Elsevier

Applied Soft Computing

Volume 11, Issue 8, December 2011, Pages 5081-5091
Applied Soft Computing

Parallel genetic algorithm in bus route headway optimization

https://doi.org/10.1016/j.asoc.2011.05.051Get rights and content

Abstract

In this paper, a model for optimizing bus route headway is presented in a given network configuration and demand matrix, which aims to find an acceptable balance between passenger costs and operator costs, namely the maximization of service quality and the minimization of operational costs. An integrated approach is also proposed in the paper to determine the relative weights between passenger costs and operator costs. A parallel genetic algorithm (PGA), in which a coarse-grained strategy and a local search algorithm based on Tabu search are applied to improve the performance of genetic algorithm, is developed to solve the headway optimization model. Data collected in Dalian City, China, is used to verify the feasibility of the model and the algorithm. Results show that the reasonable resource assessment can increase the benefits of transit system.

Introduction

With the increase in concern on the environment pollution and traffic congestion, authorities of most cities in China have formed many strategies on giving priority to the development of urban public transportation system. During transit operation, there are some important tasks including network design, frequency design (headway design), setting timetables, scheduling vehicles to trips, and assignment of drivers [12]. Among these tasks, timetable (dispatching schedule) of bus vehicles is one of the most important aspects in transit operation. The determination of dispatching time of each vehicle is based on the pre-planned time interval between two adjacent vehicles.

In this study, a bus headway (i.e., scheduled dispatching time interval of two successive buses) optimization model is proposed to minimize the total costs of passengers and operators in a given network configuration and demand matrix. At the same time, an integrated approach is proposed to explore the trade-off between passenger costs and operator costs, in which the relative importance and the difference between the two conflicting objectives are considered.

Transit scheduling problems in the real world are often inefficient to be solved by classical optimization techniques because of the large numbers of trips, bus routes and stations [13]. Recently, the heuristics are considered as feasible tools to solve combinatorial optimization problems [7]. Genetic algorithm [14], which is a multipurpose optimization tool, has successfully been applied in a wide range of optimization problems [5], [10] including transportation fields [3], [4], [23], [25]. For this reason, genetic algorithm (GA) is used in this study to determine bus headways of routes. Since the proposed model is to be applied in a real transit system, a local algorithm based on Tabu search and a coarse grain parallel strategy are introduced into GA to improve the performance of the algorithm.

This paper is organized as following: Section 2 is about the problems of basic notations and formulations; Section 3 contains the solution methods of determining bus route headway; Numerical analysis is carried out in Section 4; and lastly, the conclusions are drawn in Section 5.

Section snippets

Optimization model

In this study, the maximized social benefits are defined as minimizing the sum of passenger costs and operator costs [8]. In general, it is reasonable to provide enough capacity for all transit passengers on routes in planning stage. There are, however, the situations in which it is not feasible to provide enough transit capacity to avoid congestion, especially in the real transit system. In this study, the problem of determining bus route headways can be formulated as a nonlinear program

Parallel genetic algorithm

Genetic algorithm is a search algorithm based on the concepts of natural selection and genetic operations. Many researchers attempted to improve the performance of GA by some methods [22]. Recently, parallel genetic algorithms (PGAs) have become one of the most effective strategies. Actually, PGA basically consists of various GAs, each processing a part of the population or independent populations, with or without communication between them. Therefore, PGA can increase the diversity of

Numerical test

The model and the algorithm are tested with the data of Dalian City in China. Dalian's population is about 2 million, the build-up area is about 180 km2, and the road network consists of 3200 links and 2300 nodes. There are totally 89 bus lines (Fig. 2) and 3004 bus stops, which extend 1130 km, and with 4130 vehicles in it. Passenger origin-destination (OD) stop matrix is obtained from our former research [24].

Conclusions

Headway design is a necessary product for transit system, and it is also true that a transit agency will often evaluate and determine headways of routes. This paper presents a headway optimization model based on a given network configuration and demand matrix. This model synthetically considers the passenger costs and operator costs. Also, an objective approach integrating the functionality and proportionality to weight determination is proposed to find an acceptable balance between the

Acknowledgements

This work was supported in Humanities and Social Sciences Foundation from the Ministry of Education of China 10YJC630357,the special grade of the financial support from China Postdoctoral Science Foundation 201003611,the National Natural Science Foundation of China 71001012 and the Fundamental Research Funds for the Central Universities 2011QN037.

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