Tobias Kuen

Modeling Binary Relations in Piecewise-Linear Approximations

  • Kristin Braun
  • Robert Burlacu
  • Tobias Kuen
  • kristinarolsing
    • Categories Combinatorial Optimization, Global Optimization Theory, Nonlinear Optimization Tags , , , , ,

    Over the last decades, using piecewise-linear mixed-integer relaxations of nonlinear expressions has become a strong alternative to spatial branching for solving mixed-integer nonlinear programs. Since these relaxations give rise to large numbers of binary variables that encode interval selections, strengthening them is crucial. We investigate how to exploit the resulting combinatorial structure by integrating cutting-plane … Read more

    Energy-efficient Timetables for Railway Traffic: Incorporating DC Power Models

  • Robert Burlacu
  • Patrick Gemander
  • Tobias Kuen
  • Jorge Weston
    • Categories (Mixed) Integer Nonlinear Programming, Cutting Plane Approaches, Transportation Tags , , ,

    Efficient operation of underground railway systems is critical not only for maintaining punctual service but also for minimizing energy consumption, a key factor in reducing operational costs and environmental impact. To evaluate the energy consumption of the timetables, this paper delves into the development of mathematical models to accurately represent energy dynamics within the underground … Read more

    The Bipartite Implication Polytope: Conditional Relations over Multiple Sets of Binary Variables

  • Robert Burlacu
  • Patrick Gemander
  • Tobias Kuen
    • Categories 0-1 Programming, Polyhedra, Quadratic Programming Tags , , , , , , , ,

    Inspired by its occurrence as a substructure in a stochastic railway timetabling model, we study in this work a special case of the bipartite boolean quadric polytope. It models conditional relations across three sets of binary variables, where selections within two implying sets imply a choice in a corresponding implied set. We call this polytope … Read more