A Metro Freight Plan for Mixed Passenger and Freight Transportation

Algorithm 1

Procedure of VNS algorithm

(i)	Step 1: A solution is randomly generated in a given range, and the initial solution is brought into the objective function calculation program to obtain the initial target value , go to Step 2.
(ii)	Step 2: Let until , go to Step 3.
(iii)	Step 3: Substitute the initial solution into Shaking (Algorithm 2), and perform the k-th neighborhood operation of Shaking to generate a new solution , go to Step 4.
(iv)	Step 4: Substitute into the VND (Algorithm 3), generate multiple neighborhood solutions related to , and perform a local search among the generated multiple neighborhood solutions to obtain the local search optimal solution , go to Step 5.
(v)	Step 5: If , it means that is better than the current optimal solution , then let and continue to search within the current neighborhood structure (); otherwise, let . Meanwhile if , go to Step 6. Otherwise, go to Step 3.
(vi)	Step 6: Until the termination criterion is met, the optimal solution is returned.