Tobias Kuen

Integrating Power Profile Optimization with Timetabling for Underground Train Networks

Categories (Mixed) Integer Linear Programming, Polyhedra, Transportation Tags , , ,

We study energy-efficient operation of underground train networks by integrating power profile optimization with timetable design in a single mixed-integer optimization framework. The model minimizes traction energy by synchronizing braking and acceleration across trains sharing a power subnetwork to exploit regenerative energy and flexibly allocating running times to promote coasting. Unlike timetable-only approaches with fixed … Read more

Modeling Binary Relations in Piecewise-Linear Approximations

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

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

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