Optimization Based High-Speed Railway Train Rescheduling with Speed Restriction

Table 2

Sets defined for modeling.

Set name	Description	Size	Index; of set
Trn	All the trains	𝑇	𝑖
Seg	All the segments	𝑆	𝑘
Stn⊆Seg	All the stations	𝑁	—
Sec⊆Seg	All the sections	S−N	—
Itv	All the intervals where an interval is the possession of a segment by a train with specified start and end times	—	p
Itv𝑖⊆Itv	The ordered set of intervals for train 𝑖 according to the original timetable	—	—
Itv^stn𝑖⊆Itv𝑖	The ordered set of intervals associated with stopping at stations for trains 𝑖	—	—
Itv𝑘⊆Itv	The ordered set of intervals for segment 𝑘 according to the original timetable	—	—
Trk𝑘	All the tracks of station 𝑘	𝐿𝑘	𝑙

Remarks: (1) for the ease of understanding, we use p as the index for every interval-related set (i.e., Itv, Itv_𝑖, Itv^stn_𝑖, and Itv_𝑘). In each of the interval-related sets, p + 1 indicates the first subsequent interval of p, and 𝑝 indicates all the subsequent intervals of p.