Equity-Oriented Train Timetabling with Collaborative Passenger Flow Control: A Spatial Rebalance of Service on an Oversaturated Urban Rail Transit Line

Algorithm 1

An iterative heuristic algorithm to solve the proposed model.

	Step 1: Initiation. Set , , and . Input the original seed solution and then use the Gurobi solver to optimize the passenger flow control strategies and obtain corresponding objective value . Let , , and . Update and go to step 2.
	Step 2: generate neighbor set iteratively as follows (initially set ):
	(1) Duplicate as and then select two elements and in and generate a random variation ; then, let and .
	(2) If satisfies headway constraints Equations (1) and (2), then optimize the control strategies and obtain the corresponding objective value; insert into and set .
	(3) If , then go to step 3; otherwise, continue this iteration.
	Step 3: obtain the best solution from and its corresponding objective value . If , then let , , , and , update the next iteration seed , and insert into ; otherwise, obtain the best solution from that is not in , and let , , and ; insert into . Go to step 4.
	Step 4: if and , go to step 2; otherwise, output the optimal timetable and corresponding passenger flow control strategies and objective value and stop.