Estimating the robustness of public transport schedules using machine learning

Document Type

Journal Article

Publication Date


Subject Area

operations - performance, operations - scheduling, ridership - demand


Public transportation, Scheduling, Timetabling, Machine learning, Robustness, Optimization


The planning of attractive and cost efficient public transport schedules, i.e., timetables and corresponding vehicle schedules is a highly complex optimization process involving many steps. Integrating robustness from a passenger’s point of view makes the task even more challenging. With numerous different definitions of robustness in the literature, a standard way to evaluate the robustness of a public transport system is to simulate its performance under a large number of possible scenarios. Unfortunately, this is computationally very expensive.

In this paper, we therefore explore a new way of such a scenario-based robustness approximation by using regression models from machine learning. Training of these models is based on carefully selected key features of public transport systems and passenger demand. The trained model is then able to predict the robustness of untrained instances with high accuracy using only its key features, allowing for a robustness oracle for transport planners that approximates the robustness in constant time. Such an oracle can be used as black box to increase the robustness of public transport schedules. We provide a first proof of concept for the special case of robust timetabling, using a local search framework. In computational experiments with different benchmark instances we demonstrate an excellent quality of our predictions.


Permission to publish the abstract has been given by Elsevier, copyright remains with them.


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