To address the path optimization problem in container road-rail intermodal transportation while considering hub delays,triangular fuzzy numbers are employed to characterize the uncertainty associated with such delays.This uncertainty takes into account the dual uncertainty in the number of containers awaiting transshipment and the remaining rail capacity in transport,as well as the limitations of hub transshipment capacity and rail departure requirements on hub delays.Therefore,the resulting delay time,along with the associated carbon emissions and storage costs,is quantified from the perspectives of waiting for transshipment and waiting for departure schedules.A multi-objective path optimization model is then developed to minimize the total cost and total carbon emissions associated with the path scheme.The model is de-fuzzified using the expected value method and fuzzy chance-constrained programming.A self-adaptive fast nondominated sorting genetic algorithm(ANSGA-Ⅱ)is designed to solve the model.Additionally,the simulation methods are used to assess the reliability of the path scheme and to identify the optimal combination of confidence levels.The case study was conducted on a specific road-rail intermodal transportation network,and the results indicate that,compared to the NSGA-Ⅱ algorithm,the proposed method exhibits a faster convergence speed.The total cost and total carbon emissions were improved by 2.03%and 5.87%,respectively,and the reliability of the frontier solutions was greater than 0.95.Further sensitivity analysis indicates that when the number of containers awaiting transfer reaches a specific threshold,the preferred mode of transport tends to shift towards single road transport.This adjustment aims to minimize hub delays caused by waiting for transfer.At the same time,hub delays also have different effects on the path selection of goods with different time sensitivity.