The robust shortest path problem for multimodal transportation considering timetable with interval data

In the multimodal transport network, due to various uncertain factors such as weather and traffic conditions, the transport time will become uncertain accordingly, besides, railway transport and water transport are usually limited by timetable. These factors will inevitably affect the path selection. The purpose of this study is to seek an optimal transport scheme that considers both the uncertainty of the multimodal transport network and the timetable limit. In view of the uncertainties of the multimodal transport network, interval data are used to represent the uncertainty of network weights, and robust optimization method is then adopted to process the interval data. An optimal model of robust shortest path considering timetable limit is established and genetic algorithm (GA) is designed to solve the problem. The GA designed provides an encoding method for variable-length chromosomes applicable to shortest path problem solving in the multimodal transport. And the handling methods for loops and inaccessible paths due to chromosome crossover and mutation are also suggested. And finally, numerical examples are provided to verify the validity of the model and algorithm.