Door to door space-time path planning of intercity multimodal transport network using improved ripple-spreading algorithm

The main objective of this study is to solve the problem of recommending door-to-door space-time paths in an intercity multimodal transport network. The available modes include railway, metro, bus, rapid-bus, and walking. In terms of mathematical modeling, the reconstructed space-time path planning model considers multiple constraints, such as acyclic constraint, flow balance constraint and transfer constraints, to ensure the viability of the path, which is significantly different from the path in the traditional graph theory and road network. To attain the K shortest paths in two situations, the improved ripple-spreading algorithm (hereafter referred to as IRSA) is introduced, which is inspired by the ripple-spreading phenomenon and can find global optimal paths through only one iteration. A method for reducing the search space is applied to speed up the computing process. We demonstrate the feasibility and effectiveness of the proposed model and algorithm by comparing it with Gurobi Solver and Dijkstra algorithm using a small-scale network. The experiment results are evaluated by solving the door-to-door itinerary problem from Taiyuan to Beijing. Results indicate that the proposed approach can find constrained K shortest paths within an acceptable computing time. A set of experiments are conducted to test the performance of different methods, and results show that the speed-up method provides a significant improvement in problem-solving efficiency, while attempting to guarantee path optimality, which could reduce the CPU time by 51% to 92% for the tested OD pairs.