arXiv subjects

Yanfeng Ouyang

Publications and source records attributed to Yanfeng Ouyang.

15 recordsLinked to original sources

arXiv2026

Deterministic and Random Bipartite Matching on General Networks: Convex Flow Reformulation, Asymptotic Properties, and Fast Algorithms

Minimum-distance bipartite matching on general networks has numerous applications various fields. This paper first focuses on deterministic problems and presents an exact edgewise-separable convex-flow reformulation. By introducing a smooth monotone rearrangement approximation of the edge-wise imbalance profiles, the convex-flow reformulation's can be solved efficiently. If we further conduct a first-order resistance-based approximation of the convex program, a one-step Laplacian-based estimator can be analytically derived in closed forms. The paper also studies random problems where supply and demand points are randomly distributed. We show that the expected optimal matching distance scales with the square root of the number of points if the supply/demand point distributions are identical, or linearly otherwise. In the former case, the optimal flow is proven to be centered, symmetric, and sub-Gaussian. In the latter case, the limiting resistance network characterizes how supply-demand imbalance is redistributed and motivates a fast algorithm that approximate the optimal flow based on the limiting resistance. Numerical experiments show that the proposed estimators closely approximate the exact matching cost while substantially reducing computation time. The proven theoretical properties of the random matching solution are numerically verified by large-scale Monte Carlo simulations.

math.OC↗

arXiv2026

Developing Fundamental Diagrams for Urban Air Mobility Traffic Based on Physical Experiments

Urban Air Mobility (UAM) is an emerging application of unmanned aerial vehicles that promises to reduce travel time and alleviate congestion in urban transportation systems. As drone density increases, UAM traffic is expected to experience congestion similar to that in ground traffic. However, the fundamental characteristics of UAM traffic, particularly under real-world operating conditions, remain largely unexplored. This study proposes a general framework for constructing the fundamental diagram (FD) of UAM traffic by integrating theoretical analysis with physical experiments. To the best of our knowledge, this is the first study to derive UAM FDs using real-world physical experiment data. On the theoretical side, we design two drone control laws for collision avoidance and develop simulation-based traffic generation methods to produce diverse UAM traffic scenarios. Based on Edie's definition, traffic flow theory is then applied with a near-stationary traffic condition filtering method to construct the FD. To account for real-world disturbances and modeling uncertainties, we further conduct physical experiments on a reduced-scale testbed using Bitcraze Crazyflie drones. Both simulation and physical experiment trajectory data are collected and organized into the UAMTra2Flow dataset, which is analyzed using the proposed framework. Preliminary results indicate that classical FD structures for ground transportation, especially the Underwood model, are applicable to UAM systems. Notably, FD curves obtained from physical experiments exhibit deviations from simulation-based results, highlighting the importance of experimental validation. Finally, results from the reduced-scale testbed are scaled to realistic operating conditions to provide practical insights for future UAM traffic systems. The dataset and code for this paper are publicly available at https://github.com/CATS-Lab/UAM-FD.

cs.RO↗

arXiv2025

Toward Engineering AGI: Benchmarking the Engineering Design Capabilities of LLMs

Modern engineering, spanning electrical, mechanical, aerospace, civil, and computer disciplines, stands as a cornerstone of human civilization and the foundation of our society. However, engineering design poses a fundamentally different challenge for large language models (LLMs) compared with traditional textbook-style problem solving or factual question answering. Although existing benchmarks have driven progress in areas such as language understanding, code synthesis, and scientific problem solving, real-world engineering design demands the synthesis of domain knowledge, navigation of complex trade-offs, and management of the tedious processes that consume much of practicing engineers' time. Despite these shared challenges across engineering disciplines, no benchmark currently captures the unique demands of engineering design work. In this work, we introduce EngDesign, an Engineering Design benchmark that evaluates LLMs' abilities to perform practical design tasks across nine engineering domains. Unlike existing benchmarks that focus on factual recall or question answering, EngDesign uniquely emphasizes LLMs' ability to synthesize domain knowledge, reason under constraints, and generate functional, objective-oriented engineering designs. Each task in EngDesign represents a real-world engineering design problem, accompanied by a detailed task description specifying design goals, constraints, and performance requirements. EngDesign pioneers a simulation-based evaluation paradigm that moves beyond textbook knowledge to assess genuine engineering design capabilities and shifts evaluation from static answer checking to dynamic, simulation-driven functional verification, marking a crucial step toward realizing the vision of engineering Artificial General Intelligence (AGI).

cs.CE↗

arXiv2025

Dynamic Random Bipartite Matching under Spatiotemporal Heterogeneity: General Models and Application to Mobility Services

This paper explores a variant of bipartite matching problem, referred to as the Spatiotemporal Random Bipartite Matching Problem (ST-RBMP), that accommodates randomness and heterogeneity in the spatial distributions and temporal arrivals of bipartite vertices. This type of problem can be applied to many location-based services, such as shared mobility systems, where randomly arriving customers and vehicles must be matched dynamically. This paper proposes a new modeling framework to address ST-RBMP's challenges associated with the spatiotemporal heterogeneity, dynamics, and stochastic decision-making. The objective is to dynamically determine the optimal vehicle/customer pooling intervals and maximum matching radii that minimize the system-wide matching costs, including customer and vehicle waiting times and matching distances. Closed-form formulas for estimating the expected matching distances under a maximum matching radius are developed for static and homogeneous RBMPs, and then extended to accommodate spatial heterogeneity via continuum approximation. The ST-RBMP is then formulated as an optimal control problem where optimal values of pooling intervals and matching radii are solved over time and space. A series of experiments with simulated data are conducted to demonstrate that the proposed formulas for static RBMPs under matching radius and spatial heterogeneity yield very accurate results on estimating matching probabilities and distances. Additional numerical results are presented to demonstrate the effectiveness of the proposed ST-RBMP modeling framework in designing dynamic matching strategies for mobility services under various demand and supply patterns, which offers key managerial insights for mobility service operators.

math.OC↗

arXiv2025

Expected Optimal Distances of Random Bipartite Matching in $D$-dimensional Spaces: Approximate Formulas and Applications to Mobility Services

Although many well-known algorithms can solve each bipartite matching problem instance efficiently, it remains an open question how one could estimate the expected optimal matching distance for arbitrary numbers of randomly distributed vertices in $D$-dimensional spaces (referred to as a random bipartite matching problem, or RBMP). This paper proposes a comprehensive modeling framework that yields closed-form approximate formulas for estimating the expected optimal matching cost across three interrelated but increasingly complex versions of RBMPs: (i) RBMP-I, where edge costs are independently and identically distributed (i.i.d.); (ii) RBMP-S, where edge costs represent distances between vertices uniformly distributed on the surface of a hyper-sphere in a $D$-dimensional Euclidean space; and (iii) RBMP-B, where the vertices are uniformly distributed in a hyper-ball within a $D$-dimensional L$^p$ metric space. A series of Monte-Carlo simulation experiments are conducted to verify the accuracy of the proposed formulas under varying parameter combinations. These proposed distance estimates could be key for strategic performance evaluation and resource planning in a wide variety of application contexts. As an illustration, we focus on on-demand mobility services (e.g., e-hailing taxi system). We show how the proposed distance formulas provide a theoretical foundation for the empirically assumed Cobb-Douglas matching function in the field, and reveal conditions under which it can work well. Our formulas can also be easily incorporated into optimization models to select on-demand mobility operation strategies (e.g., whether newly arriving customers shall be instantly matched or pooled into a batch for matching). Agent-based simulations are conducted to verify the predicted performance of the demand pooling strategy for two types of e-hailing taxi systems.

math.OC↗

arXiv2025

Average Distance of Random Bipartite Matching in One-dimensional Space and Networks

The bipartite matching problem is widely applied in the field of transportation; e.g., to find optimal matches between supply and demand over time and space. Recent efforts have been made on developing analytical formulas to estimate the expected matching distance in bipartite matching with randomly distributed vertices in two- or higher-dimensional spaces, but no accurate formulas currently exist for one-dimensional problems. This paper presents a set of closed-form formulas, without curve-fitting, that can provide accurate average distance estimates for one-dimensional random bipartite matching problems (RBMP). We first focus on a lattice case and propose a new method that relates the corresponding matching distance to the area size between a random walk path and the x-axis. This result directly leads to a straightforward closed-form formula for balanced RBMPs. For unbalanced RBMPs on a lattice, we first analyze the properties of an unbalanced random walk that can be related to balanced RBPMs after optimally removing a subset of unmatched points, and then derive a set of approximate formulas. Additionally, we build upon an optimal point removal strategy to derive a set of recursive formulas that can provide more accurate estimates. Then, we extend the results to three problem variants, including RBMPs with periodic boundaries, uniformly distributed points, and arbitrary-length line. Last, we shift our focus to regular networks, and use the one-dimensional results as building blocks to derive RBMP formulas. To verify the accuracy of the proposed formulas, a set of Monte-Carlo simulations are generated for a variety of matching problems settings. Results indicate that our proposed formulas provide quite accurate distance estimations for one-dimensional line segments and networks under a variety of conditions.

math.OC↗

arXiv2025

Rebalancing Modular Transit Systems: A Hierarchical Graph-Based Optimization Framework for Fleet Sizing and Routing

This study addresses the rebalancing of empty modular transit pods between scheduled service trips in fixed-route bus systems. A two-stage hierarchical optimization framework is proposed. The first stage determines the minimum fleet size and initial vehicle assignments by solving a maximum matching problem on a bipartite graph, using a GPU-accelerated push-relabel algorithm. The second stage formulates detailed routing as a series of minimum-cost flow problems on time-space networks. To manage memory usage in large instances, a capped-interval heuristic limits the size of each network by dividing long scheduling intervals into subintervals. Computational experiments on the Manhattan bus network show that the proposed method achieves performance comparable to the full-scale time-space network formulation in terms of objective value, while enabling the solution of instances that are otherwise intractable due to memory limitations.

math.OC↗

arXiv2024

Benchmarking the Capabilities of Large Language Models in Transportation System Engineering: Accuracy, Consistency, and Reasoning Behaviors

In this paper, we explore the capabilities of state-of-the-art large language models (LLMs) such as GPT-4, GPT-4o, Claude 3.5 Sonnet, Claude 3 Opus, Gemini 1.5 Pro, Llama 3, and Llama 3.1 in solving some selected undergraduate-level transportation engineering problems. We introduce TransportBench, a benchmark dataset that includes a sample of transportation engineering problems on a wide range of subjects in the context of planning, design, management, and control of transportation systems. This dataset is used by human experts to evaluate the capabilities of various commercial and open-sourced LLMs, especially their accuracy, consistency, and reasoning behaviors, in solving transportation engineering problems. Our comprehensive analysis uncovers the unique strengths and limitations of each LLM, e.g. our analysis shows the impressive accuracy and some unexpected inconsistent behaviors of Claude 3.5 Sonnet in solving TransportBench problems. Our study marks a thrilling first step toward harnessing artificial general intelligence for complex transportation challenges.

cs.AI↗

arXiv2024

Planning Charging Stations and Service Operations of Dockless Electric Micromobility Systems

Dockless electric micro-mobility services (e.g., shared e-scooters and e-bikes) have been increasingly popular in the recent decade, and a variety of charging technologies have emerged for these services. The use of charging stations, to/from which service vehicles are transported by the riders for charging, poses as a promising approach because it reduces the need for dedicated staff or contractors. However, unique challenges also arise, such as how to incentivize riders to drop off vehicles at stations and how to efficiently utilize the vehicles being charged at the stations. This paper focuses on dockless e-scooters as an example and develops a new spatial queuing network model to capture the steady-state scooter service cycles, battery consumption and charging processes, and the associated pricing and management mechanisms. Building upon this model, a system of closed-form equations is formulated and incorporated into a constrained nonlinear program to optimize the deployment of the service fleet, the design of charging stations (i.e., number, location, and capacity), user-based charging price promotions and priorities, and repositioning truck operations (i.e., headway and truck load). The proposed queuing network model is found to match very well with agent-based simulations. It is applied to a series of numerical experiments to draw insights into the optimal designs and the system performance. The numerical results reveal strong advantages of using charging stations for shared dockless electric micro-mobility services as compared to state-of-the-art alternatives. The proposed model can also be used to analyze other micromobility services and other charging approaches.

math.OC↗

arXiv2023

Planning ride-pooling services with detour restrictions for spatially heterogeneous demand: A multi-zone queuing network approach

This study presents a multi-zone queuing network model for steady-state ride-pooling operations that serve heterogeneous demand, and then builds upon this model to optimize the design of ride-pooling services. Spatial heterogeneity is addressed by partitioning the study region into a set of relatively homogeneous zones, and a set of criteria are imposed to avoid significant detours among matched passengers. A generalized multi-zone queuing network model is then developed to describe how vehicles' states transition within each zone and across neighboring zones, and how passengers are served by idle or partially occupied vehicles. A large system of equations is constructed based on the queuing network model to analytically evaluate steady-state system performance. Then, we formulate a constrained nonlinear program to optimize the design of ride-pooling services, such as zone-level vehicle deployment, vehicle routing paths, and vehicle rebalancing operations. A customized solution approach is also proposed to decompose and solve the optimization problem. The proposed model and solution approach are applied to a hypothetical case and a real-world Chicago case study, so as to demonstrate their applicability and to draw insights. Agent-based simulations are also used to corroborate results from the proposed analytical model. These numerical examples not only reveal interesting insights on how ride-pooling services serve heterogeneous demand, but also highlight the importance of addressing demand heterogeneity when designing ride-pooling services.

math.OC↗

arXiv2019

Dynamic Vaccination Game in a Heterogeneous Mixing Population

Opposition to vaccination has long been a non-negligible public health phenomenon resulted from people's varied perceptions toward vaccination (e.g., vaccine-phobia). This paper investigates the voluntary vaccination behavior of a heterogeneous population during an epidemic outbreak, where each individual makes its own vaccination decision to minimize its expected disutility from both vaccine-phobia and the risk of infection. Such a problem is known as a vaccination game, as people's vaccination decisions not only affect their own disutilities but those of all others through probabilistic disease transmissions. To study the vaccination game, the susceptible-infected-removed disease propagation process is generalized into a new epidemic dynamics model to allow dynamic vaccination and immunity activation in a heterogeneous mixing population. An efficient computation method is proposed to evaluate the final state of the dynamic epidemic system. Then, a classic game-theoretical equilibrium model is built upon these results to examine the impacts of people's vaccination behavior on the overall risk of epidemic outbreak. A hypothetical case study is used to validate the dynamics model and the derived results, and extensive numerical experiments are conducted to identify the key factors that affect people's vaccination decisions and the risk of an outbreak. Moreover, three alternative vaccination schemes are also studied to examine the effects of early and non-differential vaccination treatments, respectively.

physics.soc-ph↗

arXiv2018

A General Model of Ridesharing Services

The paper presents a general analytic framework to model transit systems that provide door-to-door service. The model includes as special cases non-shared taxi and demand responsive transportation (DRT). In the latter we include both, paratransit services such as dial-a-ride (DAR), and the form of ridesharing (shared taxi) currently being used by crowd-sourced taxi companies like Lyft and Uber. The framework yields somewhat optimistic results because, among other things, it is deterministic and does not track vehicles across space. By virtue of its simplicity however, the framework yields approximate closed form formulas for many cases of interest.

math.OC↗

arXiv2017

Advancements in Continuum Approximation Models for Logistics and Transportation Systems: 1996 - 2016

Continuum Approximation (CA) is an efficient and parsimonious technique for modeling complex logistics problems. In this paper,we review recent studies that develop CA models for transportation, distribution and logistics problems with the aim of synthesizing recent advancements and identifying current research gaps. This survey focuses on important principles and key results from CA models. In particular, we consider how these studies fill the gaps identified by the most recent literature reviews in this field. We observe that CA models are used in a wider range of applications, especially in the areas of facility location and integrated supply chain management. Most studies use CA as an alternative to exact solution approaches; however, CA can also be used in combination with exact approaches. We also conclude with promising areas of future work.

math.OC↗

arXiv2015

Parking Space Management via Dynamic Performance-Based Pricing

In congested urban areas, it remains a pressing challenge to reduce unnecessary vehicle circling for parking while at the same time maximize parking space utilization. In observance of new information technologies that have become readily accessible to drivers and parking agencies, we develop a dynamic non-cooperative bi-level model (i.e. Stackelberg leader-follower game) to set parking prices in real-time for effective parking access and space utilization. The model is expected to fit into an integrated parking pricing and management system, where parking reservations and transactions are facilitated by sensing and informatics infrastructures, that ensures the availability of convenient spaces at equilibrium market prices. It is shown with numerical examples that the proposed dynamic parking pricing model has the potential to virtually eliminate vehicle circling for parking, which results in significant reduction in adverse socioeconomic externalities such as traffic congestion and emissions.

cs.GT↗

arXiv2014

Optimal Layout of Transshipment Facilities on An Infinite Homogeneous Plane

This paper studies optimal spatial layout of transshipment facilities and the corresponding service regions on an infinite homogeneous plane $\mathbb{R}^2$ that minimize the total cost for facility set-up, outbound delivery and inbound replenishment transportation. The problem has strong implications in the context of freight logistics and transit system design. This paper first focuses on a Euclidean plane and presents a new proof for the known Gersho's conjecture, which states that the optimal shape of each service region should be a regular hexagon if the inbound transportation cost is ignored. When inbound transportation cost becomes non-negligible, however, we show that a tight upper bound can be achieved by a type of elongated cyclic hexagons, while a cost lower bound based on relaxation and idealization is also obtained. The gap between the analytical upper and lower bounds is within 0.3%. This paper then shows that a similar elongated non-cyclic hexagon shape is actually optimal for service regions on a rectilinear metric plane. Numerical experiments and sensitivity analyses are conducted to verify the analytical findings and to draw managerial insights.

math.OC↗