Research Article

Collaborative Optimization Model for the Design and Operation of Feeder Bus Routes Based on Urban Metro

Table 1

Parameters and variables in the model.

IndexDefinitionUnit

Feeder bus stop
Feeder bus route

Collections
Collection of feeder buses
Collection of feeder bus stops
Collection of metro stations
Candidate collection of feeder bus routes
Collection of feeder bus transfer stations

Parameters
Number of passengers taking feeder bus route at stop Person
Number of passengers transferring from feeder bus to metroPerson
Maximum cross section passenger flow of feeder bus route Person
Departure interval of feeder bus route min
Service time of feeder bush
Operating cost per unit mileage of feeder busCNY/km
Average time for each passenger to get on the feeder buss
Average time for each passenger to get off the feeder buss
Time spent by passengers in elevators and other facilities in metro stationsmin
Parking time of the metro train at the metro stationmin
Minimum service time of each feeder bush
Maximum service time of each feeder bush
The average speed of the feeder buskm/h
The walking distance from the bus transfer station to the metro stationkm
The average walking speed of passengerskm/h
The average waiting time factor of passengers
Average load factor of feeder bus%
Approved passenger capacity of feeder busPerson
Average travel time value of passengersCNY/h
Importance factor
Number of available feeder busesveh
The minimum load factor of the feeder bus%
The maximum load factor of the feeder bus%
The path length between the feeder bus stop and the bus transfer stationkm
Length of feeder bus route km
The minimum length of the feeder bus route km
The maximum length of the feeder bus route km
Departure frequency of feeder bus route veh/h
Minimum departure frequency of feeder bus route veh/h
Maximum departure frequency of feeder bus route veh/h
The arrival time of the feeder bus at the bus transfer station
The arrival time of the metro train at the metro station
The departure time of the metro train at the metro station
Decision variables
Whether the feeder bus route passes the bus stop immediately after passing the bus demand stop ; yes means ; otherwise,
Group size
The position of the particle
The speed of the particle
Inertia weight
Acceleration weights for particles flying towards individual extremum and group extremum
A random number between 0 and 1
The position of the optimal solution found so far by the particle itself
The location of the optimal solution found so far is in the neighbourhood of the particle
The position of the optimal solution found so far in the subgroup of the particle