Bilevel Optimization

Robust Network Design for Potential-Based Flows with Controllable Elements

  • Kristina Rolsing
  • Johannes Thürauf
    • Categories (Mixed) Integer Nonlinear Programming, Bilevel Optimization, Robust Optimization Tags , , , ,

    We study adjustable robust network design for potential-based flows with controllable elements under load uncertainty. The resulting problem combines discrete here-and-now expansion decisions with wait-and-see operational decisions governed by nonconvex flow constraints. Moreover, controllable elements introduce adjustable integer decisions, which are algorithmically challenging. We equivalently characterize robust feasibility and robust optimality of a fixed network … Read more

    Stochastic Bilevel Optimization for the Network Design of Multimodal Transit Systems with Heterogeneous Rider Preferences under Uncertain Travel Times and Demand

  • Yiling Zhang
  • Beste Basciftci
    • Categories Bilevel Optimization, Stochastic Programming, Transportation

    Designing efficient and user-friendly multimodal transit networks is critical for modern urban mobility. We study a novel stochastic multimodal transit network design problem that integrates fixed-route services with on-demand shuttles, explicitly accounting for heterogeneous rider preferences, uncertain travel times, and passenger demand. The hierarchical decision-making process is modeled using a two-stage stochastic bilevel optimization problem, … Read more

    Nested Benders Decomposition for Large-Scale Multi-Follower Bilevel Optimization

  • Dominic C. Flocco
  • Philine Schiewe
  • Steven A. Gabriel
    • Categories Bilevel Optimization, Parallel Algorithms, Transportation Tags , , , ,

    We propose a scalable nested Benders decomposition (BD) framework for single-leader, multi-follower bilevel optimization problems. The proposed framework is applicable to bilevel optimization problems in which each follower solves a linear program and is particularly well suited for instances involving a large number of followers. By identifying the upper-level decisions as complicating variables, the method … Read more

    Calmness of the Solution-Set Mapping for Linear Bilevel and Pricing Problems

  • Henri Lefebvre
  • Martin Schmidt
  • Anton Svensson
  • Johannes Thürauf
    • Categories Bilevel Optimization Tags , , , , ,

    We study linear bilevel and pricing problems in which the upper- and lower-level constraints’ right-hand sides are perturbed. In this setting, it is an important question, also for the validity of numerical solution schemes, if the solution-set mapping of the parametric bilevel problem is calm at the zero-perturbation. We provide the complete picture both for … Read more

    Robust Bilevel Optimization with a Wait-and-See Follower: A Column-and-Constraint Generation Approach

  • Henri Lefebvre
  • Johannes Thürauf
    • Categories Bilevel Optimization, Robust Optimization Tags , , , ,

    We study optimistic robust bilevel problems with uncertainty in the follower’s problem, where the follower adopts a so-called wait-and-see approach. In this setting, the leader decides without knowledge of the specific realization of the uncertainty. Then, the uncertainty realizes in a worst-case manner, and afterward the follower makes her own decisions. For this challenging problem … Read more

    Multi-Leader Single-Follower Power-Market Modeling: The Impact of DC Market-Clearing on AC Feasibility

  • Martina Cerulli
  • Claudia D'Ambrosio
  • Leo Liberti
  • Martin Schmidt
    • Categories Bilevel Optimization, Energy Tags , , , ,

    We study the impact of DC power flow modeling in multi-leader single-follower market models on the AC feasibility of the market outcome. To this end, we consider strategically bidding power producers that are connected to an electricity network and a market-clearing executed by an ISO. The focus is on a pay-as-bid electricity market in which … Read more

    Bilevel Learning

  • Alain Zemkoho
    • Categories Bilevel Optimization, Optimization in Data Science Tags , , ,

    Bilevel learning refers to machine learning problems that can be formulated as bilevel optimization models, where decisions are organized in a hierarchical structure. This paradigm has recently gained considerable attention in machine learning, as gradient-based algorithms built on the implicit function reformulation have enabled the computation of large-scale problems involving possibly millions of variables. Despite … Read more

    Modeling Network Congestion under Demand Uncertainty Using Wardrop Principles

  • Yasmine Beck
  • Francesca Giancola
  • Ivana Ljubić
  • Sara Mattia
    • Categories (Mixed) Integer Nonlinear Programming, Bilevel Optimization, Global Optimization Tags , , ,

    Motivated by the need for reliable traffic management under fluctuating travel demand, we study the problem of determining the worst-case congestion in a multi-commodity traffic network subject to demand uncertainty. To this end, we stress-test a given network by identifying demand realizations and corresponding travelers’ route choices that maximize congestion. The users of the traffic … Read more

    A Successive Proximal DC Penalty Method with an Application to Mathematical Programs with Complementarity Constraints

  • Dominic C. Flocco
  • Steven A. Gabriel
  • Trine Krogh Boomsma
  • Martin Schmidt
  • Miguel A. Lejeune
    • Categories Bilevel Optimization, Constrained Nonlinear Optimization, Global Optimization Tags , , , ,

    We develop a successive, proximal difference-of-convex (DC) function penalty method for solving DC programs with DC constraints. The proposed approach relies on a DC penalty function that measures the violation of constraints and leads to a penalty reformulation sharing the same solution set as the original problem. The resulting penalty problem is a DC program … Read more

    Integral Inverse Optimization Problems

  • Eva Ley
  • Maximilian Merkert
    • Categories (Mixed) Integer Linear Programming, Bilevel Optimization Tags , ,

    Inverse optimization problems are bilevel optimization problems in which the leader modifies the follower’s objective such that a prescribed feasible solution becomes an optimal solution of the follower. They capture hierarchical decision-making problems like parameter estimation tasks or situations where a planner wants to steer an agent’s choice. In this work, we study integral inverse … Read more