Parallel genetic algorithm in bus route headway optimization
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.
References (28)
- et al.
Solving transportation problems with nonlinear side constraints with Tabu search
Computers & Operations Research
(1995) - et al.
Transit network design and scheduling: a global review
Transportation Research Part A
(2008) - et al.
A comparative analysis of bus transit vehicle scheduling models
Transportation Research Part B
(2003) - et al.
Tabu search algorithms for job-shop problems with a single transport robot
European Journal of Operational Research
(2005) - et al.
Multi-objective optimization using genetic algorithms: a tutorial
Reliability Engineering & System Safety
(2006) - et al.
Transportation planning in freight forwarding companies: Tabu search algorithm for the integrated operational transportation planning problem
European Journal of Operational Research
(2009) - et al.
A subjective and objective integrated approach to determine attribute weights
European Journal of Operational Research
(1999) - et al.
A Tabu search approach to an urban transport problem in northern Spain
Computers & Operations Research
(2009) - et al.
A Tabu search heuristic procedure for the fixed charge transportation problem
European Journal of Operational Research
(1998) - et al.
Parallel genetic algorithm with parameter adaptation
Information Processing Letters
(2002)
A genetic algorithm for public transport driver scheduling
Computers & Operations Research
Optimizing the distribution of shopping centers with parallel genetic algorithm
Engineering Applications of Artificial Intelligence
Large-scale transit network optimization by minimizing user cost and transfers
Journal of Public Transportation
A model for holding strategy in public transit systems with real-time information
International Journal of Transport Management
Cited by (68)
Integrated optimization of timetable, bus formation, and vehicle scheduling in autonomous modular public transport systems
2023, Transportation Research Part C: Emerging TechnologiesDeep Reinforcement Learning based dynamic optimization of bus timetable
2022, Applied Soft ComputingCitation Excerpt :This is vital to meet passengers’ demand and save the operational cost of the bus company [3]. There were several prior bus timetable optimization methods reported, such as, Genetic Algorithm (GA) [4–6] and its variants [7,8], graphical heuristics algorithm [9], mathematical method [10], and exhaustive method [11]. All these approaches generate bus timetables in an offline manner according to historical passenger flow.
Integrating COVID-19 health risks into crowding costs for transit schedule planning
2022, Transportation Research Interdisciplinary PerspectivesCitation Excerpt :Studies on addressing pandemic related issues in transit scheduling attempt to allocate transit agency resources optimally while introducing capacity reductions brought on by social distancing measures as constraints (Gkiotsalitis and Cats 2020; Tirachini and Cats 2020). This approach can be further explored through models that set frequencies for a single line (Furth and Wilson 1981) or for a network with limited resources as constraints (Yu et al. 2011); models that maximize resource allocation can also be used (Verbas and Mahmassani 2013; Verbas and Mahmassani, 2015). Gkiotsalitis and Cats (2021) extend the approach of Furth and Wilson (1981) to a network-wide problem of optimal frequency setting.
Approximate multi-objective optimization for integrated bus route design and service frequency setting
2022, Transportation Research Part B: MethodologicalSolving urban electric transit network problem by integrating Pareto artificial fish swarm algorithm and genetic algorithm
2022, Journal of Intelligent Transportation Systems: Technology, Planning, and OperationsBus arrival time prediction and reliability analysis: An experimental comparison of functional data analysis and Bayesian support vector regression
2021, Applied Soft ComputingCitation Excerpt :Timely and accurate prediction of bus arrival time can improve the quality of public transport service as well as the satisfaction level of passengers, which in turn has a strong impact on transit ridership [7–11]. On the other hand, transit agencies need accurate information on bus operations to maintain the stability, punctuality and to improve the level of service of bus systems [12] since unreliable transit service not only increases operation cost but also discourages users from continuing to use public transportation. Bus arrival time can be disseminated to the travelers via ubiquitous communication networks and internet of things, e.g. mobile APPs and electronic billboards at bus stations, to reduce travelers’ waiting time and to alleviate their anxiety at bus stations.