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.

Heure:	10:30 - 11:30
Lieu:	Salle B107, bâtiment B, Université de Villetaneuse
Résumé:	Covering some vertices with paths and a Hamiltonian degree condition for tough graphs
Description:	Cléophée Robin A graph G is Hamiltonian if it exists a cycle in G containing all vertices of G exactly once. A graph G is t-tough if, for all subsets of vertices S, the number of connected components in G ? S is at most |S| / t. In 1973, Chvàtal conjecture the following : There exists a constant t such that every t-tough graphs is Hamiltonian. Let t be a positive integer. A graph G with degree sequence d_1,d_2,...,d_n is P(t) (t being a positive integer) If for all i, t ? i

Heure:	10:30 - 11:30
Lieu:	Salle B107, bâtiment B, Université de Villetaneuse
Résumé:	Optimal Planning and Pricing of Electric Vehicle Charging Services
Description:	Miguel Anjos The increase of electric vehicle (EV) adoption in recent years has correspondingly increased the importance of providing adequate public charging services for EV users. For a charging service provider, a key question is to determine the optimal location and sizing of charging stations, as well as the price for charging, with respect to a given objective and subject to budget and other practical constraints. Practical objectives include maximizing EV adoption as part of a public policy on electric transportation, and maximizing the profit gained from providing this service. I will present an overview of work to which I have contributed in this area, and discuss directions for ongoing and future research

Heure:	10:00 - 11:00
Lieu:	Salle B107, bâtiment B, Université de Villetaneuse
Résumé:	Optimisation de la réserve de charge dans un réseau électrique
Description:	Dimitri Watel Dans un réseau électrique, le flot électrique n'est pas choisi librement pas l'opérateur. Il découle des appels de puissance effectués par les consommateurs et du graphe du réseau. Connaissant ces deux paramètres, on peut déduire la valeur du flot dans chaque câble du réseau. L'opérateur peut jouer sur le réseau avec deux paramètres : en désactivant un ou plusieurs nœuds ou en forçant l'orientation du courant électrique. Une fois ces actions choisies, l'opérateur peut estimer la valeur du flot dans tout le réseau. L'objectif de ce dernier est d'éviter une surcharge des sources électriques, ce qui pourrait provoquer son arrêt et donc une surcharge d'autres sources. Avec cet effet boule-de-neige, l'opérateur cours le risque d'un black-out total. Une possibilité pour éviter ce phénomène est d'optimiser la réserve de charge. La charge d'une source est le pourcentage d'utilisation de sa capacité de production, qui doit rester loin de 100% pour éviter une surcharge. La réserve de charge est la différence entre la charge maximum et la charge minimum de l'ensemble des sources. Ainsi, un réseau équilibré est un réseau où toutes les sources sont utilisées avec le même pourcentage. Ce type d'optimisation garanti aussi un revenu équitable quand les acteurs produisant de l'énergie n'ont pas tous la même capacité de production. Notre problème se décrit donc ainsi : connaissant un réseau électrique et les appels de charge des consommateurs, quelles sont les actions de désactivation et d'orientation que l'opérateur doit effectuer pour minimiser la réserve de charge. Nous nous intéressons dans ce problème à la complexité et l'approximabilité de ce problème. Nous montrons que ce problème est NP-Difficile et inapproximable dans le cas général. Il reste NP-Difficile même dans le cas où le réseau électrique est un arbre ; mais, dans ce cas, il existe un schémas d'approximation avec un rapport d'approximation absolu. La fin de la présentation abordera la difficulté de la production d'instances réalistes et l'évaluation de ces algorithmes.

Heure:	10:30 - 11:30
Lieu:	Salle B107, bâtiment B, Université de Villetaneuse
Résumé:	Heuristic and Exact Algorithms for Solving the Electric Autonomous Dial-A-Ride Problem
Description:	Yue Su We propose highly efficient heuristic and exact algorithms to solve the Electric Autonomous Dial-A-Ride Problem (E-ADARP), which consists in designing a set of minimum-cost routes that accommodates all customer requests for a fleet of Electric Autonomous Vehicles (EAVs). The E-ADARP has two important features: (i) the employment of EAVs and a partial recharging policy; (ii) the weighted-sum objective function that minimizes the total travel time and the total excess user ride time. We first propose a Deterministic Annealing (DA) algorithm to solve the E-ADARP. Partial recharging (i) is handled by an exact route evaluation scheme of linear time complexity. To tackle (ii), we propose a new method that allows effective computations of minimum excess user ride time by introducing a fragment-based representation of paths. To validate the performance of the DA algorithm, we compare our algorithm results to the best-reported Branch-and-Cut (B&C) algorithm results on existing instances. Our DA algorithm provides 25 new best solutions and 45 equal solutions for 84 existing instances. To test the algorithm's performance on larger-sized instances, we establish new instances with up to 8 vehicles and 96 requests, and we provide 19 new solutions for these instances. Then, we present a highly efficient CG algorithm, which is integrated into the Branch-and-price (B&P) scheme to solve the E-ADARP exactly. Our CG algorithm relies on an effective labeling algorithm to generate columns with negative reduced costs. In the extension of labels, the key challenge is determining all excess-user-ride-time optimal schedules to ensure finding the minimum-negative-reduced-cost route. To handle this issue, we apply the fragment-based representation and propose a novel approach to abstract fragments to arcs while ensuring excess-user-ride-time optimality. We then construct a new graph that preserves all feasible routes of the original graph by enumerating all feasible fragments, abstracting them to arcs, and connecting them with each other, depots, and recharging stations in a feasible way. On the new graph, we apply strong dominance rules and constant-time feasibility checks to compute the shortest paths efficiently. In the computational experiments, we solve 71 out of 84 instances optimally, improve 30 previously reported lower bounds, and generate 41 new best solutions on previously solved and unsolved instances.