4 Presentations

• 
  02:45 PM - 03:07 PM

  A bilevel approach for compensation and routing decisions in last-mile delivery

  • Cerulli Martina, presenter, University of Salerno
  • Archetti Claudia, University of Brescia
  • Fernandez Elena, University of Cadiz
  • Ljubic Ivana, ESSEC Business School

  In last-mile delivery logistics, peer-to-peer logistic platforms play an important role in connecting senders, customers, and independent carriers to fulfill delivery requests. Since the carriers are not under the platform’s control, the platform has to anticipate their reactions, while deciding how to allocate the delivery operations. In this work, we model this problem using bilevel programming. At the upper level, the platform decides how to assign the orders to the carriers together with the compensation paid for each accepted request; at the lower level, each carrier solves a profitable tour problem to determine which offered requests to accept, based on her own profit maximization. For the resulting bilevel formulation, we propose a single-level reformulation and an alternative formulation where the lower-level routing variables are projected out. A branch-and-cut algorithm is proposed to solve the bilevel models and extensive computational tests are performed to compare the proposed formulations and analyze solution characteristics.

• 
  03:07 PM - 03:29 PM

  Single-level reformulations of the network design problem under traffic equilibrium

  • Nagisa Sugishita, presenter, Université de Montréal
  • Ismail Sevim , University of Montreal
  • Margarida Carvalho , University of Montreal
  • Ribal Atallah, Hydro-Québec

  This study addresses the bilevel network design problem under traffic equilibrium. The upper-level decision maker selects a set of arcs to be added to an existing transportation network, while the lower-level decision makers (commodities) respond by choosing routes that minimize their individual travel times, resulting in a user equilibrium. In this work, we propose two novel single-level reformulations: one based on strong duality and the other based on the value function of the lower-level problem. Unlike existing approaches in the literature, which are specialized methods for the network design problem with specific objectives and constraints, our approach is more flexible and the reformulations can be solved using a general-purpose convex mixed-integer nonlinear programming solver. We also discuss the differences between the two reformulations, as well as their computational performance.

• 
  03:29 PM - 03:51 PM

  Optimal Electric Vehicle Charging with Dynamic Pricing

  • Luce Brotcorne, presenter, INRIA Lille

  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.

• 
  03:51 PM - 04:13 PM

  Bilevel Optimization for Neural Architecture Search

  • Ankur Sinha, presenter, Indian Institute of Management Ahmedabad
  • Shukla Abhishek, Indian Institute of Technology Kanpur
  • Hamid Faiz, Indian Institute of Technology Kanpur

  Bilevel optimization has emerged as a powerful framework for addressing complex machine learning tasks like neural architecture search (NAS). NAS is a bilevel optimization problem where the architecture parameters are optimized at the upper-level, while the model parameters are optimized at the lower-level. We propose an algorithm for differentiable NAS using bilevel principles. The lower-level optimization employs stochastic gradient descent (SGD) to update model parameters, while information from SGD steps is used to compute an approximate Hessian in a fast and memory efficient manner. This approximate Hessian is integrated into a second-order conic program (SOCP) at the upper level to guide efficient updates for both architecture and model parameters. Our method is evaluated on CIFAR-10 and CIFAR-100, demonstrating superior performance over standard differentiable NAS approaches in terms of model quality and computational efficiency.