## 2 Literature Review  
The mathematical foundation for researching highway toll rate optimization schemes is the traffic network equilibrium model, which is typically formulated as a bi-level programming model. Generally, the upper level aims to maximize the benefits of the highway network or toll revenue, while the lower level aims to minimize the travel time costs for highway users. For instance, [PERSON] et al. [5] and [PERSON] et al. [6] established a bi-level programming model with the upper level maximizing highway revenue and the lower level minimizing user travel impedance, based on the perspectives of highway managers and travelers. [PERSON] et al. [7] proposed a bi-level programming model to solve optimal tolls based on the equilibrium of heterogeneous household residential location choices, with the upper-level objective being the minimization of the total city system travel time and the lower-level planning problem combining residential location choice and traffic distribution using fixed-point theory. [PERSON] et al. [8] proposed optimizing dynamic credit strategies and constructed a bi-level programming model based on the Stackelberg game between road managers and travelers, adjusting the path choice behavior of users with high travel times to achieve traffic network flow allocation and carbon reduction targets. [PERSON] et al. [9] combined parking fees with congestion pricing to construct an elastic demand user equilibrium model under dual constraints, designing a pattern search algorithm for the solution. The results indicated that combined pricing promotes a more balanced distribution of road network traffic, alleviates congestion on tolled links, and suppresses some travel demand. Lots of research [10; 11; 12; 13; 14; 15] has established bi-level programming models to solve road pricing schemes. In recent years, with the development of theoretical and practical aspects of differentiated highway tolls, various studies have explored differentiated pricing methods based on time links, vehicle types, and road links [16]. Additionally, similar to the bi-level programming modeling approach, there is the multi-objective optimization pricing method. The main difference is that the former separates objectives into different levels, while the latter sets the objectives of different stakeholders at the same level, optimizing with different weights. For example, [PERSON] [17] conducted real-vehicle tests to study the driving conditions and fuel consumption characteristics of six types of trucks and established a carbon emission calculation model based on driving speed for different road types. The study also established a multi-objective optimization model for carbon reduction benefits, operational benefits, and travel impedance, determining the optimal toll scheme. The pricing method based on bi-level programming models provide theoretical and empirical support for highway toll rate optimization schemes. However, two main issues persist. On one hand, the lower-level model in bi-level programming describes user path choice behavior but remains based on generalized travel cost, ignoring the influence of individual behavioral preference. On the other hand, bi-level programming models struggle to capture the dynamic interrelationships among highway toll rate, travel demand, and toll revenue. Highway path choice behavior is a key variable linking toll rate, demand volume, and toll revenue, and it is a crucial aspect of exploring their relationships. The existing research on path choice behavior is predominantly based on random utility theory, assuming that travelers are perfectly rational, have access to all travel information, and make decisions according to the principle of utility maximization [18; 19; 20]. For instance, [PERSON] et al. [21] utilized household travel survey data from Texas to establish a nested multinomial Logit choice model, investigating the influencing factors on the use of toll roads and High-Occupancy Vehicle lanes.