Integrated Multi-Modal Transit Network Design via Dynamic Line Generation

Hybrid Scheduling and Routing for Rural Transit with Flexible and Fixed-Route Integration

Rural public transit systems frequently face challenges in balancing operational efficiency and passenger convenience. Addressing the issue of transportation insecurity in rural areas, this study analyzes the total cost and effectiveness of public transit service in regions characterized by low demand density. Flexible-route services generally perform well in low-demand environments due to their adaptability, but they cannot accommodate long-distance trips required by passengers without access to personal vehicles. Conversely, traditional fixed-route buses are cost-effective along core corridors while suffering from limited coverage, forcing inconvenient transfers and extra travel times beyond the established network. Consequently, neither purely flexible nor purely fixed-route approaches effectively meet the transportation needs of low-density communities. To overcome these limitations, this paper proposes an integrated public transit framework formulated as a deterministic two-stage optimization model, combining flexible-route services with scheduled fixed-route operations to achieve seamless door-to-door connectivity. The framework explores controlled deviations of fixed-route buses with limited headway adjustments and coordinates flexible shuttles to effectively serve first- and last-mile segments. This integrated approach aims to minimize overall system operating costs while maintaining acceptable passenger waiting and in-vehicle travel times. Computational experiments and sensitivity analyses on synthetic rural networks demonstrate the scalability and effectiveness of the model in reducing combined vehicle-mileage and passenger-time costs.

Optimization of Multimodal Public Transit Networks Considering Spatial Equity

Public transport equity is usually assessed after a network has been designed rather than treated as a requirement that shapes the design itself. This study develops an equity-oriented optimization framework for hierarchical multimodal transit networks in which a fixed rail backbone, main-bus routes, and feeder-bus routes are designed jointly. The model minimizes an integrated objective combining total system cost and the modal accessibility gap between public transport and private cars, while spatial equity is imposed as a binding constraint through two alternative Gini-based standards: a demand-proportional (horizontal) index and a need-sensitive (vertical) index. The problem is solved by a genetic algorithm that embeds a strategy-based passenger assignment with crowding effects and tracks the best-so-far solution across generations. Experiments on Mandl’s benchmark network across eight scenarios, combining the two equity standards with four threshold levels, yield average travel times of 11.8–13.9 min. The two standards produce structurally different networks, and stricter equity does not necessarily degrade performance: the strictest need-sensitive scenario attains the lowest average travel time, although it also records the largest modal gap relative to cars. The framework thus supports scenario-based comparison, in which the equity formulation and threshold serve as explicit policy levers rather than fixed technical bounds.

Real-Time Design of Public Transport Lines: Reconciling Adaptivity and Efficiency

Demand-responsive transport (DRT) is typically routed by solving Dynamic Vehicle Routing Problems (DVRPs), where individual vehicle trajectories are adjusted on incoming requests. This limits demand consolidation and thus efficiency. On the other hand, Conventional Public Transport (CPT) bus systems are based on a network of lines and users find their routes on it, which provides high demand consolidation. However, such a network is built offline and cannot adapt to the demand. We propose a public transport management strategy that reconciles efficiency and adaptivity by dynamically designing a structured network of lines via a receding-horizon optimization approach. Using real-world trip requests, we show that we nearly double the fraction of served requests compared to DVRP-based routing, and we serve more requests than CPT with lower user trip times.

Integrated Routing and Controlled-Segment Scheduling in Corridor-Based Drone Logistics Systems Under Minimum Headway Constraints

Predefined low-altitude corridors create a coupled routing–scheduling problem when multiple drone routes enter the same controlled segment. This study separates an upstream control hub from its scarce directed hub–segment resource and develops an event-expanded continuous-time mixed-integer linear programming model with optional fleet activation, complete-route energy and capacity checks, release precedence, minimum entry headway, holding, and downstream delay propagation. A headway-aware large neighborhood search (HA-LNS) combines route neighborhoods with a finite serial event decoder. Gurobi proves optimality on three small instances, and fixed-route timing MILPs exactly match the decoder, including for a repeated physical-hub visit. Across ten matched networks per scale, HA-LNS changes the mean objective relative to route-only LNS by 0.01%, 0.90%, and 2.33% at nominal scales 30, 50, and 100. Under high conflict-resource density, the reduction reaches 5.77%, while mean holding falls from 2.054 to 0.025 min. Simulated annealing is 1.04% better at scale 50 and statistically indistinguishable at scales 30 and 100, showing that the contribution is conflict-aware integration rather than universal heuristic dominance. The framework identifies directed-resource density as the main condition under which temporal coordination materially improves route decisions.

Joint pricing and matching for dynamic high-capacity ride-sharing considering passengers'choice uncertainty

This work investigates the uncertainty-aware joint pricing and matching problem for dynamic high-capacity ride-sharing services, where passengers are assumed to be price-elastic and decide whether to accept a ride-sharing offer based on the upfront prices provided by the platform. We formulate the studied problem as a two-stage stochastic program, where the first stage optimizes upfront price decisions for passengers, and the second-stage recourse problem captures passenger-vehicle assignment based on passengers'uncertain choices. To enhance computational efficiency, we introduce a novel relaxation-based gradient descent-guided search algorithm that leverages the problem's structural properties. Initially, the algorithm generates a feasible solution for the first-stage problem via relaxation. It then iteratively improves the solution via a search process guided by the derived gradient information. In particular, scenario reduction is applied to eliminate unnecessary scenarios when calculating the gradient, thereby reducing the overall computational burden. Numerical experiments demonstrate that, compared to solving the stochastic program directly, the proposed algorithm can accelerate computation speed by thousands of times while achieving optimality gaps of no more than 1.1%. Finally, we validate the benefits of considering passengers'choice uncertainty through large-scale simulation using real-world datasets and road networks over two large cities. The results demonstrate that, on average, the proposed method can increase the revenue by 5.2% and the service rate by 8.2% compared to the baseline approaches. This study provides a valuable reference for transportation network companies to design pricing strategies for ride-sharing to enhance service efficiency and improve revenue.

A Dynamic-Programming Labeling Approach to Hydrogen-Powered Route Selection in Aviation Networks