A two-stage decision dependent stochastic approach for airline flight network expansion

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

“…Input: Te maximum number of iterations Maxiter; Output: Get a suboptimal solution x (1) Use the DFS algorithm to generate an initial set O and initial path; (2) while T ≠ ∅ do (3) Using the Solver to fnd the optimal solution x of RMP and dual solutions π v and π k ; (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 O � O ∪ T (7) end while (8) Use the solver to fnd the integer solution x of RMP; (9) t � 0; (10) while t < Maxiter do (11) k � 0; (12) while k < k max do (13) Shaking: Randomly choose a solution x′ from the k th neighbor N k (x); (14) VND: local search (15) l � 0; (16) while l < l max do (17) fnd a neighbor x″ in N l (x′);…”

“…end if (23) end while (24) if F(x′) < F(x) then, (25) x l � 0; (10) whilel < l max do (11) fnd a neighbor x″ in N l (x′); (12) ifF(x″) < σF(x′)then (13) ifmax v∈V F(x, v) < max v∈V F(x′, v)then (14) x′ � x″, l � 0; (15) else (16) l � l + 1; (17) end if (18) end if (19) end while (20) ifmax v∈V F(x′, v) < robthen (21) rob…”

“…Xu et al [12] proposed a mixed integer programming model considering the infuence of propagation delay and fight retiming decisions and proposed column generation as well as variable neighborhood search for a solution. S ¸afak et al [13] proposed a new two-stage stochastic decision-dependency programming model for airline network expansion. In fact, the daily fight route problem for aircraft is a routing problem.…”