2024

Heure:	10:30 - 11:30
Lieu:	Salle B107, bâtiment B, Université de Villetaneuse
Résumé:	Rule-based machine learning via mathematical optimization
Description:	Cristina Molero del Río Rule-based machine learning models are appealing because of their simple decision structure. In this talk, we will present two examples, decision trees and rule sets, with special focus on the former. Contrary to classic classification and regression trees, built in a greedy heuristic manner, designing the tree model through an optimization problem allows us to easily include desirable properties in Machine Learning in addition to prediction accuracy. We present a Non-Linear Optimization approach that is scalable with respect to the size of the training sample, and illustrate this flexibility to model several important issues in Explainable and Fair Machine Learning. These include sparsity, as a proxy for interpretability, by reducing the amount of information necessary to predict well; fairness, by aiming to avoid predictions that discriminate against sensitive features such as gender or race; the cost-sensitivity for groups of individuals in which prediction errors are more critical, such as patients of a disease, by ensuring an acceptable accuracy performance for them; local explainability, where the goal is to identify the predictor variables that have the largest impact on the individual predictions; as well as data complexity in the form of observations of functional nature. The performance of our approach is illustrated on real and synthetic data sets

Heure:	10:30 - 11:30
Lieu:	Salle B107, bâtiment B, Université de Villetaneuse
Résumé:	A branch-and-bound method for multiobjective mixed integer quadratic programs based on dual relaxations
Description:	Marianna De Santis Most real-world optimization problems in the areas of applied sciences, engineering and economics involve multiple, often conflicting and nonlinear, goals. In the mathematical model of these problems, under the necessity of reflecting discrete quantities, logical relationships or decisions, integer and 0-1-variables need to be introduced, leading to MultiObjective Mixed Integer Nonlinear Programming problems (MO-MINLPs). The practical relevance of MO-MINLPs is pointed out in many publications, where tailored approaches for specific applications have been proposed. MO-MINLPs are intrinsically nonconvex, implying that the design of exact and efficient solution methods is particularly challenging and requires global optimization techniques. In this talk, we present a branch-and-bound method for multiobjective mixed-integer convex quadratic programs that computes a superset of efficient integer assignments and a coverage of the nondominated set. The method relies on outer approximations of the upper image set of continuous relaxations. These outer approximations are obtained addressing the dual formulations of specific subproblems where the values of certain integer variables are fixed. The devised pruning conditions and a tailored preprocessing phase allow a fast enumeration of the nodes. Despite the fact that we do not require any boundedness of the feasible set, we are able to prove that the method stops after having explored a finite number of nodes. Numerical experiments on instances with two, three, and four objectives are presente

Heure:	10:30 - 11:30
Lieu:	Salle B107, bâtiment B, Université de Villetaneuse
Résumé:	Exponentially large arc-flow models
Description:	François Clautiaux Network flow formulations are among the most successful tools to solve optimization problems. Such formulations correspond to determining an optimal flow in a network. One particular class of network flow formulations is the arc flow, where variables represent flows on individual arcs of the network. In this talk, we will review classical and recent results on integer linear programming models based on arc-flow formulations in exponentially or pseudo-polynomial size networks. We will study the limitations of these approaches, and how various almost disconnected groups have addressed these limitations. We will describe a recent approach based on the generalization of these models to flow in hypergraphs, and propose some research directions.

Heure:	10:30 - 11:30
Lieu:	https://bbb.lipn.univ-paris13.fr/b/wol-ma9-vjn
Résumé:	Efficacité et équité dans le problème d'ordonnacement multi-organisation
Description:	Martin Durand On considère le problème d'ordonnancement multi-organisation (POMO). Un ensemble de N organisations possèdent chacune un ensemble de machines et de tâches. Chacune de ses organisations dispose d'un ordonnancement, dit local, dans lequel elle ordonnance ses tâches sur ses machines. Notre but est de trouver un ordonnancement de toutes les tâches sur toutes les machines et tel que chaque organisation soit au moins aussi satisfaite dans cette solution globale qu'avec son ordonnancement local, cette contrainte est appelée contrainte de rationalité. On montre que la coopération peut permettre à toutes les organisations d'obtenir simultanément une meilleure solution. On étudie egalement à quel point la contrainte de rationalité impacte la qualité de la solution globale. Dans un second temps, on introduit un nouveau problème centré sur l'équité: on formule le bénéfice qu'une organisation obtient en coopérant et on étudie le problème de maximisation du plus petit bénéfice. On montre que ce problème est fortement NP-difficile et inapproximable dans le cas général et on propose une heuristique polynomiale qui retourne de bonnes solutions dans nos expérimentations.