Efficient reformulations for deterministic and choice-based network design problems

La conception de réseaux est un riche sous-domaine de l'optimisation combinatoire ayant de nombreuses applications pratiques. Du point de vue méthodologique, la plupart des problèmes de cette classe sont notoirement difficiles en raison de leur nature combinatoire et de l'interdépendance des décisions qu'ils impliquent. Ce mémoire aborde deux problèmes de conception de réseaux dont les structures respectives posent des défis bien distincts. Tout d'abord, nous examinons un problème déterministe dans lequel un client doit acquérir au prix minimum un certain nombre d'unités d'un produit auprès d'un ensemble de fournisseurs proposant différents coûts fixes et unitaires, et dont les stocks sont limités. Ensuite, nous étudions un problème probabiliste dans lequel une entreprise entrant sur un marché existant cherche, en ouvrant un certain nombre d'installations parmi un ensemble de sites disponibles, à maximiser sa part espérée d'un marché composé de clients maximisant une fonction d'utilité aléatoire. Ces deux problèmes, soit le problème de transport à coût fixe à un puits et le problème d'emplacement d'installations compétitif basé sur les choix, sont étroitement liés au problème du sac à dos et au problème de couverture maximale, respectivement. Nous introduisons de nouvelles reformulations prenant avantage de ces connexions avec des problèmes classiques d'optimisation combinatoire. Dans les deux cas, nous exploitons ces reformulations pour démontrer de nouvelles propriétés théoriques et développer des méthodes de résolution efficaces. Notre nouvel algorithme pour le problème de transport à coûts fixes à un puits domine les meilleurs algorithmes de la littérature, réduisant le temps de résolution des instances de grande taille jusqu'à quatre ordres de grandeur. Une autre contribution notable de ce mémoire est la démonstration que la fonction objectif du problème d'emplacement d'installations compétitif basé sur les choix est sous-modulaire sous n'importe quel modèle de maximisation d’utilité aléatoire. Notre méthode de résolution basée sur la simulation exploite cette propriété et améliore l'état de l'art pour plusieurs groupes d'instances.Network design is a rich subfield of combinatorial optimization with wide-ranging real-life applications. From a methodological standpoint, most problems in this class are notoriously difficult due to their combinatorial nature and the interdependence of the decisions they involve. This thesis addresses two network design problems whose respective structures pose very distinct challenges. First, we consider a deterministic problem in which a customer must acquire at the minimum price a number of units of a product from a set of vendors offering different fixed and unit costs and whose supply is limited. Second, we study a probabilistic problem in which a firm entering an existing market seeks, by opening a number of facilities from a set of available locations, to maximize its expected share in a market composed of random utility-maximizing customers. These two problems, namely the single-sink fixed-charge-transportation problem and the choice-based competitive facility location problem, are closely related to the knapsack problem and the maximum covering problem, respectively. We introduce novel model reformulations that leverage these connections to classical combinatorial optimization problems. In both cases, we exploit these reformulations to prove new theoretical properties and to develop efficient solution methods. Our novel algorithm for the single-sink fixed-charge-transportation problem dominates the state-of-the-art methods from the literature, reducing the solving time of large instances by up to four orders of magnitude. Another notable contribution of this thesis is the demonstration that the objective function of the choice-based competitive facility location problem is submodular under any random utility maximization model. Our simulation-based method exploits this property and achieves state-of-the-art results for several groups of instances

A model-free approach for solving choice-based competitive facility location problems using simulation and submodularity

This paper considers facility location problems in which a firm entering a market seeks to open a set of available locations so as to maximize its expected market share, assuming that customers choose the alternative that maximizes a random utility function. We introduce a novel deterministic equivalent reformulation of this probabilistic model and, extending the results of previous studies, show that its objective function is submodular under any random utility maximization model. This reformulation characterizes the demand based on a finite set of preference profiles. Estimating their prevalence through simulation generalizes a sample average approximation method from the literature and results in a maximum covering problem for which we develop a new branch-and-cut algorithm. The proposed method takes advantage of the submodularity of the objective value to replace the least influential preference profiles by an auxiliary variable that is bounded by submodular cuts. This set of profiles is selected by a knee detection method. We provide a theoretical analysis of our approach and show that its computational performance, the solution quality it provides, and the efficiency of the knee detection method it exploits are directly connected to the entropy of the preference profiles in the population. Computational experiments on existing and new benchmark sets indicate that our approach dominates the classical sample average approximation method on large instances, can outperform the best heuristic method from the literature under the multinomial logit model, and achieves state-of-the-art results under the mixed multinomial logit model.Comment: 36 pages, 6 figures, 6 table

StepMix: A Python Package for Pseudo-Likelihood Estimation of Generalized Mixture Models with External Variables

StepMix is an open-source software package for the pseudo-likelihood estimation (one-, two- and three-step approaches) of generalized finite mixture models (latent profile and latent class analysis) with external variables (covariates and distal outcomes). In many applications in social sciences, the main objective is not only to cluster individuals into latent classes, but also to use these classes to develop more complex statistical models. These models generally divide into a measurement model that relates the latent classes to observed indicators, and a structural model that relates covariates and outcome variables to the latent classes. The measurement and structural models can be estimated jointly using the so-called one-step approach or sequentially using stepwise methods, which present significant advantages for practitioners regarding the interpretability of the estimated latent classes. In addition to the one-step approach, StepMix implements the most important stepwise estimation methods from the literature, including the bias-adjusted three-step methods with BCH and ML corrections and the more recent two-step approach. These pseudo-likelihood estimators are presented in this paper under a unified framework as specific expectation-maximization subroutines. To facilitate and promote their adoption among the data science community, StepMix follows the object-oriented design of the scikit-learn library and provides interfaces in both Python and R.Comment: Sacha Morin and Robin Legault contributed equall

Management of Cerebral Venous Thrombosis Due to Adenoviral COVID-19 Vaccination

Objective Cerebral venous thrombosis (CVT) caused by vaccine-induced immune thrombotic thrombocytopenia (VITT) is a rare adverse effect of adenovirus-based severe acute respiratory syndrome-coronavirus 2 (SARS-CoV-2) vaccines. In March 2021, after autoimmune pathogenesis of VITT was discovered, treatment recommendations were developed. These comprised immunomodulation, non-heparin anticoagulants, and avoidance of platelet transfusion. The aim of this study was to evaluate adherence to these recommendations and its association with mortality. Methods We used data from an international prospective registry of patients with CVT after the adenovirus-based SARS-CoV-2 vaccination. We analyzed possible, probable, or definite VITT-CVT cases included until January 18, 2022. Immunomodulation entailed administration of intravenous immunoglobulins and/or plasmapheresis. Results Ninety-nine patients with VITT-CVT from 71 hospitals in 17 countries were analyzed. Five of 38 (13%), 11 of 24 (46%), and 28 of 37 (76%) of the patients diagnosed in March, April, and from May onward, respectively, were treated in-line with VITT recommendations (p < 0.001). Overall, treatment according to recommendations had no statistically significant influence on mortality (14/44 [32%] vs 29/55 [52%], adjusted odds ratio [OR] = 0.43, 95% confidence interval [CI] = 0.16-1.19). However, patients who received immunomodulation had lower mortality (19/65 [29%] vs 24/34 [70%], adjusted OR = 0.19, 95% CI = 0.06-0.58). Treatment with non-heparin anticoagulants instead of heparins was not associated with lower mortality (17/51 [33%] vs 13/35 [37%], adjusted OR = 0.70, 95% CI = 0.24-2.04). Mortality was also not significantly influenced by platelet transfusion (17/27 [63%] vs 26/72 [36%], adjusted OR = 2.19, 95% CI = 0.74-6.54). Conclusions In patients with VITT-CVT, adherence to VITT treatment recommendations improved over time. Immunomodulation seems crucial for reducing mortality of VITT-CVT. ANN NEUROL 2022Peer reviewe

Sex differences in cerebral venous sinus thrombosis after adenoviral vaccination against COVID-19

Introduction: Cerebral venous sinus thrombosis associated with vaccine-induced immune thrombotic thrombocytopenia (CVST-VITT) is a severe disease with high mortality. There are few data on sex differences in CVST-VITT. The aim of our study was to investigate the differences in presentation, treatment, clinical course, complications, and outcome of CVST-VITT between women and men. Patients and methods: We used data from an ongoing international registry on CVST-VITT. VITT was diagnosed according to the Pavord criteria. We compared the characteristics of CVST-VITT in women and men. Results: Of 133 patients with possible, probable, or definite CVST-VITT, 102 (77%) were women. Women were slightly younger [median age 42 (IQR 28–54) vs 45 (28–56)], presented more often with coma (26% vs 10%) and had a lower platelet count at presentation [median (IQR) 50x109/L (28–79) vs 68 (30–125)] than men. The nadir platelet count was lower in women [median (IQR) 34 (19–62) vs 53 (20–92)]. More women received endovascular treatment than men (15% vs 6%). Rates of treatment with intravenous immunoglobulins were similar (63% vs 66%), as were new venous thromboembolic events (14% vs 14%) and major bleeding complications (30% vs 20%). Rates of good functional outcome (modified Rankin Scale 0-2, 42% vs 45%) and in-hospital death (39% vs 41%) did not differ. Discussion and conclusions: Three quarters of CVST-VITT patients in this study were women. Women were more severely affected at presentation, but clinical course and outcome did not differ between women and men. VITT-specific treatments were overall similar, but more women received endovascular treatment.</p

An efficient probabilistic approach to vibro-acoustic analysis based on the Gaussian orthogonal ensemble

Vibro-acoustic analysis of complex systems at higher frequencies faces two challenges: how to compute the response without using an excessive number of degrees of freedom (DOFs), and how to quantify the uncertainty of the response due to small spatial variations in geometry, material properties, and boundary conditions, which have a wave scattering effect? In this study, a general method of analysis is presented that provides an answer to both questions while overcoming most limitations of statistical energy analysis. The fundamental idea is to numerically compute an artificial ensemble of realizations for the components of the built-up system that are highly sensitive to small random wave scatterers. This can be efficiently performed because their eigenvalue spacings and mode shapes conform to Gaussian orthogonal ensemble spacings and Gaussian random fields, respectively. The DOFs of the overall system are therefore limited to those of the deterministic components and the interface DOFs of the random components. The method is extensively validated by application to plate structures. Good agreement between the predicted response probability distributions and the results of detailed parametric probabilistic models is obtained, also for cases of low modal overlap, single point loading, and strong subsystem coupling.status: publishe