A Matheuristic Iterative Approach for Profit-Oriented Line Planning Applied to the Chinese High-Speed Railway Network

Algorithm 1

Pseudocode of the MHIA of line planning.

(1)	;
(2)	Repeat
(3)	= 0,  = 0,  = 0;
(4)	Repeat
(5)	Reduction method
(6)	;
(7)	Select the and calculate the profit of by MILP;
(8)	if > do
(9)	, ,  = 0;
(10)	if > do
(11)	, ;
(12)	else
(13)	;
(14)	if > MaxNumberOfIterations
(15)	go to step 36;
(16)	else if > MaxNeighbours
(17)	go to step 20;
(18)	else
(19)	go to step 5;
(20)	Extension method
(21)	;
(22)	Select the and calculate the profit of by MILP;
(23)	if > do
(24)	, ,  = 0;
(25)	if  > do
(26)	, ;
(27)	else
(28)	;
(29)	if > MaxNumberOfIterations
(30)	go to step 36
(31)	else if > MaxNeighbours
(32)	go to step 5;
(33)	else
(34)	go to step 20;
(35)	until the terminal conditions are satisfied
(36)	Disturb
(37)	Removal or Insertion
(38)	;
(39)	Select the and calculate the profit of by MILP;
(40)	, , go to step 3
(41)	until
(42)	Output the best line plan and objective profit