High-Speed Rail Train Timetabling Problem: A Time-Space Network Based Method with an Improved Branch-and-Price Algorithm

Algorithm 1

Heuristic time-space path generation

Input: train matrix

(1)  Assign a feasible time-space path for each train by trains’ matrix with time-space arcs in the sections and stations of the train.

(2)  for all section do

(4) Get a headway path on each section and reassign time-space arc for each train

(5)  Copy all stations into the adjustment station set

(5)  While adjustment station set is not empty do.

(6) Sorte the adjustment stations by the number of passing trains. Select the maximum number station.

  If more than one station’s number of passing trains is the maximum number, the down-bound station is selected firstly.

  Moreover, if all the stations have the same direction, the station is selected by down-bound direction.

(7) For the selected station, find a headway path. Reassign the time-space arc inside the station.

(8) Adjust the connect section time-space arc and remove the station from adjustment station set.

(11) end while

Output: the feasible timetable