A Fast Approach for Reoptimization of Railway Train Platforming in Case of Train Delays

Table 1

Summary of relevant publications on the optimization and reoptimization of the train platforming problems.

Publication	Modeling approach	Objective	Solution method	Train delay	Reassignment of platform	Deviations from scheduled train times	Largest instance solved	Computation times (in seconds) of the largest instance
Zwaneveld et al. [10]	BILP	Max the number of routed trains	Branch-and-cut			√	A railway station with 17 platforms and 27 trains	85
Cardillo and Mione [23]	GC	Feasibility	Iterative heuristic algorithm				A railway station with 16 tracks and 242 trains	0.67
Billionnet [24]	BILP	Feasibility	Optimization software				A railway station with 14 tracks and 200 trains	1.64
Carey and Carville [26]	MILP	Min the costs of deviations from preferred times, platforms, and lines	Iterative sequential searching method		√	√	A railway station with 29 subproblems and 491 trains	—
Rodriguez [32]	CP	Min train delays	Tree search	√		√	A 15.18 km long railway junction with 24 trains	54.76
Lusby et al. [12]	BILP	Max total benefits	Branch-and-price				A railway junction with 64 block sections and 45 trains	26.4
Caprara et al. [21]	BQP	Min total costs	Branch-and-cut-and-price				A railway station with 14 platforms and 237 trains	350
Sels et al. [25]	MILP	Min total penalties	Commercial solvers		√		A railway station with 14 platforms and 160 trains	3.0
Zhang et al. [8]	MILP	Min total train journey times and maintenance tardiness costs	Iterative heuristic algorithm				A railway network with 27 stations, 55 segments, and 58 trains	7200
Liu et al. [37]	MINLP	Min average use time of groups of turnouts	Genetic simulated annealing algorithm		√		A railway station with 11 tracks and 30 trains	1800
Kang et al. [22]	MILP	Min total occupation times and balanced track occupation	Simulated annealing	√			A railway station with 11 tracks and 28 trains	726
Chakroborty and Vikram [20]	MILP	Min total costs	Commercial solver	√	√	√	A railway station with 9 platforms and 110 trains	600
Lusby et al. [13]	BILP	Min total deviations	Branch-and-price	√		√	A railway junction with 524 track sections and 66 trains	151.55
This paper	MILP	Min total costs	Genetic and simulated annealing hybrid algorithm	√	√	√	A railway station with 11 platforms and 70 trains	32.92

Note. BILP represents 0-1 integer linear programming; GC represents graph colouring; MILP represents mixed integer linear programming; CP represents constraint programming; BQP represents 0-1 quadratic programming; “—” represents no specific information is available.