A MultiObjective Optimization Approach for Integrated Timetabling and Vehicle Scheduling with Uncertainty

Table 1

Summary of relevant studies on the integration of TTP and VSP.

Approach type	Publication	Objectives	Solution method	Data type
Recursive approach	Ceder [9]	Maximize the correspondence of vehicle departure times, the fleet size	Deficit function approach	Fixed passenger load at each stop, fixed trip time
	Ceder [4]	Even-headways and even-load with different vehicle types, minimize vehicle scheduling cost	Heuristics	Fixed passenger load at each stop, fixed trip time
	Schmid and Ehmke [11]	Minimize costs of operation, maximize quality of timetables	Hybrid metaheuristic	Fixed time windows, fixed trip time
Integrated model	Petersen et al. [13]	Minimize the costs of vehicles usage and passenger transfers	LNS approach	Fixed passenger volume estimates, fixed trip time
	Carosi et al. [14]	Minimum deviation from the ideal frequency of service, vehicle schedule cost	Diving-type approach	Changeable time window, fixed trip time
	Yue et al. [15]	Minimizing infeasible trains, waiting times for passengers	SA algorithm	Fixed passenger volume, fixed trip time
Multi-objective model	Ibarra-Rojas et al. [16]	Maximize the number of passengers benefited, minimize the fleet size	ε-constraint method	Fixed passenger volume estimates, fixed trip time
	Teng and Chen [17]	Smooth the vehicle departure intervals, minimize the number of vehicles and total charging costs	MOPSO algorithm	Fixed trip time
	Wang et al. [18]	Minimize the load factor variation and the headway variation of trains, the number of entering and existing depot operations	MINLP approach	Fixed passenger traveling rates, fixed trip time limits