A Dantzig-Wolfe decomposition-based algorithm for capacitated passenger assignment problem with time-varying demand in high-speed railway networks

This paper proposes an algorithm for solving the schedule-based passenger assignment problem, with explicit consideration of continuous time-varying demand and tight capacity constraints for large-scale high-speed railway (HSR) networks. We construct the space-time travel network and formulate the assignment model by destination-based arc flow variables, then design a Dantzig-Wolfe (D-W) decomposition-based algorithm to solve the large-scale model of this problem with less memory requirement and computational complexity. The sub-problem in each iteration can be solved as a single-source (destination) minimum cost flow problem without capacity constraint by the "rooftops" method, which provides an effective technique to tackle both continuous and discrete time-varying demand in the assignment problem. It is further demonstrated that the assignment solutions for discrete time-varying demand can converge to that for continuous time-varying demand with the increase of demand discretization number. Three real case studies with different HSR network scales show that the proposed algorithm is efficient in memory and computational complexity, especially when highly accurate solutions for passenger assignment on large-scale HSR networks are needed.