Learn to Tour: Operator Design For Solution Feasibility Mapping in Pickup-and-delivery Traveling Salesman Problem

This paper aims to develop a learning method for a special class of traveling salesman problems (TSP), namely, the pickup-and-delivery TSP (PDTSP), which finds the shortest tour along a sequence of one-to-one pickup-and-delivery nodes. One-to-one here means that the transported people or goods are associated with designated pairs of pickup and delivery nodes, in contrast to that indistinguishable goods can be delivered to any nodes. In PDTSP, precedence constraints need to be satisfied that each pickup node must be visited before its corresponding delivery node. Classic operations research (OR) algorithms for PDTSP are difficult to scale to large-sized problems. Recently, reinforcement learning (RL) has been applied to TSPs. The basic idea is to explore and evaluate visiting sequences in a solution space. However, this approach could be less computationally efficient, as it has to potentially evaluate many infeasible solutions of which precedence constraints are violated. To restrict solution search within a feasible space, we utilize operators that always map one feasible solution to another, without spending time exploring the infeasible solution space. Such operators are evaluated and selected as policies to solve PDTSPs in an RL framework. We make a comparison of our method and baselines, including classic OR algorithms and existing learning methods. Results show that our approach can find tours shorter than baselines.

Physics-Informed Deep Learning For Traffic State Estimation: A Survey and the Outlook

For its robust predictive power (compared to pure physics-based models) and sample-efficient training (compared to pure deep learning models), physics-informed deep learning (PIDL), a paradigm hybridizing physics-based models and deep neural networks (DNN), has been booming in science and engineering fields. One key challenge of applying PIDL to various domains and problems lies in the design of a computational graph that integrates physics and DNNs. In other words, how physics are encoded into DNNs and how the physics and data components are represented. In this paper, we provide a variety of architecture designs of PIDL computational graphs and how these structures are customized to traffic state estimation (TSE), a central problem in transportation engineering. When observation data, problem type, and goal vary, we demonstrate potential architectures of PIDL computational graphs and compare these variants using the same real-world dataset.

Quantifying Uncertainty In Traffic State Estimation Using Generative Adversarial Networks

This paper aims to quantify uncertainty in traffic state estimation (TSE) using the generative adversarial network based physics-informed deep learning (PIDL). The uncertainty of the focus arises from fundamental diagrams, in other words, the mapping from traffic density to velocity. To quantify uncertainty for the TSE problem is to characterize the robustness of predicted traffic states. Since its inception, generative adversarial networks (GAN) have become a popular probabilistic machine learning framework. In this paper, we will inform the GAN based predictions using stochastic traffic flow models and develop a GAN based PIDL framework for TSE, named ``PhysGAN-TSE". By conducting experiments on a real-world dataset, the Next Generation SIMulation (NGSIM) dataset, this method is shown to be more robust for uncertainty quantification than the pure GAN model or pure traffic flow models. Two physics models, the Lighthill-Whitham-Richards (LWR) and the Aw-Rascle-Zhang (ARZ) models, are compared as the physics components for the PhysGAN, and results show that the ARZ-based PhysGAN achieves a better performance than the LWR-based one.

TrafficFlowGAN: Physics-informed Flow based Generative Adversarial Network for Uncertainty Quantification

This paper proposes the TrafficFlowGAN, a physics-informed flow based generative adversarial network (GAN), for uncertainty quantification (UQ) of dynamical systems. TrafficFlowGAN adopts a normalizing flow model as the generator to explicitly estimate the data likelihood. This flow model is trained to maximize the data likelihood and to generate synthetic data that can fool a convolutional discriminator. We further regularize this training process using prior physics information, so-called physics-informed deep learning (PIDL). To the best of our knowledge, we are the first to propose an integration of flow, GAN and PIDL for the UQ problems. We take the traffic state estimation (TSE), which aims to estimate the traffic variables (e.g. traffic density and velocity) using partially observed data, as an example to demonstrate the performance of our proposed model. We conduct numerical experiments where the proposed model is applied to learn the solutions of stochastic differential equations. The results demonstrate the robustness and accuracy of the proposed model, together with the ability to learn a machine learning surrogate model. We also test it on a real-world dataset, the Next Generation SIMulation (NGSIM), to show that the proposed TrafficFlowGAN can outperform the baselines, including the pure flow model, the physics-informed flow model, and the flow based GAN model.

A Physics-Informed Deep Learning Paradigm for Traffic State Estimation and Fundamental Diagram Discovery

Traffic state estimation (TSE) bifurcates into two main categories, model-driven and data-driven (e.g., machine learning, ML) approaches, while each suffers from either deficient physics or small data. To mitigate these limitations, recent studies introduced hybrid methods, such as physics-informed deep learning (PIDL), which contains both model-driven and data-driven components. This paper contributes an improved paradigm, called physics-informed deep learning with a fundamental diagram learner (PIDL+FDL), which integrates ML terms into the model-driven component to learn a functional form of a fundamental diagram (FD), i.e., a mapping from traffic density to flow or velocity. The proposed PIDL+FDL has the advantages of performing the TSE learning, model parameter discovery, and FD discovery simultaneously. This paper focuses on highway TSE with observed data from loop detectors, using traffic density or velocity as traffic variables. We demonstrate the use of PIDL+FDL to solve popular first-order and second-order traffic flow models and reconstruct the FD relation as well as model parameters that are outside the FD term. We then evaluate the PIDL+FDL-based TSE using the Next Generation SIMulation (NGSIM) dataset. The experimental results show the superiority of the PIDL+FDL in terms of improved estimation accuracy and data efficiency over advanced baseline TSE methods, and additionally, the capacity to properly learn the unknown underlying FD relation.

CVLight: Deep Reinforcement Learning for Adaptive Traffic Signal Control with Connected Vehicles

This paper develops a reinforcement learning (RL) scheme for adaptive traffic signal control (ATSC), called "CVLight", that leverages data collected only from connected vehicles (CV). Seven types of RL models are proposed within this scheme that contain various state and reward representations, including incorporation of CV delay and green light duration into state and the usage of CV delay as reward. To further incorporate information of both CV and non-CV into CVLight, an algorithm based on actor-critic, A2C-Full, is proposed where both CV and non-CV information is used to train the critic network, while only CV information is used to update the policy network and execute optimal signal timing. These models are compared at an isolated intersection under various CV market penetration rates. A full model with the best performance (i.e., minimum average travel delay per vehicle) is then selected and applied to compare with state-of-the-art benchmarks under different levels of traffic demands, turning proportions, and dynamic traffic demands, respectively. Two case studies are performed on an isolated intersection and a corridor with three consecutive intersections located in Manhattan, New York, to further demonstrate the effectiveness of the proposed algorithm under real-world scenarios. Compared to other baseline models that use all vehicle information, the trained CVLight agent can efficiently control multiple intersections solely based on CV data and can achieve a similar or even greater performance when the CV penetration rate is no less than 20%.

Physics-Informed Deep Learning for Traffic State Estimation

Traffic state estimation (TSE), which reconstructs the traffic variables (e.g., density) on road segments using partially observed data, plays an important role on efficient traffic control and operation that intelligent transportation systems (ITS) need to provide to people. Over decades, TSE approaches bifurcate into two main categories, model-driven approaches and data-driven approaches. However, each of them has limitations: the former highly relies on existing physical traffic flow models, such as Lighthill-Whitham-Richards (LWR) models, which may only capture limited dynamics of real-world traffic, resulting in low-quality estimation, while the latter requires massive data in order to perform accurate and generalizable estimation. To mitigate the limitations, this paper introduces a physics-informed deep learning (PIDL) framework to efficiently conduct high-quality TSE with small amounts of observed data. PIDL contains both model-driven and data-driven components, making possible the integration of the strong points of both approaches while overcoming the shortcomings of either. This paper focuses on highway TSE with observed data from loop detectors, using traffic density as the traffic variables. We demonstrate the use of PIDL to solve (with data from loop detectors) two popular physical traffic flow models, i.e., Greenshields-based LWR and three-parameter-based LWR, and discover the model parameters. We then evaluate the PIDL-based highway TSE using the Next Generation SIMulation (NGSIM) dataset. The experimental results show the advantages of the PIDL-based approach in terms of estimation accuracy and data efficiency over advanced baseline TSE methods.

A Physics-Informed Deep Learning Paradigm for Car-Following Models

Car-following behavior has been extensively studied using physics-based models, such as the Intelligent Driver Model. These models successfully interpret traffic phenomena observed in the real-world but may not fully capture the complex cognitive process of driving. Deep learning models, on the other hand, have demonstrated their power in capturing observed traffic phenomena but require a large amount of driving data to train. This paper aims to develop a family of neural network based car-following models that are informed by physics-based models, which leverage the advantage of both physics-based (being data-efficient and interpretable) and deep learning based (being generalizable) models. We design physics-informed deep learning for car-following (PIDL-CF) architectures encoded with two popular physics-based models - IDM and OVM, on which acceleration is predicted for four traffic regimes: acceleration, deceleration, cruising, and emergency braking. Two types of PIDL-CFM problems are studied, one to predict acceleration only and the other to jointly predict acceleration and discover model parameters. We also demonstrate the superior performance of PIDL with the Next Generation SIMulation (NGSIM) dataset over baselines, especially when the training data is sparse. The results demonstrate the superior performance of neural networks informed by physics over those without. The developed PIDL-CF framework holds the potential for system identification of driving models and for the development of driving-based controls for automated vehicles.