Transit Network Optimization – Minimizing Transfers and Optimizing Route Directness

This paper presents a mathematical methodology for transit route network optimization. The goal is to provide an effective computational tool for the optimization of large-scale transit route networks. The objectives are to minimize transfers and optimize route directness while maximizing service coverage. The formulation of the methodology consists of three parts: (1) representation of transit route network solution space; (2) representation of transit route and network constraints; and (3) solution search schemes. The methodology has been implemented as a computer program and has been tested using previously published results. Results of these tests and results from the application of the methodology to a large-scale realistic network optimization problem in Miami-Dade County, Florida are presented. Introduction Transit route network (TRN) design is an important component in the transit planning process, which also includes transit network schedule (TNS) design. A TRN optimization process attempts to find the route network structure with optimal transfer, route directness, and ridership coverage. Unfortunately, TRN design optimization processes suffer from combinatorial intractability, and thus far for practical transit network problems of large scales, TRN designs seem to be Journal of Public Transportation, Vol. 7, No. 1, 2004 6 4 limited to the use of various heuristic approaches where the solution search schemes are based on a collection of design guidelines, criteria established from past experiences, and cost and feasibility constraints. A systematic mathematical methodology applicable to large-scale transit networks for TRN optimization design seems to be missing. The quality of a TRN may be evaluated in terms of a number of network parameters, such as route directness, service coverage, network efficiency, and number of transfers required. Route directness refers to the difference between the trip lengths,1 if the trip is to be made by transit or by a car following the shortest path. Service coverage refers to the percentage of the total estimated demand (measured by transit trips) that potentially can be satisfied by the transit services based on a given transit route network. In this study, if the origin and destination of a potential transit trip are within walking distance of a transit stop and are connected by transit routes, the trip is considered served by the network or “covered.” Network efficiency reflects the cost of providing transit services within a given network, other things being equal. Transfers are a result of the inability of a given network to provide direct service between all pairs of origins and destinations. Stern (1996) conducted a survey of various transit agencies in the United States, and about 58% of the respondents believed that transit riders were only willing to transfer once per trip. This suggests that the ridership of a transit system may be increased by merely reducing required transfers through the optimization of a TRN configuration. In addition to increasing ridership, an improved TRN configuration may also reduce transit operating cost and allow more services to be provided. For transit systems with small bus route networks, a seasoned planner may be able to obtain near optimal bus route network results based on personal knowledge, experience, and certain guidelines. For large transit systems, intuition, experiences, and simple guidelines may be insufficient to produce even near-optimal transit route network configurations, due to the problem complexity. Therefore, systematic methodologies are needed to obtain better TRN configurations. This paper presents a methodology for TRN structure optimization based on a mathematical approach with the objectives of minimizing transfers, optimizing route directness, and maximizing service coverage (Zhao 2003). The methodology has been implemented as a computer program and has been tested using previously published results and a large-scale realistic network optimization problem in Miami, Florida. Transit Network Optimization—Minimizing Transfers and Optimizing Route Directness 6 5 Formulation of A TRN Optimization Problem A TRN optimization problem may be stated as the determination of a set of transit routes, given a transit demand distribution in a transit service area and subject to a set of feasibility constraints, to achieve objectives that optimize the overall quality of a TRN. Mathematically, a typical network optimization process may be stated as: optimize an objective function f(x,y,O) x X and y Y, subject to certain constraints, where x is a real vector, y is an integer vector (or a set of vectors), and O is a matrix defined on the network’s node set. X is a space of real vectors, and Y is a set of integer vectors