Session: Bilevel Programming and applications
Chair: Luce Brotcorne
Cluster: Optimization Applications (Communication, Energy, Health, ML, ...)
Talk 1: Optimal Electric Vehicle Charging with Dynamic Pricing, Customer Preferences and Power Peak Reduction
Speaker: Luce Brotcorne
Abstract: We consider a provider of electric vehicle charging stations that operates a network of charging stations and use time varying pricing to maximize profit and reduce the impact on the electric grid. We propose a bilevel model with a single leader and multiple disjoint followers. The provider (leader) sets the price of charging for each station at each time slot, and ensures there is enough energy to charge. The charging choice of each customer is represented by a combination of a preference list of (station, time) pairs and a reserve price. The proposed model takes thus into accounts for the heterogeneity of customers with respect to price sensitivity. We define a single-level reformulation based on a reformulation approach from the literature on product line optimization, and we report computational results that highlight the efficiency of the new reformulation and the potential impact for reducing peaks on the electricity grid.
Talk 2: A Benders decomposition algorithm for thMinimum Spanning Tree Interdiction Problem..
Speaker: Frederic Semet
Abstract: In this presentation, we consider the Minimum Spanning Tree Interdiction (MSTI) problem. This problem is a two-player game between a network operator and an interdictor. The former aims to determine a Minimum Spanning Tree (MST) in a network. Constrained by a budget, the latter seeks to change the network topology to increase the weight of a MST. Two types of interdiction are considered: total and partial interdiction. A total interdicted edge is considered absent, while the weight of a partial interdicted edge is augmented by a predefined amount. The interdictor's budget is modeled as a knapsack constraint. In the first part of the presentation a mathematical formulation is introduced and valid inequalities are proposed to strengthen the model. Since a commercial solver can only solve instances of limited size, we describe a Benders decomposition algorithm in the second part. A MSTI formulation is decomposed into a Master Problem (MP) and a subproblem. A family constraints for the MP, called optimality constraints, are introduced and lifted. A family of valid inequalities is also proposed to tighten the linear relaxation of the MP. The subproblem, parameterized by the solution of the MP, consists only in the computation of a MST. Computational results show that instances with up to 200 nodes can be solved to optimality.
Talk 3: ..
Speaker: Pablo Escalona
Abstract: ..
