Autonomous vessels (AVs) have attracted growing attention due to their potential advantages in operational efficiency and navigational safety. However, their voyages may be affected by stochastic disturbances, which can lead to delayed arrivals at ports and the unavailability of pre-assigned berths. This paper first proposes a dynamic optimization approach for AV speed optimization and berth reallocation to mitigate the impacts of stochastic disturbances. Specifically, the sailing speeds of AVs are dynamically adjusted if stochastic disturbances affect their expected arrival times. Meanwhile, the real-time berth reallocation for AVs is performed when their originally allocated berths become unavailable. To meet real-time operational requirements, a rolling horizon framework is employed, which supports dynamic and adaptive adjustments to sailing speeds and berth reallocation based on the latest information on stochastic disturbances and berth occupancy. In each decision period, the problem is formulated as a mixed integer nonlinear programming model to minimize the total cost. To solve the proposed model efficiently, a tailored branch-and-cut algorithm incorporating an outer approximation method is developed. To evaluate the performance and effectiveness of the proposed model and solution method, extensive numerical experiments based on the operational data of a maritime logistics company were conducted. The results demonstrate that the proposed algorithm significantly outperforms both the Gurobi solver and a “first-come-first-served” greedy algorithm in terms of solution quality. Sensitivity analyses revealed that greater sailing time disturbances and lower penalty costs for arrival delays tend to reduce the punctuality of AVs at ports. Moreover, higher fuel prices prompt AVs to adopt lower sailing speeds to reduce energy costs.

Maximum platoon size (MPS) playing a crucial role in the configuration of connected and automated vehicle (CAV) platoons can significantly affect the traffic operation performance at intersections. The study addresses the MPS for platoon-based cooperative signal-free intersection control (PCSIC) problem considering the platoon formation process of the CAVs, which manage the CAVs to form the CAV platoons under the tactical platoon size limit to pass the intersection cooperatively. A mixed-integer nonlinear programming model is first developed to solve the proposed problem by minimizing the total travel delays of all CAVs while guaranteeing the feasible trajectories of the CAVs for platoon formation. A hybrid artificial bee colony algorithm integrating the artificial bee colony approach and dynamic programming algorithm for an optimal control scheme is proposed to solve the proposed model. Numerical experiments are conducted to examine the efficacy of the proposed model and solution algorithm. The impacts of balanced and unbalanced motion states between approaching directions on the MPS are investigated, and the traffic throughput performance of the platoon-based control strategy under balanced and unbalanced scenarios is evaluated. The findings can provide useful insights to transport authorities and automotive operators for signal-free intersection management.

Stochastic programming involves large-scale optimization with exponentially many scenarios. This paper proposes an optimization-based scenario reduction approach to generate high-quality solutions and tight lower bounds by only solving small-scale instances, with a limited number of scenarios. First, we formulate a scenario subset selection model that optimizes the recourse approximation over a pool of solutions. We provide a theoretical justification of our formulation, and a tailored heuristic to solve it. Second, we propose a scenario assortment optimization approach to compute a lower bound—hence, an optimality gap—by relaxing nonanticipativity constraints across scenario “bundles.” To solve it, we design a new column-evaluation-and-generation algorithm, which provides a generalizable method for optimization problems featuring many decision variables and hard-to-estimate objective parameters. We test our approach on stochastic programs with continuous and mixed-integer recourse. Results show that (i) our scenario reduction method dominates scenario reduction benchmarks, (ii) our scenario assortment optimization, combined with column-evaluation-and-generation, yields tight lower bounds, and (iii) our overall approach results in stronger solutions, tighter lower bounds, and faster computational times than state-of-the-art stochastic programming algorithms. History: Accepted by Andrea Lodi, Area Editor for Design and Analysis of Algorithms–Discrete. Supplemental Material: The e-companion is available at https://doi.org/10.1287/ijoc.2023.1295 .

To estimate the accurate fundamental relationship in traffic flow, this paper proposes a novel framework that extends classical fundamental diagram (FD) models to incorporate more dimensions of traffic state variables and allow for the impact of the supply-side factors of roads. The proposed framework is suitable for real-time traffic management, especially in urban areas, due to its reliance on minimal assumptions, its flexibility in adapting to various data sources, and its scalability to higher-dimensional data. The Gaussian process (GP) model is adopted as the base model for learning the optimal mapping from these input features to traffic volume. To enhance the GP model, an in-depth analysis of the properties of its kernel and likelihood function is provided. To cope with the hyperparameter optimisation of the GP, a modified Newton method for GP-based traffic flow model is also designed, which can jump over regions with small gradients. Experiments based on simulation data demonstrate the ability of the proposed framework to capture complex relationships between traffic state variables and supply-side factors, and show its value for estimating dynamic road capacity.

Vehicle platoon has the potential to significantly improve traffic throughput and reduce fuel consumption and emissions and thus has attracted extensive attention recently. In this study, we propose a vehicle platoon of connected and automated vehicles (CAVs) with a combined spacing policy to enhance traffic performance. First, a combined spacing policy composed of the constant time gap (CTG) and constant spacing (CS) is formulated for the proposed vehicle platoon, where the leader adopts the CTG and the followers use the CS policy. Based on the$h_{2}$-norm string stability criteria, the notion of exogenous-head-to-tail string stability is newly introduced, and the sufficient conditions of the local stability and string stability in the frequency domain are derived using the Routh-Hurwitz criterion and Laplace transform respectively. Numerical experiments are conducted to validate the string stability. The effectiveness of the proposed vehicle platoons is verified by theoretical analysis and numerical experiments using two typical scenarios and several measurements of effectiveness (MOE) in various performance aspects, including efficiency, safety, energy, and emission. The results show that the proposed vehicle platoon performs better than the CS-based vehicle platoon in all aspects except for efficiency. It also indicates that the proposed vehicle platoon has obvious advantages over the CTG-based vehicle platoon in efficiency and safety aspects. The findings have demonstrated the merits of the combined application of CTG and CS policies for the vehicle platoon in enhancing stability and traffic performance.

Gaussian process regression (GPR) is an emerging machine learning model with potential in a wide range of transportation system estimation and prediction problems, especially those where the uncertainty of estimation needs to be measured, for instance, traffic flow analysis, the transportation infrastructure performance estimation problems and transportation simulation-based optimization problems. The kernel function is the core component of GPR, and the radial basis function (RBF) kernel is the most commonly used one, suitable for tasks without special knowledge about the patterns of data, like trend and periodicity. However, an inappropriate hyperparameter of the kernel function may lead to over-fitting or under-fitting of GPR. During hyperparameter optimization, the usage of the RBF kernel often suffers from the issue of failing to find the optimal hyperparameter. This paper aims to address this problem by promoting the use of the hat kernel, which can reduce the risk of under-fitting. Moreover, we propose the notion of deformation, corresponding to severe over-fitting of a GPR. To further address this issue, we investigate the connection between deformation and the Bayesian generalization error of GPR. Two lower bounds for the hyperparameter of the hat kernel are also proposed to avoid deformation of GPR.