The Urban Transportation Network Design Problem is an important challenge in urban planning that aims to design effective transportation networks in urban environments. This research addresses three significant gaps in the existing literature. First, much of the research has remained focused on traditional objectives, such as minimizing costs and travel times or maximizing satisfied travel demand. This study, however, shifts the focus to optimizing for accessibility, thus explicitly incorporates equity into the transportation planning process. Second, while most studies concentrate on designing new networks or enhancing uni-modal networks, this research focuses on existing multi-modal networks, offering a more realistic approach to transportation planning. Finally, the study applies a novel approach to the Urban Transportation Network Design Problem through the use of Reinforcement Learning, specifically Tabular Q-learning.

The research methodology is structured in three parts. We begin by operationalizing equity through accessibility to employment opportunities. This metric is transformed using three notions of justice formalized as Social Welfare Functions: utilitarian, Atkinson, and lowest quintile. The second part involves gathering, cleaning, and integrating data to construct and simplify a comprehensive spatial model of the urban area, forming the foundation for subsequent optimization. The final part applies Reinforcement Learning, using the previously defined equity metrics and spatial model. The model is trained across different equity-driven reward functions to generate optimized network expansions.

A case study in Cape Town, South Africa, demonstrates the practical application of this approach, chosen for its its complex multi-modal transportation network and significant socio-economic disparities. The study's results reveal that each notion of justice leads to radically different expansion generations in entirely separate regions of the urban area. The results indicate that a traditional, utilitarian reward function leads to maintaining existing the existing distribution of accessibility, while the Atkinson reward function improves access for disadvantaged central regions by connecting these vulnerable areas to the Central Business District. The lowest quintile approach focuses on improving access for the most disadvantaged regions, particularly in the central southern areas, ensuring that the expansions provide maximum benefit to areas with the poorest access. The study also highlights the limitations of Tabular Q-learning in handling large state-action spaces and sparse rewards, suggesting the need for Deep Reinforcement Learning methods in future research.

Overall, this research contributes to the growing body of literature on equitable transportation planning by providing a versatile framework that can be adapted to other urban contexts. The study concludes with recommendations for future research and practical applications in urban planning, advocating for the continued exploration of equity-focused approaches in the design and expansion of transportation networks.