# Multi-Class Freeway Congestion and Emission Based on Robust Dynamic Multi-Objective Optimization
## 2 Literature Review  
Considering the problems solved in this paper, a literature review will be conducted below from four aspects: freeway models, freeway traffic control strategies, robust dynamic multi-objective optimization algorithms and Pareto front exploration. Traffic flow theory is fundamentally applied in fields such as intelligent traffic system, traffic management and control, traffic engineering design, and so on [3]. In general, traffic flow models can be divided into microscopic and macroscopic models. Macroscopic models often contain fewer parameters than microscopic models, which will be used in this paper. Partial differential equations are used to describe the macroscopic traffic flow models. These macroscopic traffic flow models can be classified into first-order, second-order or higher-order models. Some models, such as the Lighthill-Whitham-Richards (LWR) [4] and cell transmission model (CTM) [5], are representative of first-order models, while the METANET model is a common second-order traffic flow model [6]. Since the speed variations of vehicles and the reaction time of drivers are not considered, capacity decreases and oscillations due to freeway congestion cannot be reflected in first-order models. However, such deficiencies can be remedied in second-order traffic flow models, since second-order models can reproduce highly realistic traffic phenomena. In second order models, the real traffic networks can be reproduced by the METANET model more accurately. For instance, the paper [7] extended a multi-class macroscopic traffic flow model, METANET, and proved that the model can lead to better fitting results because the heterogeneity of the traffic flow network structure was taken into account. Based on the above, this paper integrates the multi-class model proposed in paper [7] and a dynamic model proposed in paper [8]; therefore, a more comprehensive multi-class macroscopic traffic flow model is proposed. Variable speed limits (VSL) and ramp metering (RM) are the most common strategies used in traffic control [9]. Based on fixed speed limits, VSL is a mainline control strategy where both frequent and incidental traffic congestion are considered. By using this strategy, dynamic speed limit suggestions can be provided to drivers in advance; therefore, the mainline flow upstream of the bottleneck can be well-managed to maximize the traffic throughput and prevent traffic congestion effectively [10]. In paper [7], a VSL-based cell transmission model was proposed to control the main roadway of a freeway, and the travel time was found to be reduced effectively. RM considers the traffic conditions and capacity on the downstream of the mainline. By using this strategy, the vehicle proportion of the ramp inflow can be determined without causing mainline traffic breakdown, therefore improving the network operation efficiency [11]. However, freeways still cannot be well-managed and controlled based on a single traffic control strategy due to the sophistication of expressway systems. Therefore, integrated control strategy is one of the present research directions [12]. The main idea is to regulate the expressway through coordinating more than one traffic control method. In paper [13], an integrated strategy was developed to coordinate multiple on-ramps and maximize the motorway bottleneck throughput. The limitations of the model in paper [13] include that only the throughput was taken into account, while the differences in vehicle classes were neglected. In conclusion, there are few studies on the integrated control strategy of VSL and RM on the aspect of multi-class expressways. Therefore, the research in this paper is meaningful. In the process of optimizing practical problems, normally the original problem will be described as dynamic optimization problems (DOPs) when the environment changes dynamically [14].