Public Transport Network Design for Equality of Accessibility via Message Passing Neural Networks and Reinforcement Learning

Graph learning involves embedding relevant information about a graph’s structure into a vector space. However, graphs often represent objects within a physical or social context, such as a Public Transport (PT) graph, where nodes represent locations surrounded by opportunities. In these cases, the performance of the graph depends not only on its structure but also on the physical and social characteristics of the environment. Optimizing a graph may require adapting its structure to these contexts. This paper demonstrates that Message Passing Neural Networks (MPNNs) can effectively embed both graph structure and environmental information, enabling the design of PT graphs that meet complex objectives. Specifically, we focus on accessibility, an indicator of how many opportunities can be reached in a unit of time. We set the objective to design a “equitable” PT graph with a lower accessibility inequality. We combine MPNN with Reinforcement Learning (RL) and show the efficacy of our method against metaheuristics in a use case representing in simplified terms the city of Montreal. Our superior results show the capacity of MPNN and RL to capture the intricate relations between the PT graph and the environment, which metaheuristics do not achieve.