. This problem models the design of routes of drones or other vehicles that must visit a number of geographical elements to deliver some good or service and then move directly to the n...

This paper addresses the optimization of routing problems with drones. It analyzes the coordination of one mothership with one drone to obtain optimal routes that have to visit some target objects modeled as general graphs. The goal is to minimize the overall weighted distance traveled by both vehicles while satisfying the requirements in terms of...

We consider a cooperative game defined by an economic lot-sizing problem with heterogeneous costs over a finite time horizon, in which each firm faces demand for a single product in each period and coalitions can pool orders. The model of cooperation works as follows: ordering channels and holding and backlogging technologies are shared among the m...

This paper studies the Graph-Connected Clique-Partitioning Problem (GCCP), a clustering optimization model in which units are characterized by both individual and relational data. This problem, introduced by Benati, Puerto, and Rodríguez-Chía (2017) under the name of Connected Partitioning Problem, shows that the combination of the two data types i...

We consider a cooperative game defined by an economic lot-sizing problem with heterogeneous costs over a finite time horizon, in which each firm faces demand for a single product in each period and coalitions can pool orders. The model of cooperation works as follows: ordering channels and holding and backlogging technologies are shared among the m...

In this paper, we propose an extension of the uncapacitated hub location problem where the potential positions of the hubs are not fixed in advance. Instead, they are allowed to belong to a region around an initial discrete set of nodes. We give a general framework in which the collection, transportation, and distribution costs are based on norm‐ba...

This paper studies the Graph-Connected Clique-Partitioning Problem (GCCP), a clustering optimization model in which units are characterized by both individual and relational data. This problem, introduced by Benati et al. (2017) under the name of Connected Partitioning Problem, shows that the combination of the two data types improves the clusterin...

Cooperative lot-sizing models with backlogging and heterogeneous costs are studied in Guardiola et al (2020). In that model several firms participate in a consortium aiming at satisfying their demand over the planning horizon with minimal operation cost. Each firm uses the best ordering channel and holding technology provided by the participants in...

We consider a cooperative game defined by an economic lot-sizing
problem with heterogeneous costs over a finite time horizon, in which each firm faces demand for a single product in each period and coalitions can pool orders. The model of cooperation works as follows: ordering channels and holding and backlogging technologies are shared among the m...

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...

In this paper we study the problem of finding a discrete subtree of minimum variance with bounded size of a given tree. We show that the problem is NP-hard on very simple trees and it remains difficult even if we consider the Mean Absolute Deviation criterion on star graphs. Referring to the variance criterion, we first propose a reformulation of t...

In this paper we propose a novel methodology to construct Optimal Classification Trees that takes into account that noisy labels may occur in the training sample. Our approach rests on two main elements: (1) the splitting rules for the classification trees are designed to maximize the separation margin between classes applying the paradigm of SVM;...

Multiobjective stochastic programming is a field that is well suited to tackling problems that arise in many fields: energy, financial, emergencies, among others; given that uncertainty and multiple objectives are usually present in such problems. A new concept of solution is proposed in this work, which is especially designed for risk-averse solut...

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...

In this paper we study the problem of locating a given number of hyperplanes minimizing an objective function of the closest distances from a set of points. We propose a general framework for the problem in which norm-based distances between points and hyperplanes are aggregated by means of ordered median functions. A compact Mixed Integer Linear (...

This paper deals with a portfolio selection problem with transaction costs and two levels of decision-making. It is assumed that the decision making structure is twofold: there is a broker-dealer that controls the fees to be charged on the different securities in order to maximize his benefit and there is an investor who chooses his portfolio tryin...

Multiobjective stochastic programming is a field well located to tackle problems arising in emergencies, given that uncertainty and multiple objectives are usually present in such problems. A new concept of solution is proposed in this work, especially designed for risk-aversion solutions. A linear programming model is presented to obtain such solu...

This paper deals with the capacitated version of discrete ordered median problems. We present different formulations considering three-index variables or covering variables to address the order requirements in this problem. Some preprocessing phases for fixing variables and some valid inequalities are developed to enhance the initial formulations....

In this paper we analyze the extension of the classical smallest enclosing disk problem to the case of the location of a polyellipsoid to fully cover a set of demand points in Rd. We prove that the problem is polynomially solvable in fixed dimension and analyze mathematical programming formulations for it. We also consider some geometric approaches...

In this paper, we propose the Ordered Median Tree of Hub Location Problem (OMTHL). The OMTHL is a single-allocation hub location problem where p hubs must be placed on a network and connected by a non-directed tree. Each non-hub node is assigned to a single hub and all the flow between origin–destination pairs must cross at least one hub. The objec...

This paper presents a first continuous, linear, conic formulation for the discrete ordered median problem (DOMP). Starting from a binary, quadratic formulation in the original space of location and allocation variables that are common in location analysis (L.A.), we prove that there exists a transformation of that formulation, using the same space...

As a generalisation of p-center location problems, p-k-max problems minimise the k-th largest weighted distance to the customers. In this way, outlier facilities can be detected automatically and excluded from consideration when locating new facilities. Similar to p-center problems, p-k-max problems often have many alternative optimal solutions. Kn...

Given a set of assets and an investment capital, the classical portfolio selection problem consists in determining the amount of capital to be invested in each asset in order to build the most profitable portfolio. The portfolio optimization problem is naturally modeled as a mean-risk bi-criteria optimization problem where the mean rate of return o...

In this paper we propose novel methodologies to construct Support Vector Machine -based classifiers that takes into account that label noises occur in the training sample. We propose different alternatives based on solving Mixed Integer Linear and Non Linear models by incorporating decisions on relabeling some of the observations in the training da...

This paper presents new results for the Discrete Ordered Median Problem (DOMP). It exploits properties of k-sum optimization to derive specific formulations for the monotone DOMP (MDOMP), that arises when the λ weights are non-decreasing monotone, and new formulations for the general non-monotone DOMP. The main idea in our approach is to express or...

This chapter analyzes multicriteria continuous, network, and discrete location problems. In the continuous framework, we provide a complete description of the set of weak Pareto, Pareto, and strict Pareto locations for a general Q-criteria location problem based on the characterization of three criteria problems. In the network case, the set of Par...

The International Workshop on Locational Analysis and Related Problems will take place during January 23-24, 2020 in Seville (Spain). It is organized by the Spanish Location Network and the Location Group GELOCA from the Spanish Society of Statistics and Operations Research(SEIO). The Spanish Location Network is a group of more than 140 researchers...

In this paper we study the problem of locating a given number of hyperplanes minimizing an objective function of the closest distances from a set of points. We propose a general framework for the problem in which norm-based distances between points and hyperplanes are aggregated by means of ordered median functions. A compact Mixed Integer Linear (...

The concept of Owen point, introduced in Guardiola et al. (2009), is an appealing solution concept that for Production-Inventory games (PI-games) always belongs to their core. The Owen point allows all the players in the game to operate at minimum cost but it does not take into account the cost reduction induced by essential players over their foll...

In this paper we propose an extension of the Uncapacitated Hub Location Problem where the potential positions of the hubs are not fixed in advance. Instead, they are allowed to belong to a region around an initial discrete set of nodes. We give a general framework in which the collection, transportation and distribution costs are based on norm-base...

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...

In this paper we present a Mixed Integer Linear Programming model that we developed as part of a pilot study requested by the R&D company Metrolab® in order to design tools for finding solutions for line planning and timetable situations in automated urban metro subway networks. Our model incorporates important factors in public transportation syst...

In this paper we analyze the extension of the classical smallest enclosing disk problem to the case of the location of a polyellipsoid to fully cover a set of demand points in $\mathbb{R}^d$. We prove that the problem is polynomially solvable in fixed dimension and analyze mathematical programming formulations for it. We also consider some geometri...

This paper deals with a bilevel approach of the location-allocation problem with dimensional facilities. We present a general model that allows us to consider very general shapes of domains for the dimensional facilities, and we prove the existence of optimal solutions under mild assumptions. To achieve these results, we borrow tools from optimal t...

This paper introduces a row and column generation algorithm for finding the nucleolus, based on a linear programming model proposed in an earlier research. Since this approach cannot return an allocation for large games, we also propose a heuristic approach, which is based on sampling the coalitions space. Experiments over medium sized games show t...

In this paper, a bilevel programming model is proposed to study a problem of market regulation through government intervention. One of the main characteristics of the problem herein analyzed is that the government monopolizes the raw material in one industry, and competes in another industry with private firms for the production of commodities. Und...

In this paper, we present a novel SVM-based approach to construct multiclass classifiers by means of arrangements of hyperplanes. We propose different mixed integer (linear and non linear) programming formulations for the problem using extensions of widely used measures for misclassifying observations where the kernel trick can be adapted to be app...

Given a set of assets and an investment capital, the classical portfolio selection problem consists in determining the amount of capital to be invested in each asset in order to build the most profitable portfolio. The portfolio optimization problem is naturally modeled as a mean-risk bi-criteria optimization problem where the mean rate of return o...

Computing additive values in cooperative games, like the Shapley value, is a hard task because, in general, it involves the summation of an exponential number of terms. We propose a new method, based on the stochastic approximation of deterministic games and sampling theory, to calculate a statistic estimate of these values and, at the same time, k...

Let be a given graph whose edge set is partitioned into a set R of red edges and a set B of blue edges, and assume that red edges are weighted and contain a spanning tree of G. Then, the Stackelberg minimum spanning tree game (StackMST) is that of pricing (i.e., weighting) the blue edges in such a way that the total weight of the blue edges selecte...

In this paper we present a Mixed Integer Nonlinear Programming model that we developed as part of a pilot study requested by the R&D company Metrolab in order to design tools for finding solutions for line planning and timetable situations in automated urban metro subway networks. Our model incorporates important factors in public transportation sy...

Motivated by recent real-life applications in Location Theory in which the location decisions generate controversy, we propose a novel bilevel location model in which, on the one hand, there is a leader that chooses among a number of fixed potential locations which ones to establish. Next, on the second hand, there is one or several followers that,...

This paper introduces a new algorithmic scheme for two-stage stochastic mixed-integer programming assuming a risk averse decision maker. The focus is the minimization of the conditional value at risk for a hard combinatorial optimization problem. Some properties of a mixed-integer non-linear programming formulation for conditional value at risk are...

This chapter analyzes the ordered median location problem in three different frameworks: continuous, discrete and networks; where some classical but also new results have been collected. For each solution space we study general properties that lead to solution algorithms. In the continuous case, we present two solution approaches for the planar cas...

In this paper, we present a novel approach to construct multiclass clasifiers by means of arrangements of hyperplanes. We propose different mixed integer non linear programming formulations for the problem by using extensions of widely used measures for misclassifying observations. We prove that kernel tools can be extended to these models. Some st...

This paper presents a first continuous, linear, conic formulation for the Discrete Ordered Median Problem (DOMP). Starting from a binary, quadratic formulation in the original space of location and allocation variables that are common in Location Analysis (L.A.), we prove that there exists a transformation of that formulation, using the same space...

In this paper, the identification and exclusion of very distant facilities in center location problems is modeled by k-max functions: One or several new facilities are to be located such that not the largest, but the kth largest weighted distance to the customers is minimized, with k ≥ 1. It is shown that k-max location problems on networks can be...

This paper addresses centered and non centered equipartition tree problems into p connected components (p-partitions). In the former case, each partition must contain exactly one special vertex called center, whereas in the latter, partitions are not required to fulfill this condition. Among the different equipartition problems considered in the li...

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 thes...

This paper deals with a bilevel approach of the location-allocation problem with dimensional facilities. We present a general model that allows us to consider very general shapes of domains for the dimensional facilities and we prove the existence of optimal solutions under mild, natural assumptions. To achieve these results we borrow tools from op...

Public transportation systems in metropolitan areas carry a high density of daily traffic, heterogeneously distributed, and exposed to the negative consequences derived from service disruptions. Breakdowns, accidents, strikes, etc., require on-line operation adjustments to address these incidents and thus reduce their side effects, such as passenge...

This paper presents novel bilevel leader-follower portfolio selection models in which the financial intermediary, that becomes a decision-maker, has to decide on the unit price transaction cost for investing in some securities, maximizing its benefits, and the investor has to choose his optimal portfolio, minimizing risk and ensuring a given expect...

Location problems with extensive facilities represent a challenging field of research. According to the specialized literature, a facility is called extensive if, for purposes of location, it is too large in relation to its environment to be considered a point. There are many examples of this type of structures that appear in real-world application...

We consider a shortest path problem where the arc costs depend on their relative position on the given path and there exist uncertain cost parameters. We study a minmax regret version of the problem under different types of uncertainty of the involved parameters. First, we provide a Mixed Integer Linear Programming (MILP) formulation by using stron...

This paper presents a family of methods for locating/fitting hyperplanes with respect to a given set of points. We introduce a general framework for a family of aggregation criteria, based on ordered weighted operators, of different distance-based errors. The most popular methods found in the specialized literature, namely least sum of squares, lea...

Railway systems in metropolitan areas support a high density of daily traffic that is exposed to different types of disturbances in the service. An interesting topic in the literature is to obtain action protocols in the presence of contingencies which can affect the system operation, avoiding the propagation of perturbation and minimizing its nega...

This paper studies the problem of selecting relevant features in clustering problems , out of a data set in which many features are useless, or masking. The data set comprises a set U of units, a set V of features, a set R of (tentative) cluster centres and distances d ijk for every i ∈ U , k ∈ R, j ∈ V. The feature selection problem consists of fi...

Given the position of some facilities, we study the shape of optimal partitions of the customers’ area in a general planar demand region minimizing total average cost that depends on a set up cost plus some function of the travelling distances. By taking into account different norms, according to the considered situation of the location problem, we...

In this paper, we extend the methodology developed for Support Vector Machines (SVM) using $\ell_2$-norm ($\ell_2$-SVM) to the more general case of $\ell_p$-norms with $p\ge 1$ ($\ell_p$-SVM). The resulting primal and dual problems are formulated as mathematical programming problems; namely, in the primal case, as a second order cone optimization p...

In this paper we address the problem of electing a committee among a set of $m$ candidates and on the basis of the preferences of a set of $n$ voters. We consider the approval voting method in which each voter can approve as many candidates as she/he likes by expressing a preference profile (boolean $m$-vector). In order to elect a committee, a vot...

This paper studies Minimum Spanning Trees under incomplete information assuming that it is only known that vertices belong to some neighborhoods that are second order cone representable and distances are measured with a ℓq-norm. Two mixed integer non linear mathematical programming formulations are presented, based on alternative representations of...

A location problem occurs whenever a set of users have to agree on the position of one or several facilities in order to provide some service for them. The goal is to minimize the overall service cost and depending on the framework space, nature of the service and the globalizing cost function many different models appear: median, center, ordered m...

In this paper we propose the problem of finding the cyclic sequence which best represents a set of cyclic sequences. Given a set of elements and a precedence cost matrix we look for the cyclic sequence of the elements which is at minimum distance from all the ranks when the permutation metric distance is the Kendall Tau distance. In other words, th...