arXiv subjects

Yuan-Zheng Lei

Publications and source records attributed to Yuan-Zheng Lei.

6 recordsLinked to original sources

arXiv2026

Improving Feasibility in Quantum Approximate Optimization Algorithm for Vehicle Routing via Constraint-Aware Initialization and Hybrid XY-X Mixing

The Quantum Approximate Optimization Algorithm (QAOA) is a leading framework for quantum combinatorial optimization. The Vehicle Routing Problem (VRP), a core problem in logistics and transportation, is a natural application target, but it poses a major feasibility challenge for standard QAOA because feasible solutions occupy only a tiny fraction of the search space, and the conventional Pauli-$X$ mixer can disrupt partial solution structures that satisfy key local constraints. To address this issue, we propose a constraint-aware QAOA framework with two complementary components. First, we design a lightweight initialization strategy that encodes a selected subset of simple yet informative local one-hot constraints into the initial state, thereby reducing the initial superposition space and increasing the probability mass on states with important local structure. Second, we introduce a hybrid XY-$X$ mixer that preserves the constraint structure imposed at initialization while retaining exploratory flexibility over the remaining unconstrained degrees of freedom during QAOA evolution. We evaluate the proposed framework against standard QAOA under three progressively more realistic regimes: ideal statevector simulation, finite-shot sampling, and noisy finite-shot sampling. Across all regimes, the proposed method consistently achieves lower average energy and higher feasible-solution ratios than standard QAOA, indicating more effective guidance toward structurally valid, lower-cost VRP solutions. However, the performance gap narrows in the noisy regime. Because this setting adopts a hardware-inspired error model based on near-best-reported laboratory-level qubit gate and readout fidelities, the observed attenuation suggests that the practical advantage of the more structured mixer is likely to grow as quantum hardware improves and error rates decline.

cs.ET↗

arXiv2026

Potential failures of physics-informed machine learning in traffic flow modeling: theoretical and experimental analysis

This study investigates why physics-informed machine learning (PIML) can fail in macroscopic traffic flow modeling. We define failure as cases where a PIML model underperforms both purely data-driven and purely physics-based baselines by a given threshold. Unlike in other fields, physics residuals themselves do not hinder optimization in this setting. Instead, effective updates require both data and physics gradients to form acute angles with the true gradient, a condition difficult to satisfy with low-resolution loop data. In such cases, neural networks cannot accurately approximate density and speed, and the constructed physics residuals, already degraded by discrete sampling and temporal averaging, lose their ability to capture PDE dynamics, which directly leads to PIML failure. Theoretically, although LWR and ARZ solutions are weak solutions, for piecewise $C^k$ initial data they remain $C^k$ off the shock set under mild conditions, which has Lebesgue measure zero. Thus, almost all detector or collocation points lie in smooth regions where residuals are valid, and the MLP's inability to exactly represent discontinuities is immaterial. Finally, we establish MSE lower bounds of physics residuals: higher-order models such as ARZ have strictly larger consistency error bounds than LWR under mild conditions. This explains why LWR-based PIML can outperform ARZ-based PIML even with high-resolution data, with the gap shrinking as resolution increases, consistent with prior empirical findings.

cs.LG↗

arXiv2026

Customized Generative AI Agent for Transportation Engineering Practice: A Development and Continued Pre-training Guideline

Recent advancements in generative artificial intelligence (AI) and large language models (LLMs) have shown significant promise in automating complex reasoning, summarization, and question-answering tasks. However, the effectiveness of general-purpose LLMs in specialized engineering domains remains limited due to insufficient exposure to technical standards, engineering terminology, and domain-specific semantics. This study proposes a systematic approach to developing a customized generative AI agent for transportation engineering applications. A curated corpus of U.S. transportation manuals, design guidelines, and regulatory documents is used to conduct continued pretraining of six state-of-the-art LLMs through a unified low-rank adaptation (LoRA) framework. The training process is monitored to ensure convergence and model stability. Performance is evaluated using standard natural language processing metrics, including BLEU-4 and ROUGE, with Qwen2.5-7B and LLaMA-3.1-8B demonstrating the highest domain alignment and response quality. Results validate the effectiveness of LoRA-based adaptation in improving LLM performance on technical content interpretation and context-specific reasoning. This work contributes a reproducible development framework for constructing domain-specialized generative AI agents, supporting broader deployment in transportation research, design, planning, and policy analysis.

cs.AI↗

arXiv2026

A Scalable Min-Max Multi-Gradient Descent Method for Multi-Objective Transportation Problems

This paper develops a scalable min-max multi-gradient descent framework for multi-objective transportation problems with competing objectives and high-dimensional constraints. Unlike linear scalarization, which may conceal trade-offs behind pre-specified weights, and evolutionary heuristics, which can be inefficient in highly constrained feasible regions, the proposed method directly uses gradient information to construct a balanced common descent direction. At each iteration, it solves a constrained min-max problem that minimizes the worst directional derivative across all objectives, thereby prioritizing the least-improved objective and promoting robust progress. With linear constraints, the direction-finding problem reduces to a linear program. We prove the existence of the proposed direction, establish its relationship with Pareto criticality, and analyze convergence for a fixed-step update. Under a dense worst-case interior-point model, the linear-programming formulation has the same asymptotic complexity order as classical quadratic-programming-based steepest descent, while providing a distinct and more balanced direction-selection mechanism. Experiments on two transportation applications demonstrate its effectiveness. For a physics-informed car-following model, the method removes the need for manually fixed loss weights, achieves the best average predictive accuracy, reduces average RMSE by approximately /(5.81/%/) relative to the baseline, and substantially lowers variability across random seeds. For a multi-criteria traffic assignment problem balancing user equilibrium and system optimum, it produces stable common descent directions and performs favorably on large networks. Overall, the framework provides a robust, scalable, and theoretically grounded gradient-based approach to multi-objective transportation optimization.

math.OC↗

arXiv2025

Reconstructing Physics-Informed Machine Learning for Traffic Flow Modeling: a Multi-Gradient Descent and Pareto Learning Approach

Physics-informed machine learning (PIML) is crucial in modern traffic flow modeling because it combines the benefits of both physics-based and data-driven approaches. In conventional PIML, physical information is typically incorporated by constructing a hybrid loss function that combines data-driven loss and physics loss through linear scalarization. The goal is to find a trade-off between these two objectives to improve the accuracy of model predictions. However, from a mathematical perspective, linear scalarization is limited to identifying only the convex region of the Pareto front, as it treats data-driven and physics losses as separate objectives. Given that most PIML loss functions are non-convex, linear scalarization restricts the achievable trade-off solutions. Moreover, tuning the weighting coefficients for the two loss components can be both time-consuming and computationally challenging. To address these limitations, this paper introduces a paradigm shift in PIML by reformulating the training process as a multi-objective optimization problem, treating data-driven loss and physics loss independently. We apply several multi-gradient descent algorithms (MGDAs), including traditional multi-gradient descent (TMGD) and dual cone gradient descent (DCGD), to explore the Pareto front in this multi-objective setting. These methods are evaluated on both macroscopic and microscopic traffic flow models. In the macroscopic case, MGDAs achieved comparable performance to traditional linear scalarization methods. Notably, in the microscopic case, MGDAs significantly outperformed their scalarization-based counterparts, demonstrating the advantages of a multi-objective optimization approach in complex PIML scenarios.

cs.LG↗

arXiv2024

Unraveling stochastic fundamental diagrams considering empirical knowledge: modeling, limitation and further discussion

Traffic flow modeling relies heavily on fundamental diagrams. However, deterministic fundamental diagrams, such as single or multi-regime models, cannot capture the uncertainty pattern that underlies traffic flow. To address this limitation, a sparse non-parametric regression model is proposed in this paper to formulate the stochastic fundamental diagram. Unlike parametric stochastic fundamental diagram models, a non-parametric model is insensitive to parameters, flexible, and applicable. The computation complexity and the huge memory required for training in the Gaussian process regression have been reduced by introducing the sparse Gaussian process regression. The paper also discusses how empirical knowledge influences the modeling process. The paper analyzes the influence of modeling empirical knowledge in the prior of the stochastic fundamental diagram model and whether empirical knowledge can improve the robustness and accuracy of the proposed model. By introducing several well-known single-regime fundamental diagram models as the prior and testing the model's robustness and accuracy with different sampling methods given real-world data, the authors find that empirical knowledge can only benefit the model under small inducing samples given a relatively clean and large dataset. A pure data-driven approach is sufficient to estimate and describe the pattern of the density-speed relationship.

stat.AP↗