Designing bus line plans for realistic cases - the Utrecht case study

Highlights

• Case study on the transit network design and frequency setting problem.

• Alternative lines plans are generated using a bi-objective memetic algorithm.

• Realistic characteristics are incorporated in the model.

• A large instance is proposed using real data, explaining the generation process.

• The results are compared with the current situation using newly proposed metrics.

Abstract

This paper presents an approach to design better line plans for realistic cases. The planning problem is modelled as a realistic instance of the Transit Network Design and Frequency Setting Problem (TNDFSP). It incorporates additional assumptions taken from practice such as discrete frequencies, a subset of allowed terminal nodes and circular lines. A bi-objective memetic algorithm minimizes the average travel time (ATT) of the passengers and the fleet size. The method to generate the TNDFSP instance from real data is described in detail. Moreover, a new metric is proposed to compare different transit networks.

In order to illustrate the approach, it is applied to the area of Utrecht, The Netherlands. The results show that the current network is modelled accurately and that the algorithm successfully generates alternative bus line plans within reasonable CPU time. It returns a subset of non-dominated solutions from which a compromise solution can be selected for practice. There are solutions with the same fleet size as the current solution, but a 6% lower ATT, or solutions with the same ATT, but a fleet size which is 19% smaller. Compared to the current network, the algorithm finds that it is convenient to substantially reduce the number of lines and to leave a small portion of demand unsatisfied. This paper also presents extensive experiments to test the impact of different assumptions about demand, bus capacity and minimum frequency.

Introduction

High-quality public transport systems are fundamental for the normal functioning of cities. They provide many benefits, but they also represent large costs, so it is very important to design and operate them efficiently. In research and practice, the problem of designing bus networks is commonly divided into five stages, namely: route network design, frequency setting, timetabling, fleet assignment and crew assignment (Ceder & Wilson, 1986). Given the complexity of these problems, they have been commonly solved sequentially. However, the current developments in computer capacity and solution techniques allow to combine some of these stages to solve them in an integrated manner. For example, one can solve the transit network design problem, also known as line planning, deciding at the same time the frequencies of the lines, giving as a result the Transit Network Design and Frequency Setting Problem (TNDFSP) (López-Ramos, 2014).

Despite the increasing interest in the TNDFSP, the problem is still very difficult to solve and therefore it is mostly only considered for small theoretical examples. There is also scarce literature on case studies and practical applications of optimization techniques for the TNDFSP. Indeed, in practice the line planning process is still mostly an iterative manual process, that relies on the experience of the transit planners and their knowledge of the areas under study. The lack of application of optimization techniques is in part due to the many assumptions that are done in theory and the long computing times required to solve large instances. A common misunderstanding when discussing the TNDFSP is that the computation time is not a pressing issue since bus lines are typically only modified every several years. However, solving the TNDFSP is only one step in a long and iterative planning process, so efficient algorithms that take a few hours to solve large instances are required for practical application.

The objective of this study is to bridge this gap between theory and practice and to propose an alternative bus line plan for the area of Utrecht, The Netherlands, using optimization techniques that take into account the service frequencies. In order to generate a meaningful solution for practical purposes, for Utrecht and more generally, several modifications are required to the models typically used in scientific studies, in order to get a realistic representation of reality. Furthermore, the network used to represent the city is much larger than the instances commonly solved in literature. By addressing these challenges, we are able to design a more efficient bus line plan for the city of Utrecht.

The contributions of this paper are:

• To show the benefits of decision support when designing a realistic line plan in a large-scale case study.

• To provide a detailed explanation on the construction of a realistic TNDFSP instance from real data.

• The development of an appropriate solution approach, a memetic algorithm (MA) in this case, that is able to address constraints from practice, such as a subset of terminal nodes, discrete frequencies, allowing circular lines and using a flexible number of lines.

• The proposition of new metrics to compare and evaluate different line plans for an instance from practice.

• The data for the case study is made available allowing future researchers to use this as a benchmark instance.

The rest of the paper is structured as follows: Section 2 presents an overview of the related literature. Section 3 describes the case study and how a realistic instance of the TNDFSP was generated. Section 4 describes the algorithm used to solve the problem and to generate alternative line plans. In Section 5, the computational results are presented and discussed. Finally, conclusions and future work are presented in Section 6.