Considering the optimization of container multimodal transport under uncertain conditions, it has been defined as a chance-constrained programming problem in this paper. Firstly, a multi-objective optimization model has been established by using the triangular fuzzy number method. And then, the vessel waiting time was added into constraint conditions, and carbon emissions were calculated by introducing the forest accumulation conversion factor method. Finally, the improved ant colony algorithm was used to calculate the weight coefficient of each element. The results show that the route optimization method exhibits the excellent performance of convergence and provides a theoretical basis for transport scheming.


With the rapid development of global trade, In the inland area, it is far from enough to rely on railway transportation or inland waterway transportation for bulk goods. As an important organizational form of modern logistics transportation, the Water-Rail combined operation can make use of the advantages of waterway and railway transportation to provide more flexible and reliable options for cargo transportation, so it has attracted widespread attention.

In recent years, domestic and foreign scholars have mainly studied the multimodal transport route optimization problem. The establishment of multimodal transport route selection models is generally optimized from the aspects of the objective function, constraint conditions, and random factors. Ji et al. (2017) considered carbon emission factors, reloading time, and cost, and established an optimization model to minimize the total transportation cost and time. Cheng et al. (2019) established a multimodal transport route selection model under four carbon emission policies (mandatory carbon emissions, carbon tax, carbon trading, and carbon compensation). Wang et al. (2017) took transportation time, cost, carbon emissions, and comprehensive energy consumption as targets, and determined the final weights of the four objective functions with an entropy weight-analytic hierarchy process. Marjani et al.(2015) considered the mixed time window as a constraint condition and converted the time window into penalty cost. Wang et al. (2019) established a multi-task container transportation scheme optimization model with time and capacity constraints. Chen et al., (2020) considered the receiving time window as the soft constraint of the model. Martin et al. (2015) considered the uncertainty associated with travel time. Zhen et al. (2018) optimized the model for the uncertainty of transportation time and carbon emissions. Jiang et al. (2020) established a mathematical programming model based on demand uncertainty and used robust optimization to deal with constraints. For multimodal transport route selection, commonly used algorithms include the Dijkstra algorithm (Zhang et al.,2015), the genetic algorithm (Xiong et al.,2014; Yuan. et al.,2021), the ant colony algorithm (Goel et al.,2019), particle swarm algorithm (Yu et al.,2019; Deng et al.,2021) and the hybrid algorithm of the above algorithms (Wan et al.,2019; Liu et al.,2020).

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