Demand-Driven Vertiport Siting and Discrete-Event Fleet Simulation for On-Demand Urban Air Mobility Network Design

This paper presents a demand-driven framework for on-demand Urban Air Mobility (UAM) network design that links vertiport siting, fleet simulation, and door-to-door travel-time feasibility. Demand is estimated from commuter and passenger activity data, converted into spatial trip-end points, and clustered using K-means to generate candidate vertiport locations. Candidate networks are screened using range and minimum station-spacing constraints, then evaluated with a discrete-event simulation that models multi-vehicle dispatch, deadhead relocation, battery swaps, and service regularity. Flight time and energy consumption are computed using a point-mass eVTOL performance model. In a Greater Los Angeles case study, the preferred design expands from four stations and four eVTOLs at low demand to sixteen stations and twelve eVTOLs at the highest tested demand level. Results show that larger fleets improve completion time and vehicle-arrival regularity but do not eliminate deadhead flights, indicating that spatial demand imbalance remains an operational burden. The travel-time savings analysis further suggests that UAM is most defensible for longer or congestion-heavy trips where sufficient non-flight time remains after accounting for flight time.

The Proxy Benders Decomposition

Benders decomposition is a fundamental framework for solving large-scale mixed-integer optimization problems with complicating variables that, when fixed, yield significantly easier subproblems. However, classical Benders decomposition repeatedly solves highly similar subproblems and often exhibits zigzagging behavior across iterations, leading to slow convergence in large-scale settings. Motivated by the repetitive structure and parametric nature of Benders subproblems, this paper introduces the proxy Benders decomposition (Proxy-BD), a new decomposition framework in which subproblem optimization is replaced by certified optimization proxies rather than repeated exact solves. The proposed proxy follows a self-supervised predict-project-and-complete mechanism that produces dual-feasible solutions for generating provably valid Benders cuts. The framework preserves the theoretical validity of the decomposition independently of prediction quality through a projection-and-completion certification layer. A formal characterization of proxy-induced cuts is established, and the framework naturally extends to modern decomposition schemes, including branch-and-Benders-cut algorithms. Computational experiments on large-scale facility location and network design problems demonstrate that Proxy-BD substantially reduces the computational effort of subproblems while maintaining near-optimal solution quality. On large-scale uncapacitated facility location instances up to 2000x2000, Proxy-BD achieves median optimality gaps below 0.5%, yields up to 161x median speedups, and reduces the number of generated cuts by more than 240x on the largest instances. The computational gains consistently increase with recourse complexity, indicating that proxy-based inference scales substantially more favorably than repeated exact subproblem optimization in large-scale decomposition settings.