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Hongliang Lu

Publications and source records attributed to Hongliang Lu.

At least 55 records · Page 3Linked to original sources

Automating Traffic Model Enhancement with AI Research Agent

Developing efficient traffic models is crucial for optimizing modern transportation systems. However, current modeling approaches remain labor-intensive and prone to human errors due to their dependence on manual workflows. These processes typically involve extensive literature reviews, formula tuning, and iterative testing, which often lead to inefficiencies. To address this, we propose TR-Agent, an AI-powered framework that autonomously develops and refines traffic models through a closed-loop, iterative process. We structure the research pipeline into four key stages: idea generation, theory formulation, theory evaluation, and iterative optimization, and implement TR-Agent with four corresponding modules. These modules collaborate to retrieve knowledge from external sources, generate novel hypotheses, implement and debug models, and evaluate their performance on evaluation datasets. Through iteratively feedback and refinement, TR-Agent improves both modeling efficiency and effectiveness. We validate the framework on three representative traffic models: the Intelligent Driver Model (IDM) for car-following behavior, the MOBIL model for lane-changing, and the Lighthill-Whitham-Richards (LWR) speed-density relationship for macroscopic traffic flow modeling. Experimental results show substantial performance gains over the original models. To assess the robustness and generalizability of the improvements, we conduct additional evaluations across multiple real-world datasets, demonstrating consistent performance gains beyond the original development data. Furthermore, TR-Agent produces interpretable explanations for each improvement, enabling researchers to easily verify and extend its results. This makes TR-Agent a valuable assistant for traffic modeling refinement and a promising tool for broader applications in transportation research.

cs.AI↗

Cross-cultural Deployment of Autonomous Vehicles Using Data-light Inverse Reinforcement Learning

More than the adherence to specific traffic regulations, driving culture touches upon a more implicit part - an informal, conventional, collective behavioral pattern followed by drivers - that varies across countries, regions, and even cities. Such cultural divergence has become one of the biggest challenges in deploying autonomous vehicles (AVs) across diverse regions today. The current emergence of data-driven methods has shown a potential solution to enable culture-compatible driving through learning from data, but what if some underdeveloped regions cannot provide sufficient local data to inform driving culture? This issue is particularly significant for a broader global AV market. Here, we propose a cross-cultural deployment scheme for AVs, called data-light inverse reinforcement learning, designed to re-calibrate culture-specific AVs and assimilate them into other cultures. First, we report the divergence in driving cultures through a comprehensive comparative analysis of naturalistic driving datasets on highways from three countries: Germany, China, and the USA. Then, we demonstrate the effectiveness of our scheme by testing the expeditious cross-cultural deployment across these three countries, with cumulative testing mileage of over 56084 km. The performance is particularly advantageous when cross-cultural deployment is carried out without affluent local data. Results show that we can reduce the dependence on local data by a margin of 98.67% at best. This study is expected to bring a broader, fairer AV global market, particularly in those regions that lack enough local data to develop culture-compatible AVs.

cs.LG↗

OptMATH: A Scalable Bidirectional Data Synthesis Framework for Optimization Modeling

Despite the rapid development of large language models (LLMs), a fundamental challenge persists: the lack of high-quality optimization modeling datasets hampers LLMs' robust modeling of practical optimization problems from natural language descriptions (NL). This data scarcity also contributes to the generalization difficulties experienced by learning-based methods. To address these challenges, we propose a scalable framework for synthesizing a high-quality dataset, named OptMATH. Starting from curated seed data with mathematical formulations (MF), this framework automatically generates problem data (PD) with controllable complexity. Then, a back-translation step is employed to obtain NL. To verify the correspondence between the NL and the PD, a forward modeling step followed by rejection sampling is used. The accepted pairs constitute the training part of OptMATH. Then a collection of rejected pairs is identified and further filtered. This collection serves as a new benchmark for optimization modeling, containing difficult instances whose lengths are much longer than these of NL4OPT and MAMO. Through extensive experiments, we demonstrate that models of various sizes (0.5B-32B parameters) trained on OptMATH achieve superior results on multiple modeling benchmarks, thereby validating the effectiveness and scalability of our approach. Our dataset is publicly available at https://github.com/AuroraLHL/OptMATH.

cs.AI↗

Rainbow perfect matchings in 3-partite 3-uniform hypergraphs

Let $m,n,r,s$ be nonnegative integers such that $n\ge m=3r+s$ and $1\leq s\leq 3$. Let \[δ(n,r,s)=\left\{\begin{array}{ll} n^2-(n-r)^2 &\text{if}\ s=1 , \\[5pt] n^2-(n-r+1)(n-r-1) &\text{if}\ s=2,\\[5pt] n^2 - (n-r)(n-r-1) &\text{if}\ s=3. \end{array}\right.\] We show that there exists a constant $n_0 > 0$ such that if $F_1,\ldots, F_n$ are 3-partite 3-graphs with $n\ge n_0$ vertices in each partition class and minimum vertex degree of $F_i$ is at least $δ(n,r,s)+1$ for $i \in [n]$ then $\{F_1,\ldots,F_n\}$ admits a rainbow perfect matching. This generalizes a result of Lo and Markström on the vertex degree threshold for the existence of perfect matchings in 3-partite 3-graphs. In this proof, we use a fractional rainbow matching theory obtained by Aharoni et al. to find edge-disjoint fractional perfect matching.

math.CO↗

Anti-Ramsey Number of Friendship Graphs

An edge-colored graph is called \textit{rainbow graph} if all the colors on its edges are distinct. For a given positive integer $n$ and a family of graphs $\mathcal{G}$, the anti-Ramsey number $ar(n, \mathcal{G})$ is the smallest number of colors $r$ required to ensure that, no matter how the edges of the complete graph $K_n$ are colored using exactly $r$ colors, there will always be a rainbow copy of some graph $G$ from the family $\mathcal{G}$. A friendship graph $F_k$ is the graph obtained by combining $k$ triangles that share a common vertex. In this paper, we determine the anti-Ramsey number $ar(n, \{F_k\})$ for large values of $n$. Additionally, we also determine the $ar(n, \{K_{1,k}, kK_2\}$, where $K_{1,k}$ is a star graph with $ k+1$ vertices and $kK_2$ is a matching of size $k$.

math.CO↗

Matching stability for 3-partite 3-uniform hypergraphs

Let $n,k,s$ be three integers such that $k\geq 2$ and $n\geq s\geq 1$. Let $H$ be a $k$-partite $k$-uniform hypergraph with $n$ vertices in each class. Aharoni (2017) showed that if $e(H)>(s-1)n^{k-1}$, then $H$ has a matching of size $s$. In this paper, we give a stability result for 3-partite 3-uniform hypergraphs: if $G$ is a $3$-partite $3$-uniform hypergraph with $n\geq 162$ vertices in each class, $e(G)\geq (s-1)n^2+3n-s$ and $G$ contains no matching of size $s+1$, then $G$ has a vertex cover of size $s$. Our bound is also tight.

math.CO↗

Discrepancies of perfect matchings in hypergraphs

In this paper, we determine the minimum degree threshold of perfect matchings with high discrepancy in $r$-edge-colored $k$-uniform hypergraphs for all $k\geq 3$ and $r\geq 2$, thereby completing the investigation into discrepancies of perfect matchings that has recently attracted significant attention. Our approach identifies this discrepancy threshold with a novel family of multicolored uniform hypergraphs and reveals new phenomena not covered in previous studies. In particular, our results address a question of Balogh, Treglown and Zárate-Guerén concerning 3-uniform hypergraphs.

math.CO↗

EcoFollower: An Environment-Friendly Car Following Model Considering Fuel Consumption

To alleviate energy shortages and environmental impacts caused by transportation, this study introduces EcoFollower, a novel eco-car-following model developed using reinforcement learning (RL) to optimize fuel consumption in car-following scenarios. Employing the NGSIM datasets, the performance of EcoFollower was assessed in comparison with the well-established Intelligent Driver Model (IDM). The findings demonstrate that EcoFollower excels in simulating realistic driving behaviors, maintaining smooth vehicle operations, and closely matching the ground truth metrics of time-to-collision (TTC), headway, and comfort. Notably, the model achieved a significant reduction in fuel consumption, lowering it by 10.42\% compared to actual driving scenarios. These results underscore the capability of RL-based models like EcoFollower to enhance autonomous vehicle algorithms, promoting safer and more energy-efficient driving strategies.

cs.RO↗

Enhance Planning with Physics-informed Safety Controller for End-to-end Autonomous Driving

Recent years have seen a growing research interest in applications of Deep Neural Networks (DNN) on autonomous vehicle technology. The trend started with perception and prediction a few years ago and it is gradually being applied to motion planning tasks. Despite the performance of networks improve over time, DNN planners inherit the natural drawbacks of Deep Learning. Learning-based planners have limitations in achieving perfect accuracy on the training dataset and network performance can be affected by out-of-distribution problem. In this paper, we propose FusionAssurance, a novel trajectory-based end-to-end driving fusion framework which combines physics-informed control for safety assurance. By incorporating Potential Field into Model Predictive Control, FusionAssurance is capable of navigating through scenarios that are not included in the training dataset and scenarios where neural network fail to generalize. The effectiveness of the approach is demonstrated by extensive experiments under various scenarios on the CARLA benchmark.

cs.RO↗

A stability result for almost perfect matchings

Let $n,k,s$ be three integers and $β$ be a sufficiently small positive number such that $k\geq 3$, $0<1/n\ll β\ll 1/k$ and $ks+k\leq n\leq (1+β)ks+k-2$. A $k$-graph is called non-trivial if it has no isolated vertex. In this paper, we determine the maximum number of edges in a non-trivial $k$-graph with $n$ vertices and matching number at most $s$. This result confirms a conjecture proposed by Frankl (On non-trivial families without a perfect matching, \emph{European J. Combin.}, \textbf{84} (2020), 103044) for the case when $s$ is sufficiently large.

math.CO↗

A characterization on $(g,f)$-parity orientations

Let $G$ be a graph and $g,f:V(G)\to2^N$ be two set functions such that $g(v)\le f(v)$ and $g(v)\equiv f(v)\pmod 2$ for every $v\in V(G)$. An orientation $O$ of $G$ is called a $(g,f)$-parity orientation if $g(v)\le d^+_O(v)\le f(v)$ and $g(v)\equiv d^+_O(v)\pmod 2$ for every $v\in V(G)$. In this paper, we give a Tutte-type characterization for a graph to have a $(g,f)$-parity orientation.

math.CO↗

Eigenvalues and factors: a survey

A factor of a graph is a spanning subgraph satisfying some given conditions. An earlier survey of factors can be traced back to the Akiyama and Kano [J. Graph Theory, 1985, 9: 1-42] in which they described the characterization of factors in (bipartite) graphs and digraphs, respectively. Soon after, Kouider and Vestergaard summarized the findings related to connected factors [Graphs Combin., 2005, 21(1): 1-26]. Plummer extended the aforementioned research by providing a comprehensive overview of progress made in the study of graph factors and factorization from 1985 to 2003 [Discrete Math., 2007, 7-8: 791-821]. In this paper, we aim to summarize the relevant results regarding factors from the perspective of eigenvalues.

math.CO↗

A characterization on orientations of graphs avoiding given lists on out-degrees

Let $G$ be a graph and $F:V(G)\to2^N$ be a set function. The graph $G$ is said to be \emph{F-avoiding} if there exists an orientation $O$ of $G$ such that $d^+_O(v)\notin F(v)$ for every $v\in V(G)$, where $d^+_O(v)$ denotes the out-degree of $v$ in the directed graph $G$ with respect to $O$. In this paper, we give a Tutte-type good characterization to decide the $F$-avoiding problem when for every $v\in V(G)$, $|F(v)|\leq \frac{1}{2}(d_G(v)+1)$ and $F(v)$ contains no two consecutive integers. Our proof also gives a simple polynomial algorithm to find a desired orientation. As a corollary, we prove the following result: if for every $v\in V(G)$, $|F(v)|\leq \frac{1}{2}(d_G(v)+1)$ and $F(v)$ contains no two consecutive integers, then $G$ is $F$-avoiding. This partly answers a problem proposed by Akbari et. al.(2020)

math.CO↗

BEVGPT: Generative Pre-trained Large Model for Autonomous Driving Prediction, Decision-Making, and Planning

Prediction, decision-making, and motion planning are essential for autonomous driving. In most contemporary works, they are considered as individual modules or combined into a multi-task learning paradigm with a shared backbone but separate task heads. However, we argue that they should be integrated into a comprehensive framework. Although several recent approaches follow this scheme, they suffer from complicated input representations and redundant framework designs. More importantly, they can not make long-term predictions about future driving scenarios. To address these issues, we rethink the necessity of each module in an autonomous driving task and incorporate only the required modules into a minimalist autonomous driving framework. We propose BEVGPT, a generative pre-trained large model that integrates driving scenario prediction, decision-making, and motion planning. The model takes the bird's-eye-view (BEV) images as the only input source and makes driving decisions based on surrounding traffic scenarios. To ensure driving trajectory feasibility and smoothness, we develop an optimization-based motion planning method. We instantiate BEVGPT on Lyft Level 5 Dataset and use Woven Planet L5Kit for realistic driving simulation. The effectiveness and robustness of the proposed framework are verified by the fact that it outperforms previous methods in 100% decision-making metrics and 66% motion planning metrics. Furthermore, the ability of our framework to accurately generate BEV images over the long term is demonstrated through the task of driving scenario prediction. To the best of our knowledge, this is the first generative pre-trained large model for autonomous driving prediction, decision-making, and motion planning with only BEV images as input.

cs.RO↗

Anti-Ramsey number of matchings in $3$-uniform hypergraphs

Let $n,s,$ and $k$ be positive integers such that $k\geq 3$, $s\geq 3$ and $n\geq ks$. An $s$-matching $M_s$ in a $k$-uniform hypergraph is a set of $s$ pairwise disjoint edges. The anti-Ramsey number $\textrm{ar}(n,k,M_s)$ of an $s$-matching is the smallest integer $c$ such that each edge-coloring of the $n$-vertex $k$-uniform complete hypergraph with exactly $c$ colors contains an $s$-matching with distinct colors. In 2013, Özkahya and Young proposed a conjecture on the exact value of ar$(n,k,M_s)$ for all $n \geq sk$ and $k \geq 3$. A 2019 result by Frankl and Kupavskii verified this conjecture for all $n \geq sk+(s-1)(k-1)$ and $k \geq 3$. We aim to determine the value of ar$(n,3,M_s)$ for $3s \leq n < 5s-2$ in this paper. Namely, we prove that if $3s<n<5s-2$ and $n$ is large enough, then ar$(n,3,M_s)=\textrm{ex}(n,3,M_{s-1})+2$. Here $\textrm{ex}(n,3,M_{s-1})$ is the Turán number of an $(s-1)$-matching. Thus this result confirms the conjecture of Özkahya and Young for $k=3$, $3s<n<5s-2$ and sufficiently large $n$. For $n=ks$ and $k\geq 3$, we present a new construction for the lower bound of $\textrm{ar}(n,k,M_{s})$ which shows the conjecture by Özkahya and Young is not true. In particular, for $n=3s$, we prove that $\textrm{ar}(n,3,M_s)=\textrm{ex}(n,3,M_{s-1})+5$ for sufficiently large $n$.

math.CO↗

FollowNet: A Comprehensive Benchmark for Car-Following Behavior Modeling

Car-following is a control process in which a following vehicle (FV) adjusts its acceleration to keep a safe distance from the lead vehicle (LV). Recently, there has been a booming of data-driven models that enable more accurate modeling of car-following through real-world driving datasets. Although there are several public datasets available, their formats are not always consistent, making it challenging to determine the state-of-the-art models and how well a new model performs compared to existing ones. In contrast, research fields such as image recognition and object detection have benchmark datasets like ImageNet, Microsoft COCO, and KITTI. To address this gap and promote the development of microscopic traffic flow modeling, we establish a public benchmark dataset for car-following behavior modeling. The benchmark consists of more than 80K car-following events extracted from five public driving datasets using the same criteria. These events cover diverse situations including different road types, various weather conditions, and mixed traffic flows with autonomous vehicles. Moreover, to give an overview of current progress in car-following modeling, we implemented and tested representative baseline models with the benchmark. Results show that the deep deterministic policy gradient (DDPG) based model performs competitively with a lower MSE for spacing compared to traditional intelligent driver model (IDM) and Gazis-Herman-Rothery (GHR) models, and a smaller collision rate compared to fully connected neural network (NN) and long short-term memory (LSTM) models in most datasets. The established benchmark will provide researchers with consistent data formats and metrics for cross-comparing different car-following models, promoting the development of more accurate models. We open-source our dataset and implementation code in https://github.com/HKUST-DRIVE-AI-LAB/FollowNet.

cs.CV↗

On stability of rainbow matchings

We show that for any integer $k\ge 1$ there exists an integer $t_0(k)$ such that for integers $t, k_1, \ldots, k_{t+1}, n$ with $t>t_0(k)$, $\max\{k_1, \ldots, k_{t+1}\}\le k$, and $n > 2k(t+1)$, the following holds: If $F_i \subseteq {[n]\choose k_i}$ and $|F_i|> {n\choose k_i}-{n-t\choose k_i} - {n-t-k \choose k_i-1} + 1$ for all $i \in [t+1]$, then either $\{F_1,\ldots, F_{t+1}\}$ admits a rainbow matching of size $t+1$ or there exists $W\in {[n]\choose t}$ such that $W$ is a vertex cover of $F_i$ for all $i\in [t+1]$. This may be viewed as a rainbow non-uniform extension of the classical Hilton-Milner theorem. We also show that the same holds for every $t$ and $n > 2k^3t$, generalizing a recent stability result of Frankl and Kupavskii on matchings to rainbow matchings.

math.CO↗

A proof of Frankl-Kupavskii's conjecture on edge-union condition

A 3-graph $\mathcal{F}$ is \emph{$U(s, 2s+1)$} if for any $s$ edges $e_1,...,e_s\in E(\mathcal{F})$, $|e_1\cup...\cup e_s|\leq 2s+1$. Frankl and Kupavskii (2020) proposed the following conjecture: For any $3$-graph $\mathcal{F}$ with $n$ vertices, if $\mathcal{F}$ is $U(s, 2s+1)$, then $$e(\mathcal{F})\leq \max\left\{{n-1\choose 2}, (n-s-1){s+1\choose 2}+{s+1\choose 3}, {2s+1\choose 3}\right\}.$$ In this paper, we confirm Frankl and Kupavskii's conjecture.

math.CO↗