arXiv subjects

Max Z. Li

Publications and source records attributed to Max Z. Li.

At least 19 recordsLinked to original sources

arXiv2026

Augmenting airline networks using airside-to-airside buses to strengthen system resilience under disruptions

Each year, disruptions in the air transportation network strand millions of passengers and cost airlines billions in revenue. Airline networks prioritize operational and cost efficiency through hub-and-spoke structures that maximize revenue; however, these hubs also act as critical choke points during disruptions. Previous studies have focused on reactionary measures in response to air transportation network disruptions, whereas this work proposes a proactive strategy to improve resilience by reconfiguring the network's topology. Specifically, we consider airside-to-airside bus lines as a low-cost, frequent alternative to short, regional flights, offering service that can circumvent air traffic-related delays. We develop a network construction model that augments the existing air transportation network with these bus lines. The augmented networks are analyzed through an agent-based simulation, where increased resilience is measured in terms of decreased average hourly passenger delays under both nominal and disrupted conditions. Our results demonstrate that converting 10 regional routes from air service to airside-to-airside bus service, for a baseline scenario that is constrained by a $10 million investment budget, can reduce passenger delays by an average of 8% on disrupted days and 6% on nominal days. Furthermore, through a sensitivity analysis, we show that while augmenting the system using these buses decreases operational costs compared to the historic air-only network, continuously expanding bus parameters (i.e., range and investment budget) yields diminishing returns in delay mitigation. Finally, we discuss real-world precedents alongside regulatory and political hurdles to implementation. The proposed framework offers airlines, airports, and regulators a decision-support tool for integrating multimodal strategies into future disruption management policies.

math.OC↗

arXiv2026

Optimizing Agricultural Drone Operations: From Launch and Recovery Siting to Tiered Routing Strategies

Drones are increasingly used in agriculture, where tight margins demand efficient planning. Current optimization tools suffer from exponential runtimes as problem sizes grow, necessitating practical heuristics for daily operations. This paper presents an operational framework and benchmarking analysis for drone spraying operations. We evaluate the trade-offs between facility siting methods and tiered routing parameters. For facility siting, comparing a Mixed-Integer Program (MIP) baseline against a $p$-Median heuristic shows that the heuristic reduces runtime by three orders of magnitude, from over 97 seconds to under 1.2 seconds, with only a 4\% reduction in serviced field area. For route planning, a tiered problem decomposition approach partitioning the target area into 6 to 8 spatial clusters reduces computation time by an order of magnitude with minimal degradation in serviced area. This framework achieves minute-scale planning on commodity hardware, demonstrating operational relevance. Future research will incorporate weather modeling, integrated optimization of facility location and routing, and validation across diverse field geometries.

math.OC↗

arXiv2026

Integrated Exploration-Aware UAV Route Optimization and Path Planning

Uncrewed aerial vehicles (UAVs) are increasingly used for exploration-driven monitoring in hazardous environments such as disaster zones, contaminated sites, wildfire areas, and damaged infrastructure, where limited flight endurance must be allocated between visiting reported locations and gathering new information. In these settings, prior information regarding hazards is often incomplete, spatially imprecise, and subject to change during execution. For example, initial reports may identify a region where a hazard is likely to exist, but the actual hazard may be displaced, partially observed, or entirely unreported. We present an integrated exploration-aware UAV route optimization and path planning framework for hazard monitoring under uncertain and evolving prior information. The environment is represented as a spatial risk map, where each location has an associated belief of hazardous conditions. Reported hazards are modeled as uncertain regions of interest (ROIs) rather than confirmed target locations, requiring the UAV to inspect reported areas while also using its limited flight endurance to explore informative regions. The proposed method solves a vehicle routing problem over reported ROIs, augments the route with auxiliary pseudo-nodes to improve spatial coverage, allocates the remaining flight distance budget across route segments, and optimizes dynamically feasible B-spline trajectories for local exploration. During execution, UAV measurements update a grid-based belief map, and the remaining trajectory is replanned when new information and the remaining budget justify adaptation. Across 48 scenario configurations, online replanning improves average KL reduction by 15.9% over the offline optimized planner and 48.6% over straight-line traversal.

cs.RO↗

arXiv2026

Collaborative Decision-Making and Optimal Utilization of Pathfinding Flights during Convective Weather

Air traffic operations are strongly influenced by convective weather, and one common response is pathfinder operations, in which a designated aircraft tests the viability of weather-impacted airspace and routes. Despite relatively routine use in practice, how pathfinder operations evolve under uncertainty and how the pathfinder decision-making process unfolds are largely treated as exogenous. Addressing this gap requires jointly modeling weather-driven system accessibility, flight responses to pathfinder offers, and the sequencing of those offers to improve outcomes. We develop a unified analytical framework that connects weather-driven system state transitions, flight acceptance decisions, and the sequencing of pathfinder offers. We first construct a four-state Markov chain to model stochastic closure and reopening of exit points, or fixes, out of the terminal departure airspace surrounding a major airport, pathfinder selection, and pathfinding execution, and analyze its steady-state behavior to characterize long-term capacity and delay implications. We introduce utility-based decision models for flights, air traffic control (ATC), and dispatchers, and analyze worst-case collective rejection to quantify system vulnerability under selfless behavior and uncertainty. Finally, we formulate optimization problems that model ATC-initiated and dispatcher-initated pathfinder offers, with the goal of optimizing the sequence of pathfinder offers. Using a discrete event simulation for a major US airport, we show that ATC- and dispatcher-driven objectives lead to distinct, near real-time sequencing strategies, providing the first formal decision models for pathfinder operations under weather uncertainty.

math.OC↗

arXiv2025

Bayesian Ambiguity Contraction-based Adaptive Robust Markov Decision Processes for Adversarial Surveillance Missions

Collaborative Combat Aircraft (CCAs) are envisioned to enable autonomous Intelligence, Surveillance, and Reconnaissance (ISR) missions in contested environments, where adversaries may act strategically to deceive or evade detection. These missions pose challenges due to model uncertainty and the need for safe, real-time decision-making. Robust Markov Decision Processes (RMDPs) provide worst-case guarantees but are limited by static ambiguity sets that capture initial uncertainty without adapting to new observations. This paper presents an adaptive RMDP framework tailored to ISR missions with CCAs. We introduce a mission-specific formulation in which aircraft alternate between movement and sensing states. Adversarial tactics are modeled as a finite set of transition kernels, each capturing assumptions about how adversarial sensing or environmental conditions affect rewards. Our approach incrementally refines policies by eliminating inconsistent threat models, allowing agents to shift from conservative to aggressive behaviors while maintaining robustness. We provide theoretical guarantees showing that the adaptive planner converges as credible sets contract to the true threat and maintains safety under uncertainty. Experiments under Gaussian and non-Gaussian threat models across diverse network topologies show higher mission rewards and fewer exposure events compared to nominal and static robust planners.

math.OC↗

arXiv2025

Integrated Prediction and Distributionally Robust Optimization for Air Traffic Management

Strategic Traffic Management Initiatives (TMIs) such as Ground Delay Programs (GDPs) play a crucial role in mitigating operational costs associated with air traffic demand-capacity imbalances. However, GDPs can only be planned (e.g., duration, delay assignments) with confidence if the future capacities at constrained resources (i.e., airports) are predictable. In reality, such future capacities are uncertain, and predictive models may provide predictions that are vulnerable to errors and distribution shifts. Motivated by the goal of planning optimal GDPs that are distributionally robust against airport capacity prediction errors, we study a fully integrated learning-driven optimization framework. We design a deep learning-based prediction model capable of forecasting arrival and departure capacity distributions across a network of airports. We incorporate the predictions into a distributionally robust formulation of the multi-airport ground holding program (DR-MAGHP). Our results demonstrate that DR-MAGHP can achieve up to a 15.6% improvement over the stochastic programming formulation (SP-MAGHP) under airport capacity distribution shifts. We conclude by outlining future research directions aimed at enhancing both the learning and optimization components of the framework.

math.OC↗

arXiv2025

Optimization-Guided Exploration of Advanced Air Mobility Congestion Management Strategies with Stochastic Demands

Advanced Air Mobility (AAM) represents an evolution of the air transportation system by introducing low-altitude, potentially high-traffic environments. AAM operations will be enabled by both new aircraft, as well as new safety- and efficiency-critical supporting infrastructure. Published concepts of operations from both public and private sector entities establish notions such as federated management of the airspace and public-private partnerships for AAM air traffic, but there is a gap in the literature in terms of integrated tools that consider all three critical elements: AAM fleet operators (\emph{lower} layer), airspace service providers (\emph{middle} layer), and overall system governance from the legacy air navigation service provider (\emph{upper} layer). In this work, we explore modeling congestion management within the AAM setting using a bi-level optimization approach, focusing on (1) time-varying, stochastic AAM demand, (2) differing congestion management strategies, and (3) the impact of unscheduled, \enquote{pop-up} demand. We show that our bi-level formulation can be tractably solved using a Neural Network-based surrogate which returns solution qualities within 0.1-5.2\% of the optimal solution. Additionally, we show that our congestion management strategies can reduce congestion by 25.7-39.8\% when compared to the scenario of no strategies being applied. Finally, we also show that while pop-up demand degrades congestion conditions, our congestion management strategies fare better against pop-up demand than the no strategy scenario. The work herein contributes a rigorous modeling and simulation tool to help evaluate future AAM traffic management concepts and strategies.

math.OC↗

arXiv2025

Autonomous Air-Ground Vehicle Operations Optimization in Hazardous Environments: A Multi-Armed Bandit Approach

Hazardous environments such as chemical spills, radiological zones, and bio-contaminated sites pose significant threats to human safety and public infrastructure. Rapid and reliable hazard mitigation in these settings often unsafe for humans, calling for autonomous systems that can adaptively sense and respond to evolving risks. This paper presents a decision-making framework for autonomous vehicle dispatch in hazardous environments with uncertain and evolving risk levels. The system integrates a Bayesian Upper Confidence Bound (BUCB) sensing strategy with task-specific vehicle routing problems with profits (VRPP), enabling adaptive coordination of unmanned aerial vehicles (UAVs) for hazard sensing and unmanned ground vehicles (UGVs) for cleaning. Using VRPP allows selective site visits under resource constraints by assigning each site a visit value that reflects sensing or cleaning priorities. Site-level hazard beliefs are maintained through a time-weighted Bayesian update. BUCB scores guide UAV routing to balance exploration and exploitation under uncertainty, while UGV routes are optimized to maximize expected hazard reduction under resource constraints. Simulation results demonstrate that our framework reduces the number of dispatch cycles to resolve hazards by around 30% on average compared to uninformed baseline dispatch strategies, underscoring the value of uncertainty-aware vehicle dispatch for reliable hazard mitigation.

eess.SY↗

arXiv2025

Pathfinders in the Sky: Formal Decision-Making Models for Collaborative Air Traffic Control in Convective Weather

Air traffic can be significantly disrupted by weather. Pathfinder operations involve assigning a designated aircraft to assess whether airspace that was previously impacted by weather can be safely traversed through. Despite relatively routine use in air traffic control, there is little research on the underlying multi-agent decision-making problem. We seek to address this gap herein by formulating decision models to capture the operational dynamics and implications of pathfinders. Specifically, we construct a Markov chain to represent the stochastic transitions between key operational states (e.g., pathfinder selection). We then analyze its steady-state behavior to understand long-term system dynamics. We also propose models to characterize flight-specific acceptance behaviors (based on utility trade-offs) and pathfinder selection strategies (based on sequential offer allocations). We then conduct a worst-case scenario analysis that highlights risks from collective rejection and explores how selfless behavior and uncertainty affect system resilience. Empirical analysis of data from the US Federal Aviation Administration demonstrates the real-world significance of pathfinder operations and informs future model calibration.

cs.MA↗

arXiv2025

Bi-Level Route Optimization and Path Planning with Hazard Exploration

Effective risk monitoring in dynamic environments such as disaster zones requires an adaptive exploration strategy to detect hidden threats. We propose a bi-level unmanned aerial vehicle (UAV) monitoring strategy that efficiently integrates high-level route optimization with low-level path planning for known and unknown hazards. At the high level, we formulate the route optimization as a vehicle routing problem (VRP) to determine the optimal sequence for visiting known hazard locations. To strategically incorporate exploration efficiency, we introduce an edge-based centroidal Voronoi tessellation (CVT), which refines baseline routes using pseudo-nodes and allocates path budgets based on the UAV's battery capacity using a line segment Voronoi diagram. At the low level, path planning maximizes information gain within the allocated path budget by generating kinematically feasible B-spline trajectories. Bayesian inference is applied to dynamically update hazard probabilities, enabling the UAVs to prioritize unexplored regions. Simulation results demonstrate that edge-based CVT improves spatial coverage and route uniformity compared to the node-based method. Additionally, our optimized path planning consistently outperforms baselines in hazard discovery rates across a diverse set of scenarios.

math.OC↗

arXiv2025

A Convex Formulation of Game-theoretic Hierarchical Routing

Hierarchical decision-making is a natural paradigm for coordinating multi-agent systems in complex environments such as air traffic management. In this paper, we present a bilevel framework for game-theoretic hierarchical routing, where a high-level router assigns discrete routes to multiple vehicles who seek to optimize potentially noncooperative objectives that depend upon the assigned routes. To address computational challenges, we propose a reformulation that preserves the convexity of each agent's feasible set. This convex reformulation enables a solution to be identified efficiently via a customized branch-and-bound algorithm. Our approach ensures global optimality while capturing strategic interactions between agents at the lower level. We demonstrate the solution concept of our framework in two-vehicle and three-vehicle routing scenarios.

cs.MA↗

arXiv2025

Rare event modeling with self-regularized normalizing flows: what can we learn from a single failure?

Increased deployment of autonomous systems in fields like transportation and robotics have seen a corresponding increase in safety-critical failures. These failures can be difficult to model and debug due to the relative lack of data: compared to tens of thousands of examples from normal operations, we may have only seconds of data leading up to the failure. This scarcity makes it challenging to train generative models of rare failure events, as existing methods risk either overfitting to noise in the limited failure dataset or underfitting due to an overly strong prior. We address this challenge with CalNF, or calibrated normalizing flows, a self-regularized framework for posterior learning from limited data. CalNF achieves state-of-the-art performance on data-limited failure modeling and inverse problems and enables a first-of-a-kind case study into the root causes of the 2022 Southwest Airlines scheduling crisis.

cs.LG↗

arXiv2025

Examining the Dynamics of Local and Transfer Passenger Share Patterns in Air Transportation

The air transportation local share, defined as the proportion of local passengers relative to total passengers, serves as a critical metric reflecting how economic growth, carrier strategies, and market forces jointly influence demand composition. This metric is particularly useful for examining industry structure changes and large-scale disruptive events such as the COVID-19 pandemic. This research offers an in-depth analysis of local share patterns on more than 3900 Origin and Destination (O&D) pairs across the U.S. air transportation system, revealing how economic expansion, the emergence of low-cost carriers (LCCs), and strategic shifts by legacy carriers have collectively elevated local share. To efficiently identify the local share characteristics of thousands of O&Ds and to categorize the O&Ds that have the same behavior, a range of time series clustering methods were used. Evaluation using visualization, performance metrics, and case-based examination highlighted distinct patterns and trends, from magnitude-based stratification to trend-based groupings. The analysis also identified pattern commonalities within O&D pairs, suggesting that macro-level forces (e.g., economic cycles, changing demographics, or disruptions such as COVID-19) can synchronize changes between disparate markets. These insights set the stage for predictive modeling of local share, guiding airline network planning and infrastructure investments. This study combines quantitative analysis with flexible clustering to help stakeholders anticipate market shifts, optimize resource allocation strategies, and strengthen the air transportation system's resilience and competitiveness.

cs.CY↗

arXiv2024

User Feedback-Informed Interface Design for Flow Management Data and Services (FMDS)

The transition to a microservices-based Flow Management Data and Services (FMDS) architecture from the existing Traffic Flow Management System (TFMS) is a critical enabler of the vision for an Information-Centric National Airspace System (NAS). The need to design a user-centric interface for FMDS is a key technical gap, as this interface connects NAS data and services to the traffic management specialists within all stakeholder groups (e.g., FAA, airlines). We provide a research-driven approach towards designing such a graphical user interface (GUI) for FMDS. Major goals include unifying the more than 50 disparate traffic management services currently hosted on TFMS, as well as streamlining the process of evaluating, modeling, and monitoring Traffic Management Initiatives (TMIs). Motivated by this, we iteratively designed a GUI leveraging human factors engineering and user experience design principles, as well as user interviews. Through user testing and interviews, we identify workflow benefits of our GUI (e.g., reduction in task completion time), along with next steps for developing a live prototype.

cs.HC↗

arXiv2024

CHATATC: Large Language Model-Driven Conversational Agents for Supporting Strategic Air Traffic Flow Management

Generative artificial intelligence (AI) and large language models (LLMs) have gained rapid popularity through publicly available tools such as ChatGPT. The adoption of LLMs for personal and professional use is fueled by the natural interactions between human users and computer applications such as ChatGPT, along with powerful summarization and text generation capabilities. Given the widespread use of such generative AI tools, in this work we investigate how these tools can be deployed in a non-safety critical, strategic traffic flow management setting. Specifically, we train an LLM, CHATATC, based on a large historical data set of Ground Delay Program (GDP) issuances, spanning 2000-2023 and consisting of over 80,000 GDP implementations, revisions, and cancellations. We test the query and response capabilities of CHATATC, documenting successes (e.g., providing correct GDP rates, durations, and reason) and shortcomings (e.g,. superlative questions). We also detail the design of a graphical user interface for future users to interact and collaborate with the CHATATC conversational agent.

cs.CL↗

arXiv2024

Distributionally Robust Ground Delay Programs with Learning-Driven Airport Capacity Predictions

Strategic Traffic Management Initiatives (TMIs) such as Ground Delay Programs (GDPs) play a crucial role in mitigating operational costs associated with demand-capacity imbalances. However, GDPs can only be planned (e.g., duration, delay assignments) with confidence if the future capacities at constrained resources (i.e., airports) are predictable. In reality, such future capacities are uncertain, and predictive models may provide forecasts that are vulnerable to errors and distribution shifts. Motivated by the goal of planning optimal GDPs that are \emph{distributionally robust} against airport capacity prediction errors, we study a fully integrated learning-driven optimization framework. We design a deep learning-based prediction model capable of forecasting arrival and departure capacity distributions across a network of airports. We then integrate the forecasts into a distributionally robust formulation of the multi-airport ground holding problem (\textsc{dr-MAGHP}). We show how \textsc{dr-MAGHP} can outperform stochastic optimization when distribution shifts occur, and conclude with future research directions to improve both the learning and optimization stages.

math.OC↗

arXiv2024

Spaceport Facility Location Planning within the US National Airspace System

The burgeoning commercial space transportation industry necessitates an expansion of launch infrastructure to meet rising demands. However, future operations from these large-scale infrastructures can result in new impacts, particularly to air traffic operations. To rigorously reason about where such future spaceports might be located and what their impacts might be, we introduce a facility location planning model for future US spaceports (SPFLP). Central considerations for the SPFLP include population density, space launch trajectories, and potential impacts to air traffic within the US National Airspace System (NAS). The SPFLP outputs a cost-optimal set of candidate locations for future spaceports while satisfying a range of operational constraints. By conducting sensitivity analyses on the SPFLP, we are able to examine differences in flight rerouting costs and optimal launch mission allocations. Our model and numerical experiments offer valuable insights for future spaceport site selection, contributing to the strategic development of commercial space transportation while keeping in mind the need to integrate these operations within the NAS.

math.OC↗

arXiv2023

Distributionally Robust Airport Ground Holding Problem under Wasserstein Ambiguity Sets

Ground Delay Programs (GDPs) mitigate demand-capacity imbalances by holding flights on the ground when an airport's arrival capacity is reduced, thereby reducing costly airborne holding. A central challenge is that day-to-day demand-capacity balancing relies on accurate predictions of airport capacities. However, these predictions are deeply uncertain: forecast errors, operational disruptions, and climate change-driven shifts in weather severity can induce distribution shifts in capacity outcomes. Thus, policies optimized for a single predicted distribution may be brittle out of sample. We address this challenge by developing a \emph{distributionally robust} framework for the single airport ground holding problem (dr-SAGHP). We also propose a method integrates Kelly's cutting plane method with the integer L-shaped method, and that is applicable more broadly to two-stage distributionally robust integer programs with relatively complete recourse and continuous second-stage decision variables. Our method includes a novel dual bisection and primal recovery algorithm that makes use of the structure of the distributionally robust integer program in order to quickly generate subgradients required by Kelly's cutting plane method. In computational experiments, our proposed algorithm delivers up to two orders-of-magnitude speedups compared to solving the convex reformulation directly, while maintaining negligible optimality gaps. We generate capacity scenarios via Gaussian process regression and evaluate out-of-sample performance by perturbing the posterior mean and variance. The numerical experiment results show that dr-SAGHP delivers significant out-of-sample gains under moderate-to-severe shifts, improving the resilience and effectiveness of GDP decision-making under capacity uncertainty.

math.OC↗