Combinatorial Optimization of Service Order and Overtaking for Demand-Oriented Timetabling in a Single Railway Line

Table 1

Overview of existing demand-oriented timetabling models.

Model	Type	Objective	Unset Service; order	Overtaking allowed	Skip; stop	Algorithm
Niu [42]	Non-linear	AWT	×	×	×	Genetic Algorithm
Barrena [43]	linear	AWT	×	×	×	Branch-and-cut
Barrena [44]	Non-linear	AWT	×	×	×	Adaptive large neighborhood search
Shang [58]	Non-linear	TTT	×	×	×	Branch and bound
Sun [45]	MIP	AWT	×	×	×	Branch and bound
Canca [46]	Non-linear	AWT and Operational benefit	×	×	×	Branch and bound
Niu [5]	Non-linear	AWT	×	×	√	Branch and bound
Wang [47]	Non-linear Non-convex	TTT and energy	×	×	×	Iterative convex programming
Wang [48]	Non-linear Non-convex	AWT	×	×	×	Sequential quadratic programming
Yin [59]	Stochastic	TTT and train operational costs	×	×	×	Approximate dynamic programming

Note: AWT = average passenger waiting time; TTT = total passenger travel time.
×: not considered in the model; √: considered in the model.