On Scalable Design for User-Centric Multi-Modal Shared E-Mobility Systems using MILP and Modified Dijkstra's Algorithm

In the rapidly evolving landscape of urban transportation, shared e-mobility services have emerged as a sustainable solution to meet growing demand for flexible, eco-friendly travel. However, the existing literature lacks a comprehensive multi-modal optimization framework with focus on user preferences and real-world constraints. This paper presents a multi-modal optimization framework for shared e-mobility, with a particular focus on e-mobility hubs (e-hubs) with micromobility. We propose and evaluate two approaches: a mixed-integer linear programming (MILP) solution, complemented by a heuristic graph reduction technique to manage computational complexity in scenarios with limited e-hubs, achieving a computational advantage of 93%, 72%, and 47% for 20, 50, and 100 e-hubs, respectively. Additionally, the modified Dijkstra's algorithm offers a more scalable, real-time alternative for larger e-hub networks, with median execution times consistently around 53 ms, regardless of the number of e-hubs. Thorough experimental evaluation on real-world map and simulated traffic data of Dublin City Centre reveals that both methods seamlessly adapt to practical considerations and constraints such as multi-modality, user-preferences and state of charge for different e-mobility tools. While MILP offers greater flexibility for incorporating additional objectives and constraints, the modified Dijkstra's algorithm is better suited for large-scale, real-time applications due to its computational efficiency.