Integer Programming

An Algorithm-Independent Measure of Progress for Linear Constraint Propagation

  • Ambros Gleixner
  • Sebastian Pokutta
  • Boro Sofranac
    • Categories (Mixed) Integer Linear Programming Tags ,

    Propagation of linear constraints has become a crucial sub-routine in modern Mixed-Integer Programming (MIP) solvers. In practice, iterative algorithms with tolerance-based stopping criteria are used to avoid problems with slow or infinite convergence. However, these heuristic stopping criteria can pose difficulties for fairly comparing the efficiency of different implementations of iterative propagation algorithms in a … Read more

    Long-Run Optimal Pricing in Electricity Markets with Non-Convex Costs

  • Conleigh Byers
  • Gabriela Hug
    • Categories Applications - OR and Management Sciences, Integer Programming Tags , ,

    Determining optimal prices in non-convex markets remains an unsolved challenge. Non-convex costs are critical in electricity markets, as startup costs and minimum operating levels yield a non-convex optimal value function over demand levels. While past research largely focuses on the performance of different non-convex pricing frameworks in the short-run, we determine long-run adapted resource mixes … Read more

    Optimal Eco-Routing for Hybrid Vehicles with Mechanistic/Data-Driven Powertrain Model Embedded

  • Adrian Caspari
  • Alexander Mitsos
  • Steffen Fahr
    • Categories (Mixed) Integer Linear Programming, Applications - Science and Engineering, Transportation Tags , , , , , ,

    Hybrid Electric Vehicles (HEVs) are regarded as an important (transition) element of sustainable transportation. Exploiting the full potential of HEVs requires (i) a suitable route selection and (ii) suitable power management, i.e., deciding on the split between combustion engine and electric motor usage as well as the mode of the electric motor, i.e., driving or … Read more

    Inductive Linearization for Binary Quadratic Programs with Linear Constraints: A Computational Study

  • Sven Mallach
    • Categories (Mixed) Integer Nonlinear Programming, 0-1 Programming, Quadratic Programming Tags , , ,

    The computational performance of inductive linearizations for binary quadratic programs in combination with a mixed-integer programming solver is investigated for several combinatorial optimization problems and established benchmark instances. Apparently, a few of these are solved to optimality for the first time. Citationpreprint (no internal series / number): University of Bonn, Germany June 11, 2021ArticleDownload View … Read more

    Markov Chain Sampling of Hidden Relay States for Economic Dispatch with Cascading Failures

  • John Birge
  • Arnab Sur
    • Categories (Mixed) Integer Linear Programming, Energy, Stochastic Programming Tags , , , , ,

    Independent system operators (ISO) of electric power networks aim to dispatch electricity economically while maintaining system reliability. NERC (North America Electric Reliability Council) requires the transmission network to be (N-1)-secure, i.e., to have sufficient supply to satisfy demand in the event of the failure of any single resource in the network. Such a policy is … Read more

    On the Polyhedrality of the Chvatal-Gomory Closure

  • Haoran Zhu
    • Categories (Mixed) Integer Linear Programming, Cutting Plane Approaches, Polyhedra Tags , ,

    In this paper, we provide an equivalent condition for the Chvatal-Gomory (CG) closure of a closed convex set to be finitely-generated. Using this result, we are able to prove that, for any closed convex set that can be written as the Minkowski sum of a compact convex set and a closed convex cone, its CG … Read more

    Multi-cover Inequalities for Totally-Ordered Multiple Knapsack Sets

  • Alberto Del Pia
  • Jeff Linderoth
  • Haoran Zhu
    • Categories 0-1 Programming, Cutting Plane Approaches Tags , ,

    We propose a method to generate cutting-planes from multiple covers of knapsack constraints. The covers may come from different knapsack inequalities if the weights in the inequalities form a totally-ordered set. Thus, we introduce and study the structure of a totally-ordered multiple knapsack set. The valid multi-cover inequalities we derive for its convex hull have … Read more

    Lifting convex inequalities for bipartite bilinear programs

  • Santanu S. Dey
  • Jean-Philippe P. Richard
  • Xiaoyi Gu
    • Categories Cutting Plane Approaches, Global Optimization Theory, Nonlinear Optimization Tags

    The goal of this paper is to derive new classes of valid convex inequalities for quadratically constrained quadratic programs (QCQPs) through the technique of lifting. Our first main result shows that, for sets described by one bipartite bilinear constraint together with bounds, it is always possible to sequentially lift a seed inequality that is valid … Read more

    Nonconvex Equilibrium Models for Energy Markets: Exploiting Price Information to Determine the Existence of an Equilibrium

  • Julia Grübel
  • Olivier Huber
  • Lukas Hümbs
  • Max Klimm
  • Martin Schmidt
  • Alexandra Schwartz
    • Categories (Mixed) Integer Linear Programming, Applications - OR and Management Sciences, Constrained Nonlinear Optimization Tags , , , ,

    Motivated by examples from the energy sector, we consider market equilibrium problems (MEPs) involving players with nonconvex strategy spaces or objective functions, where the latter are assumed to be linear in market prices. We propose an algorithm that determines if an equilibrium of such an MEP exists and that computes an equilibrium in case of … Read more

    High quality timetables for Italian schools

  • Claudio Crobu
  • Massimo Di Francesco
  • Enrico Gorgone
    • Categories (Mixed) Integer Linear Programming, Scheduling Tags , ,

    This work introduces a complex variant of the timetabling problem, which is motivated by the case of Italian schools. The new requirements enforce to (i) provide the same idle times for teachers, (ii) avoid consecutive \emph{heavy} days, (iii) limit daily multiple lessons for the same class, (iv) introduce shorter time units to differentiate entry and … Read more