Vehicle Routing Problems with Fuel Consumption and Stochastic Travel Speeds

Algorithm 1

Main: Improved Simulated Annealing algorithm with memory for VRPFSV

Input:

(1) customers with demand and distance matrix

(2) vehicle capacity , single vehicle cost, speed distribution parameters and of each arc

(3) simulated annealing parameters: , loop

Output: VRPS route with lowest fuel and vehicle cost

Begin

(1) Initiating: read data file and generate random route based on the above-mentioned string character.

  String length:

(2) //accepted as incumbent solution

(3) Heating: randomly change the incumbent solution to its neighbor for 1000 times. The maximum cost

  deviation between two adjacent solutions is selected as the initial temperature,

(4)

(5) While    do begin

(6)  For    to  loop  do begin

(7)  Changing to //changing to by one exchange rule randomly

(8)  Convert to //Convert to feasible solution

(9)  Calculate total cost

(10)   //calculating cost deviation

(11) Accept or reject according to the probability of Metropolis algorithm

(12)  Update VRPS with //Update VRPS

(13)     If

(14)       Update with //Update

(15)     end if

(16)  End for

(17)  If  

(18)  Terminate the ISA heuristic

(19)  End if

(20) Count the number of accepted solutions , //calculating

(21)  

(22) End while

(23) Output

End