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

Abstract

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.

The route problem of multimodal transportation with timetable under uncertainty: multi-objective robust optimization model and heuristic approach

“…In this study, the adopted method of chromosome coding, the crossover operator and the mutation operator were referred to the literature of Liu et al [17].…”

“…Rail and water transportation usually have a fixed departure timetable [16], When the goods arrived at the transfer nodes and completed the loading and unloading, it might not be transported immediately due to the timetable limitation of the next mode of transportation [33]. Liu et al [17] indicated that timetable would affect the choice of transportation routes and modes. So it makes more sense to consider timetable in multimodal transportation.…”

The route problem of multimodal transportation with timetable: stochastic multi-objective optimization model and data-driven simheuristic approach

“…As shown in Figure 2, NSGA-II mainly includes the following steps: crowding and evolution operations, fast non-dominant sort, crowding distance calculation, tournament selection and elitism strategy. In this paper, the adopted method of chromosome coding, the crossover operator and the mutation operator were referred to the literature of Liu et al (2018), and the other steps were referred to the literature of Peng et al (2021). In the study filed of elite retention strategy, Peng et al (2021) proposed the combined ( μ + λ ) selection with external archiving method to avoid the loss of excellent individuals in the evolutionary process, where μ represents the size of the parental population Z t and λ means the size of a new offspring population Q t .…”

“…Railway and waterway transportation usually have a fixed timetable of departures (Li et al , 2015), which may result in the detention time of goods due to timetable limitation when the goods arrive at the transshipment nodes and complete reloading (Yan et al , 2016). Liu et al (2018) further indicated that timetable would have an impact on the selection of transportation routes and modes.…”

Improved robust shortest paths by penalized investments

“…Experiments showed that the solutions provided excellent results when compared to the solutions of classic methods. Liu et al [2018] studied an optimal transport scheme that considered both the uncertainty of the multimodal transport network and the timetable limit. Due to the uncertainties of the multimodal transport network, interval data were used to represent the uncertainty of network weights; hence, RO was utilized.…”