Multipartite Implication Polytope – Optimization Online

Integrating Power Profile Optimization with Timetabling for Underground Train Networks

Published: 2026/07/20, Updated: 2026/08/15

(Mixed) Integer Linear Programming, Polyhedra, Transportation benders decomposition, Multipartite Implication Polytope, Power Profile Optimization, railway timetabling

We study energy-efficient operation of underground train networks, where energy from regenerative braking is usable only if another train in the same electrically isolated subnetwork accelerates simultaneously. Timetabling models for this setting typically fix one velocity profile per leg and running time, which limits the matching of braking and accelerating phases. We drop this assumption … Read more

Modeling Binary Relations in Piecewise-Linear Approximations

Published: 2026/02/28, Updated: 2026/03/02

Combinatorial Optimization, Global Optimization Theory, Nonlinear Optimization Bipartite Implication Polytope, boolean quadric polytope, cutting planes, mixed-integer nonlinear programming, Multipartite Implication Polytope, piecewise-linear approximations

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