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

TL;DR

The paper tackles scalable, user-centric multi-modal routing for shared e-mobility in urban networks by formulating a MILP model that jointly optimizes mode selection, transitions, and energy constraints, and by developing a modified multi-modal Dijkstra's algorithm for real-time operation. A graph-contraction heuristic reduces MILP complexity, achieving notable runtime improvements for networks with up to ~100 e-hubs, while a real-time capable Dijkstra variant preserves feasibility under SOC and transition constraints. Empirical evaluation on a SUMO-derived Dublin City Centre dataset demonstrates that MILP can incorporate richer objectives, but its computational cost makes the Dijkstra-based method more suitable for large-scale, real-time applications, with graph reduction offering practical gains in micro-mobility contexts. The work contributes an open-source, end-to-end framework that supports multi-modal routing with user preferences, energy considerations, and e-hub constraints, enabling scalable deployment in urban shared e-mobility systems.

Abstract

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.

Figures (12)

• Figure 1: Scenario illustration for placement and distribution of e-hubs and multi-modal options
• Figure 2: Illustration of the graph reduction methodology. a) Shows the sample graph with (k=2) e-hubs, b) Shows the shortest path between e-hub pairs c) shows the shortest path between origin and destination to e-hubs d) Illustrates the final reduced graph
• Figure 3: Objective cost comparison between Original and Reduced Graphs for the Gurobi Solver under default user preference and scenario where e-cars are not preferred
• Figure 4: Box plot visualization depicting the distribution of execution times for Original Graph (OG) and Reduced Graph (RG) using 50 and 20 e-hubs across three solvers
• Figure 5: Mean execution times for original and reduced graphs with CBC and Gurobi solvers, evaluated for varying numbers of e-hubs. Thick vertical dotted lines indicate the e-hub limits beyond which graph reduction is no longer effective for each solver.