First-Train Timetable Synchronization in Metro Networks under Origin-Destination Demand Conditions
Algorithm 1
NSGA-II.
Step 1: (Initialization)
Step 1.1: Input the number and index of the lines in the network and the number and index of the intermediate stations and transfer stations on each line;
Step 1.2: Input OD demand set K and promising routes;
Step 1.3: Input the actual schedule of each line in the network and other parameters;
Step 1.4: Input algorithm parameters, such as the population size pop_size, maximum number of iterations Gen_max, crossover probability, and mutation probability;
Step 2: (Initial population)
For i = 1 to pop_size do
Generate l_num departure times of first trains and headways of each individual randomly;
Endfor//i
Generate the parent population;
Gen = 1;
Step 3: (Sorting)
Step 3.1:
For j = 1 to pop_size do
Calculate the nondominated sorting rank of each individual;
Endfor//j
Step 3.2:
Calculate the crowded distance of each individual in the same rank;
Step 4: (Genetic operation)
According to the binary tournament selection rules, pop_size/2 individuals are selected from the parent population and the pop_size/2 individuals are genetically operated according to the randomly generated crossover probability and mutation probability until other pop_size/2 individuals are generated;
Step 5: (Offspring population)
These pop_size individuals generated in Step 4 compose the offspring population;
Step 6: (Combined population)
The parent population generated in Step 7 (if Gen = 1, generated in Step 2) and offspring population generated in Step 5 compose the combined population (2pop_size);
Step 7: (New population)
Calculate the nondominated sorting rank of each individual in the combined population and calculate the crowded distance of each individual in the same rank;
Select pop_size new individuals from the combined population to compose the new parent population;
Step 8: (Solution)
If Gen<Gen_max, then
Go to step 4;
Else
Output final solutions, such as the Pareto front, synchronized timetable, and train connection sequence.
