Resolution of coupling order and station level constraints in train unit scheduling

Abstract

Train unit scheduling assigns vehicles to cover all trips of a fixed timetable satisfying constraints such as seat demands. With a two-phase approach, this problem is first solved in Phase I as an integer multi-commodity flow problem. Train stations are simplified as single points and coupling orders of train units are left undetermined. In this paper, platforms and their layouts at the stations are restored to complete a fully operable schedule, defined as Phase II. An adaptive approach expanding Phase I to Phase II is proposed. The logistics of (de-)coupling operations, coupling orders and re-platforming are determined in detail to prevent unit blockage where possible, particularly focusing on developing a schedule with conflict-free coupling orders. If unresolvable station level conflicts still exist, the process loops back to Phase I with addressed Phase II constraints to avoid identified conflicts. Thus, the schedule is iteratively improved until it is fully operable.

An auxiliary hybrid heuristic approach for objective function design evaluation

“…The real case is usually that the solutions with very similar or even the same objective function value have rather different structural properties. This phenomenon is also observed in experiments on Train Unit Scheduling Optimization (TUSO) Kwan, 2014, 2016b;Copado-Mendez et al, 2017;Lei et al, 2018), which is further explained in Section 4.1.…”

“…The TUSO problem conducted at the University of Leeds (Lin and Kwan, 2016b,a;Copado-Mendez et al, 2017;Lei et al, 2018) has inspired this work. In ongoing work, we are going to investigate methods to improve the auxiliary heuristics to perform better in deriving reduced inputs.…”

A K-Prototype Clustering Assisted Hybrid Heuristic Approach for Train Unit Scheduling

“…In [30], TUSO with bi-level capacity needs is investigated. In [28], station level unit conflicts are resolved by a feedback mechanism with added cuts. For larger and harder TUSO instances, a hybridized algorithm called size limited iterative method (SLIM) is developed in [16,12].…”

“…One way for solving the TUSO problem in the UK's railways is a two-phase decomposition framework [29,31], wherein the first phase the assignment of train units to trips is carried out ignoring some station layout details [31]. In the second phase, the fleet assignment is implemented taking account of station infrastructure to deal with shunting movements, unit permutation in a coupled formation and blockage of units, [28]. In this research we focused on the first phase.…”