New models for the location of controversial facilities: A bilevel programming approach

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, once the leader location facilities have been set, chooses his location points in a continuous framework. The leader’s goal is to maximize some proxy to the weighted distance to the follower’s location points, while the follower(s) aim is to locate his location points as close as possible to the leader ones. We develop the bilevel location model for one follower and for any polyhedral distance, and we extend it for several followers and any ℓp-norm, p ∈ Q, p ≥ 1. We prove the NP-hardness of the problem and propose different mixed integer linear programming formulations. Moreover, we develop alternative Benders decomposition algorithms for the problem. Finally, we report some computational results comparing the formulations and the Benders decompositions on a set of instances.Fonds de la Recherche Scientique - FNRSMinisterio de Economía y CompetitividadFondo Europeo de Desarrollo Regiona

Mixed Integer Linear Programming for Feature Selection in Support Vector Machine

This work focuses on support vector machine (SVM) with feature selection. A MILP formulation is proposed for the problem. The choice of suitable features to construct the separating hyperplanes has been modelled in this formulation by including a budget constraint that sets in advance a limit on the number of features to be used in the classification process. We propose both an exact and a heuristic procedure to solve this formulation in an efficient way. Finally, the validation of the model is done by checking it with some well-known data sets and comparing it with classical classification methods.Comment: 37 pages, 20 figure

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Genetic characterization of Yersinia enterocolitica collected from tonsils of slaughtered pigs

From January to March 2009, detection of pathogenic Yersinia enterocolitica was done from 900 tonsils swabs collected from 45 pig batches in one slaughterhouse. 316 Y. enterocolitica isolates were collected and confirmed as pathogenic biotype by biochemical tests. For this study, these strains were genetically characterized on the basis of their virulence genes and their PFGE profiles. Real Time PCR was used to evaluate the presence of genes ail, myfA, and ystA on the genome and the gene yadA on the pYV plasmid. PFGE analysis using XbaI enzyme was also realised

Discussion of Fairness and Implementability in Stackelberg Security Games

International audienceIn this article we discuss the impact of fairness constraints in Stackelberg Security Games. Fairness constraints can be used to avoid discrimination at the moment of implementing police patrolling. We present two ways of modelling fairness constraints, one with a detailed description of the population and the other with labels. We discuss the implementability of these constraints. In the case that the constraints are not implementable we present models to retrieve pure strategies in a way that they are the closest in average to the set of fairness constraints

Bilevel Network Design

This chapter is devoted to network design problems involving conflicting agents, referred to as the designer and the users, respectively. Such problems are best cast into the framework of bilevel programming, where the designer anticipates the reaction or rational users to its course of action, and fits many situations of interest. In this chapter, we consider four applications of very different nature, with a special focus on algorithmic issues

An exact dynamic programming approach to segmented isotonic regression

This paper proposes a polynomial-time algorithm to construct the monotone stepwise curve that minimizes the sum of squared errors with respect to a given cloud of data points. The fitted curve is also constrained on the maximum number of steps it can be composed of and on the minimum step length. Our algorithm relies on dynamic programming and is built on the basis that said curve-fitting task can be tackled as a shortest-path type of problem. Numerical results on synthetic and realistic data sets reveal that our algorithm is able to provide the globally optimal monotone stepwise curve fit for samples with thousands of data points in less than a few hours. Furthermore, the algorithm gives a certificate on the optimality gap of any incumbent solution it generates. From a practical standpoint, this piece of research is motivated by the roll-out of smart grids and the increasing role played by the small flexible consumption of electricity in the large-scale integration of renewable energy sources into current power systems. Within this context, our algorithm constitutes an useful tool to generate bidding curves for a pool of small flexible consumers to partake in wholesale electricity markets.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. Martine Labbé has been partially supported by the Fonds de la Recherche Scientifique - FNRS under Grant(s) no PDR T0098.18

Mixed-integer formulations for the Capacitated Rank Pricing Problem with envy

Pricing under a consumer choice model has been extensively studied in economics and revenue management. In this paper, we tackle a generalization of the Rank Pricing Problem (RPP), a multi-product pricing problem with unit-demand customers and a ranking-based consumer choice model. We generalize the RPP assuming that each product has a limited amount of copies for sale, and we call this extension the Capacitated Rank Pricing Problem (CRPP). We compare the envy-free allocation of the products (a fairness criterion requiring that customers receive their highest-ranked product given the pricing) with the envy version of the problem. Next, we focus on the CRPP with envy. We introduce two integer linear formulations for the CRPP and derive valid inequalities leveraging the structure of the problem. Afterwards, we develop separation procedures for the families of valid inequalities of greater size. The performance of the formulations and the resolution algorithms developed is tested by means of extensive computational experiments

The Rank Pricing Problem with Ties

In the Rank Pricing Problem (RPP), a firm intends to maximize its profit through the pricing of a set of products to sell. Customers are interested in purchasing at most one product among a subset of products. To do so, they are endowed with a ranked list of preferences and a budget. Their choice rule consists in purchasing the highest-ranked product in their list and whose price is below their budget. In this paper, we consider an extension of RPP, the Rank Pricing Problem with Ties (RPPT), in which we allow for indifference between products in the list of preferences of the customers. Considering the bilevel structure of the problem, this generalization differs from the RPP in that it can lead to multiple optimal solutions for the second level problems associated to the customers. In such cases, we look for pessimistic optimal solutions of the bilevel problem : the customer selects the cheapest product. We present a new three-indexed integer formulation for RPPT and introduce two resolution approaches. In the first one, we project out the customer decision variables, obtaining a reduced formulation that we then strengthen with valid inequalities from the former formulation. Alternatively, we follow a Benders decomposition approach leveraging the separability of the problem into a master problem and several subproblems. The separation problems to include the valid inequalities to the master problem dynamically are shown to reduce to min-cost flow problems. We finally carry out extensive computational experiments to assess the performance of the resolution approaches