Headway

Algorithm

Control (management)

Engineering

Transport engineering

Cartography

Passenger train

Scheduling (production processes)

Operating system

Computer science

Mathematical optimization

Integer programming

Computer network

Lagrangian relaxation

Operations research

Simulation

Mathematics

Geography

Flow (mathematics)

Flow control (data)

Automotive engineering

Operations management

Artificial intelligence

Geometry

Train

Schedule

Job shop scheduling

Omega

For high-frequency metro lines, the excessive travel demand during the peak hours brings a high risk to metro system and a low comfort to passengers, so it is important to consider passenger flow control when designing the metro train scheduling strategy. This paper presents a collaborative optimization method for metro train scheduling and train connections combined with passenger control strategy on a bi-directional metro line. Specifically, the dynamic equations for the train headway and train passenger loads along the metro line, the turnaround operations and the entering/exiting depot operations are considered simultaneously. The proposed collaborative optimization problem is formulated as a mixed integer nonlinear programming model to realise the trade-off among the utilization of trains, passenger flow control strategy and the number of awaiting passengers at platforms, which is further reformulated into mixed integer linear programming (MILP) model. To handle the complexity of this MILP model, a Lagrangian relaxation-based approach is designed to decompose the original problem into two small subproblems, which reduces the computational burden of the original problem and can efficiently find a good solution of the train schedule and train connections problem combined with passenger flow control strategy. The numerical experiments are implemented to investigate the effectiveness of the proposed model and approach, which shows that the proposed model is not sensitive to uncertain passenger demand. Under the proposed collaborative optimization approach, the number of train service connections and the crowding inside stations and carriages with the proper passenger flow control strategy can be evidently balanced, and thereby the operation efficiency and safety of the metro lines are effectively improved.

Collaborative optimization for metro train scheduling and train connections combined with passenger flow control strategy