Optimization of the urban line network using a mathematical programming approach

Abstract

The paper deals with the line-planning problem related to urban public transport. Given the transportation network in a city, the origin-destination matrix of travel demands, and the fl eet of available vehicles, the goal is to design the routes and frequencies of lines. The proposed solution method is a combination of the exact mathematical programming algorithm and a trip assignment procedure. The solution process consists of three stages: (i) initialization, (ii) designing the line network and setting the initial frequencies of selected lines, (iii) solution improvement. In the fi rst stage, an initial set of feasible lines is proposed. In the second stage, an optimal subset of candidate lines is selected and initial frequencies of lines are computed by solving a mathematical programming model of the line-planning problem. The problem is formulated as a multiple criteria optimization problem, where the criteria refl ect travelers' demand for a high quality service, operator's interest in an effective service, and the environmental impact of the vehicles. The solution of this problem specifi es the number of vehicles of the given mode and type operating on the lines. The lines which are not assigned a vehicle will not operate. The assigned number of vehicles determines the frequency of a given line. At the same time, the solution specifi es optimal passengers' routes in the line network. The third stage consists of an iterative process, which computes new line frequencies with regard to in-vehicle and waiting times, transfers, and passengers' behavior in a situation when they have multiple travel alternatives. The approach has been verifi ed using real transportation data of a middle-sized city in the Slovak Republic. The paper presents the results of the case study.

A Comprehensive Survey and Future Directions on Optimising Sustainable Urban Mobility

“…For bike-sharing systems, Gámez-Pérez et al [131], in a network design problem, aimed at determining the number and location of stations and Wu et al [102] focused on creating a bike rebalancing scheduling plan using EVs. For buses, studies applied optimisation to design the main powertrain components of electric buses (fuel cell, electric motor, and battery) [120,129], for locating charging facilities [36,39,133], for network design (routes) and frequencies setting [56,57,81,118], fleet composition [81,122], and vehicle scheduling [81,119,123,132]. In rail systems, studies sought to determine station location [144] and to elaborate a dynamic operation plan for a ventilation control system in metro stations [138].…”

“…Other studies combined operators' and community's interests[36,40,61,66,102,114,119,120,122,123,129,131,133,142,146], and the three perspectives together[39, 41-44, 48, 49, 55, 57, 81, 87, 118, 132, 139-141, 143-145]. The functions itself sought to minimise uncovered/unsatisfied demand[141], passengers' travel time/cost[42-44, 48, 49, 55, 56, 81, 118, 144], staff dissatisfaction[140], minimise costs or maximise revenue[36, 55, 57, 61, 81, 87, 102, 114, 120, 122, 129, 131-133, 140-143, 145], minimise energy consumption[36,66,114,133], fuel consumption[120,139], distances travelled by vehicles[118], ecological/environmental impact[81,87,144], and minimise emissions or maximise reduction in emissions[36, 42, 44, 48, 49, 56, 114, 118, 119, 122, 123, 129, 131-133, 140, 141, 146]. Some authors applied more specific functions as maximise car ownership and total number of trips, with user equilibrium assignment models at the lower level[40,41], minimise social-cost (congestion and environment pollution)[43] and Gini coefficient[49], maximise environmental equity[39], social welfare[48,61], and trans-VOLUME 11, 2023 9 This article has been accepted for publication in IEEE Access.…”

Optimal Assignment of Vehicles to Urban Transport Routes

“…In publications [17] or [18] a multicriterial mathematical model intended for proposing public transport routes is published, it is one of possible multicriterial models. In work [19] the vehicles are assigned to routes directly for the case of a heterogeneous vehicle fleet.…”