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In this paper, we describe an approach to rank sport players based on their efficiency. Although is extremely useful to analyze the performance of team games there is no unanimity on the use of a single index to perform such a ranking. We propose a method to summarize the huge amount of information collected at different aspects of a sport team which is almost daily publicly available. The tool will allow agents involved in a player's negotiation to show the strengths (and weaknesses) of the player with respect to other players. The approach is based on applying a multicriteria outranking methodology using as alternatives the potential players and criteria different efficiency indices. A novel automatic parameter tuning approach is detailed that will allow coaches and sports managers to design templates and sports strategies that improve the efficiency of their teams. We report the results performed over the available information on the ACB Basketball League, and we show how it can be easily implemented and interpreted in practice by decision-makers non familiar with the mathematical side of the methodology., Comment: 17 pages, 6 Tables, 4 Figures

In this work, we present a modeling framework for minimax mixed 0-1 fuzzy linear problems. It is based on extending the usual rewriting of crisp minimax problems via auxiliary variables to model the maximum of a finite set of fuzzy linear functions. We establish that the considered problem can be equivalently formulated as a multiple objective mixed integer programming problem. The framework is applied to a fully fuzzy version of the capacitated center facility location problem., Comment: 18 pages, 5 Figures

In this paper, we introduce the Tree of Hubs Location Problem with Upgrading, a mixture of the Tree of Hubs Location Problem, presented by Contreras et. al (2010), and the Minimum Cost Spanning Tree Problem with Upgraded nodes, studied for the first time by Krumke (1999). In addition to locate the hubs, to determine the tree that connects the hubs and to allocate non-hub nodes to hubs, a decision has to be made about which of the hubs will be upgraded, taking into account that the total number of upgraded nodes is given. We present two different Mixed Integer Linear Programming formulations for the problem, tighten the formulations and generate several families of valid inequalities for them. A computational study is presented showing the improvements attained with the strengthening of the formulations and comparing them., Comment: 29 pages, 17 Figures, 4 Tables

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 problem and in the dual case, as a polynomial optimization problem involving homogeneous polynomials. Scalability of the primal problem is obtained via general transformations based on the expansion of functionals in Schauder spaces. The concept of Kernel function, widely applied in $\ell_2$-SVM, is extended to the more general case by defining a new operator called multidimensional Kernel. This object gives rise to reformulations of dual problems, in a transformed space of the original data, which are solved by a moment-sdp based approach. The results of some computational experiments on real-world datasets are presented showing rather good behavior in terms of standard indicators such a \textit{accuracy index} and its ability to classify new data., Comment: 27 paes, 2 Figures, 2 tables

In this paper, we introduce a new variant of the $p$-median facility location problem in which it is assumed that the exact location of the potential facilities is unknown. Instead, each of the facilities must be located in a region around their initially assigned location (the neighborhood). In this problem, two main decisions have to be made simultaneously: the determination of the potential facilities that must be open to serve the demands of the customers and the location of the open facilities in their neighborhoods, at global minimum cost. We present several mixed integer non-linear programming formulations for a wide family of objective functions which are common in Location Analysis: ordered median functions. We also develop two math-heuristic approaches for solving the problem. We report the results of extensive computational experiments., Comment: 29 pages; 6 tables; 7 figures

This paper studies Minimum Spanning Trees under incomplete information for its vertices. We assume that no information is available on the precise placement of vertices so that it is only known that vertices belong to some neighborhoods that are second order cone representable and distances are measured with a $\ell_q$-norm. Two mixed integer non linear mathematical programming formulations are presented, based on alternative representations of subtour elimination constraints. A solution scheme is also proposed, resulting from a reformulation suitable for a Benders-like decomposition, which is embedded within an exact branch-and-cut framework. Furthermore, a mathheuristic is developed, which alternates in solving convex subproblems in different solution spaces, and is able to solve larger instances. The results of extensive computational experiments are reported and analyzed., Comment: 26 pages, 4 figures, 7 tables

We present in this paper a new premium computation principle based on the use of prior information from multiple sources for computing the premium charged to a policyholder. Under this framework, based on the use of Ordered Weighted Averaging (OWA) operators, we propose alternative collective and Bayes premiums and describe some approaches to compute them. Several examples illustrates the new framework for premium computation., Comment: 8 Tables; 3 Figures

This paper presents a family of new methods for locating/fitting hyperplanes with respect to a given set of points. We introduce a general framework for a family of aggregation criteria of different distance-based errors. The most popular methods found in the specialized literature can be cast within this family as particular choices of the errors and the aggregation criteria. Mathematical programming formulations for these methods are stated and some interesting cases are analyzed. It is also proposed a new goodness of fitting index which extends the classical coefficient of determination. A series of illustrative examples and extensive computational experiments implemented in R are provided to show the performances of some of the proposed methods., Comment: 26 pages; 7 Figures; 12 Tables

Coronal Mass Ejections (CMEs) and Corotating Interaction Regions (CIRs) are major sources of magnetic storms on Earth and are therefore considered to be the most dangerous space weather events. The Observatories of Solar Corona and Active Regions (OSCAR) mission is designed to identify the 3D structure of coronal loops and to study the trigger mechanisms of CMEs in solar Active Regions (ARs) as well as their evolution and propagation processes in the inner heliosphere. It also aims to provide monitoring and forecasting of geo-effective CMEs and CIRs. OSCAR would contribute to significant advancements in the field of solar physics, improvements of the current CME prediction models, and provide data for reliable space weather forecasting. These objectives are achieved by utilising two spacecraft with identical instrumentation, located at a heliocentric orbital distance of 1~AU from the Sun. The spacecraft will be separated by an angle of 68$^{\circ}$ to provide optimum stereoscopic view of the solar corona. We study the feasibility of such a mission and propose a preliminary design for OSCAR., Comment: 28 pages, 7 figures, 6 tables, accepted for publication in Space Weather and Space Climate

In this paper we address the problem of locating a new facility on a $d$-dimensional space when the distance measure ($\ell_p$- or polyhedral-norms) is different at each one of the sides of a given hyperplane $\mathcal{H}$. We relate this problem with the physical phenomenon of refraction, and extends it to any finite dimension space and different distances at each one of the sides of any hyperplane. An application to this problem is the location of a facility within or outside an urban area where different distance measures must be used. We provide a new second order cone programming formulation, based on the $\ell_p$-norm representation given in \cite{BPE2014} that allows to solve, exactly, the problem in any finite dimension space with semidefinite programming tools. We also extend the problem to the case where the hyperplane is considered as a rapid transit media (a different third norm is also considered over $\mathcal{H}$) that allows the demand to travel faster through $\mathcal{H}$ to reach the new facility. Extensive computational experiments run in Gurobi are reported in order to show the effectiveness of the approach., Comment: 22 pages, 9 figures, 4 tables

In this work we study opinion formation on a fully-connected population participating of a public debate with two distinct choices, where the agents may adopt three different attitudes (favorable to either one choice or to the other, or undecided). The interactions between agents occur by pairs and are competitive, with couplings that are either negative with probability $p$ or positive with probability $1-p$. This bimodal probability distribution of couplings produces a behavior similar to the one resulting from the introduction of Galam's contrarians in the population. In addition, we consider that a fraction $d$ of the individuals are intransigent, that is, reluctant to change their opinions. The consequences of the presence of contrarians and intransigents are studied by means of computer simulations. Our results suggest that the presence of inflexible agents affects the critical behavior of the system, causing either the shift of the critical point or the suppression of the ordering phase transition, depending on the groups of opinions intransigents belong to. We also discuss the relevance of the model for real social systems., Comment: 19 pages, 8 figures, to appear in PRE

In this paper we propose a general methodology for solving a broad class of continuous, multifacility location problems, in any dimension and with $\ell_\tau$-norms proposing two different methodologies: 1) by a new second order cone mixed integer programming formulation and 2) by formulating a sequence of semidefinite programs that converges to the solution of the problem; each of these relaxed problems solvable with SDP solvers in polynomial time. We apply dimensionality reductions of the problems by sparsity and symmetry in order to be able to solve larger problems., Comment: 26 pages, 2 tables

This paper addresses the general continuous single facility location problems in finite dimension spaces under possibly different $\ell_p$ norms in the demand points. We analyze the difficulty of this family of problems and revisit convergence properties of some well-known algorithms. The ultimate goal is to provide a common approach to solve the family of continuous $\ell_p$ ordered median location problems in dimension $d$ (including of course the $\ell_p$ minisum or Fermat-Weber location problem for any $p\ge 1$). We prove that this approach has a polynomial worse case complexity for monotone lambda weights and can be also applied to constrained and even non-convex problems., Comment: 31 pages, 5 tables

Several algorithms are available in the literature for finding the entire set of Pareto-optimal solutions in MultiObjective Linear Programming (MOLP). However, it has not been proposed so far an interior point algorithm that finds all Pareto-optimal solutions of MOLP. We present an explicit construction, based on a transformation of any MOLP into a finite sequence of SemiDefinite Programs (SDP), the solutions of which give the entire set of Pareto-optimal extreme points solutions of MOLP. These SDP problems are solved by interior point methods; thus our approach provides a pseudo-polynomial interior point methodology to find the set of Pareto-optimal solutions of MOLP., Comment: 13 pages, 1 figure

In this paper we analyze the irreducibility of numerical semigroups with multiplicity up to four. Our approach uses the notion of Kunz-coordinates vector of a numerical semigroup recently introduced in (Blanco-Puerto, 2011). With this tool we also completely describe the whole family of minimal decompositions into irreducible numerical semigroups with the same multiplicity for this set of numerical semigroups. We give detailed examples to show the applicability of the methodology and conditions for the irreducibility of well-known families of numerical semigroups as those that are generated by a generalized arithmetic progression., Comment: 18 pages

This paper addresses the problem of decomposing a numerical semigroup into m-irreducible numerical semigroups. The problem originally stated in algebraic terms is translated, introducing the so called Kunz-coordinates, to resolve a series of several discrete optimization problems. First, we prove that finding a minimal m-irreducible decomposition is equivalent to solve a multiobjective linear integer problem. Then, we restate that problem as the problem of finding all the optimal solutions of a finite number of single objective integer linear problems plus a set covering problem. Finally, we prove that there is a suitable transformation that reduces the original problem to find an optimal solution of a compact integer linear problem. This result ensures a polynomial time algorithm for each given multiplicity m. We have implemented the different algorithms and have performed some computational experiments to show the efficiency of our methodology., Comment: 22 pages

In this paper we present a mathematical formulation for the omega invariant of a numerical semigroup for each of its minimal generators. The model consists of solving a problem of optimizing a linear function over the efficient set of a multiobjective linear integer program. We offer a methodology to solve this problem and we provide some computational experiments to show the applicability of the proposed algorithm., Comment: 23 pages, 3 tables

Arithmetical invariants---such as sets of lengths, catenary and tame degrees---describe the non-uniqueness of factorizations in atomic monoids. We study these arithmetical invariants by the monoid of relations and by presentations of the involved monoids. The abstract results will be applied to numerical monoids and to Krull monoids., Comment: 22 pages

Fuzzy optimization deals with the problem of determining 'optimal'solutions of an optimization problem when some of the elements that appear in the problem are not precise. In real situations it is usual to have information, in systems under consideration, that is not exact. Thisimprecision can be modeled in a fuzzy environment. Zadeh (1965) analyzed systems of logic that permit truth values between zero and one instead of the classical binary true-false logic. In this framework, satisfying a certain condition means to evaluate how close are the elements involved to the complete satisfaction. Then, each element in a 'fuzzy set' is coupled with a value in [0,1] that represents the membership level to the set. In linear programming some or all the elements that describe a problem may be considered fuzzy: objective function, right-hand side vector or constraint matrix, the notion of optimality (ordering over the feasible solutions), the level of satisfaction of the constraints, etc. Moreover, in integer programs, the integrality constraints may be seen as fuzzy constraints. Here, we present new complexity results about linear integer programming where some of its elements are considered fuzzy using previous results on short generating functions for solving multiobjective integer programs., Comment: 21 pages, 6 figures

Multiobjective discrete programming is a well-known family of optimization problems with a large spectrum of applications. The linear case has been tackled by many authors during the last years. However, the polynomial case has not been deeply studied due to its theoretical and computational difficulties. This paper presents an algebraic approach for solving these problems. We propose a methodology based on transforming the polynomial optimization problem in the problem of solving one or more systems of polynomial equations and we use certain Gr\"obner bases to solve these systems. Different transformations give different methodologies that are analyzed and compared from a theoretical point of view and by some computational experiments via the algorithms that they induce., Comment: 13 pages