A Game-Theoretic Approach for the Robust Daily Aircraft Routing Problem

Algorithm 1

Column generation and variable neighborhood search (CG-VNS).

	Input: The maximum number of iterations ;
	Output: Get a suboptimal solution x
(1)	Use the DFS algorithm to generate an initial set O and initial path;
(2)	whiledo
(3)	Using the Solver to find the optimal solution x of RMP and dual solutions and ;
(4)	Change arc costs in segment network using obtained dual solution;
(5)	Find the matching T that minimizes Z by the labeling algorithm;
(6)	Set
(7)	end while
(8)	Use the solver to find the integer solution x of RMP;
(9)	;
(10)	whiledo
(11)	;
(12)	whiledo
(13)	Shaking: Randomly choose a solution from the k th neighbor ;
(14)	VND: local search
(15)	;
(16)	whiledo
(17)	find a neighbor in ;
(18)	ifthen,
(19)	;
(20)	else
(21)	;
(22)	end if
(23)	end while
(24)	ifthen,
(25)	;
(26)	else
(27)	;
(28)	end if
(29)	end while
(30)	;
(31)	end while