基于消费者剩余理论，通过出行选择偏好调查，确定影响货运路径选择的关键因素，提出一种用于确定通行费折扣的双层规划模型。其中，上层模型为考虑费用成本和时间成本的路网经营者盈余最大化模型，采用遗传和模拟退火混合优化算法求解；下层模型为弹性需求下基于Logit的多车型随机用户均衡分配模型，采用Frank-Wolfe算法求解。利用高速公路收费数据、普通国省道断面交通量数据，以3组并行的实例路段验证了模型的可行性。结果表明，该模型可精准确定高速公路货车通行费折扣范围；经43次迭代后，上层模型可达到稳定值，实例路段的小型、中型、大型和特大型货车通行费折扣率范围分别78.68%~86.27%、55.82%~65.82%、47.90%~54.81%和47.52%~48.31%，货车平均流量提高了12.24%。该研究可支撑差异化收费方案制定及优化调整。

Objective: Implementing differentiated toll discounts for expressway trucks can lead to a more balanced traffic flow across the road network. Expressway operators hope to make profits by charging truck tolls, while truck groups aim to maximize profits through toll charges, whereas truck groups focus on minimizing travel costs in terms of economics and time. A balance exists between the benefits of both parties; however, determining differentiated toll discounts for expressways to reach this balance is difficult. Methods: (1) Based on consumer surplus theory, key factors affecting freight route selection are identified using the preference survey of traveling behavior, and a bi-level programming model is proposed for determining differentiated toll discounts, incorporating assumptions and constraints. (2) The upper model, considering truck cost and travel time, is a surplus maximization model for expressway operators. It is solved using a novel algorithm enhanced by combining a genetic algorithm with simulated annealing. In the upper model, a lower limit on the financial revenue targets of highway operating enterprises is included the constraints to avoid overflow of lower bound returns during the iteration process. (3) The lower model leverages a logit-based stochastic user equilibrium allocation model for multiple vehicle types under elastic demand, solved using the Frank Wolfe algorithm. A generalized impedance function considering economic and time costs is established in the lower model to demonstrate the impacts of road conditions on truck travel. Cost weighting coefficients are introduced, and calculation methods and recommended values are proposed to integrate economics and time costs. (4) Detailed execution steps are provided for solving algorithms of the upper and lower models. The model also introduces model convergence criteria to optimize the iteration efficiency of the solving algorithm. A fitness function is proposed based on the financial lower bound target, and the upper model is transformed into a minimum value problem, eliminating the constraint of discounted rates. Results: The feasibility of the model is validated using toll collection data of expressway and link traffic data of highways, with three instance highway sections. A reasonable range suitable for implementing differentiated toll discounts can attract trucks back to the expressway, and increasing the daily average traffic volume for each vehicle type. After 43 iterations, the upper model achieves a stable function value. The toll discount rates for small trucks, medium trucks, heavy trucks, and extra-heavy trucks on the instance expressway fall within the ranges of 78.68%-86.27%, 55.82%-65.82%, 47.90%-54.81% and 47.52%-48.31% respectively; consequently, the average truck flow on the expressway increases by 12.24%. Conclusions: The conclusion demonstrates that the bi-level programming model can accurately determine the toll discount range for trucks on expressways; however, even with a discount rate of 4.7% for oversized trucks on nearly 100 km of the actual expressway, attracting all oversized trucks to return to the expressway remains challenging. Fuel and toll fees remarkably impact travel path selection within the generalized impedance function; moreover, the same toll discount produces notable differences in implementation effects across truck types. The research provides support for developing differentiated toll policies for expressways, as well as their subsequent optimization and adjustment.