Bi-level programming model and algorithm for optimizing headway of public transit line

Due to the fact that headway is a key factor to be considered in bus scheduling, this paper proposes a bi-level programming model for optimizing bus headway in public transit lines. In this model, with the interests of bus companies and passengers in mind, the upper-level model＇s objective is to minimize the total cost, which is affected by frequency settings, both in time and economy in the transit system. The lower-level model is a transit assignment model used to describe the assignment of passengers＇ trips to the network based on the optimal bus headway. In order to solve the proposed model, a hybrid genetic algorithm, namely the genetic algorithm and the simulated annealing algorithm （GA-SA）, is designed. Finally, the model and the algorithm are tested against the transit data, by taking some of the bus lines of Changzhou city as an example. Results indicate that the proposed model allows supply and demand to be linked, which is reasonable, and the solving algorithm is effective.

Bi-Level Programming for the Optimal Nonlinear Distance-Based Transit Fare Structure Incorporating Principal-Agent Game

The urban transit fare structure and level can largely affect passengers’travel behavior and route choices.The commonly used transit fare policies in the present transit network would lead to the unbalanced transit assignment and improper transit resources distribution.In order to distribute transit passenger flow evenly and efficiently,this paper introduces a new distance-based fare pattern with Euclidean distance.A bi-level programming model is developed for determining the optimal distance-based fare pattern,with the path-based stochastic transit assignment(STA)problem with elastic demand being proposed at the lower level.The upper-level intends to address a principal-agent game between transport authorities and transit enterprises pursing maximization of social welfare and financial interest,respectively.A genetic algorithm(GA)is implemented to solve the bi-level model,which is verified by a numerical example to illustrate that the proposed nonlinear distance-based fare pattern presents a better financial performance and distribution effect than other fare structures.

Optimisation of a Bus Network Configuration and Frequency Considering the Common Lines Problem

Public transportation network reorganisation can be a key measure in designing more efficient networks and increasing the number of passengers. To date, several authors have proposed models for the “transit route network design problem” (TRNDP), and many of them use a transit assignment model as one component. However, not all models have considered the “common lines problem,” which is an essential feature in transit network assignment and is based on the concept that the fastest way to get to a destination is to take the first vehicle arriving among an “attractive” set of lines. Thus, we sought to reveal the features of considering the common lines problem by comparing results with and without considering the problem in a transit assignment model. For comparison, a model similar to a previous one was used, formulated as a bi-level optimisation problem, the upper problem of which is described as a multi-objective problem. As a result, although the solutions with and without considering the common lines showed almost the same Pareto front, we confirmed that a more direct service is provided if the common lines problem is considered whereas a less direct service is provided if it is not. With a small network case study, we found that considering the common lines problem in the TRNDP is important as it allows operators to provide more direct services.