Periodic Timetabling with ‘Track Choice’-PESP Based on Given Line Concepts and Mesoscopic Infrastructure

Abstract

In bilevel optimization there are two decision makers, commonly denoted as the leader and the follower, and decisions are made in a hierarchical manner: the leader makes the first move, and then the follower reacts optimally to the leader's action. It is assumed that the leader can anticipate the decisions of the follower, hence the leader optimization task is a nested optimization problem that takes into consideration the follower's response.In this talk we focus on new branch-and-cut (B&C) algorithms for dealing with mixed-integer bilevel linear programs (MIBLPs). We first address a general case in which intersection cuts are used to cut off infeasible solutions. We then focus on a subfamily of MIBLPs in which the leader and the follower share a set of items, and the leader can select some of the items to inhibit their usage by the follower. Interdiction Problems, Blocker Problems, Critical Node/Edge Detection Problems are some examples of optimization problems that satisfy the later condition. We show that, in case the follower subproblem satisfies monotonicity property, a family of "interdiction-cuts" can be derived resulting in a more efficient B&C scheme.These new B&C algorithms consistently outperform (often by a large margin) alternative state-of-the-art methods from the literature, including methods that exploit problem specific information for special instance classes.

Enhancing the interaction of railway timetabling and line planning with infrastructure awareness

“…The TTP has also been adapted to allow track allocation. In particular, the approach suggested by Wüst et al (2019) is able to allocate station tracks during the solution process. Intending to insert additional trains in a timetable, Großmann (2016) enhances a previous model (Großmann, 2011).…”

“…To this end, we introduce the concept of selectable activity (and edge), associated to the 𝑅𝐼, which means that its duration must be valid when it is part of a chosen itinerary. Note that this is more general than the formulation by Wüst et al (2019) that allows selecting headway constraints if the corresponding track is chosen. We model a selectable activity 𝑎 ∈  with…”