# Multi-Class Freeway Congestion and Emission Based on Robust Dynamic Multi-Objective Optimization
## 2 Literature Review
In general, due to the real-time traffic flow variations on the entrance of the mainline and ramps, real-time oscillations often occur on the aspect of the traffic network states, such as density, flow, and speed, while dealing with the optimization problems of multi-class freeway congestion and emissions simultaneously. Therefore, freeway network control schemes need to be changed accordingly. The real-time variations of the demands, the network states and the control schemes were denoted in the form of parameters or performance indicators in DOPs. Moreover, the paper [15] described that historical environmental conditions and corresponding optimal solutions needed to be recorded and stored in the optimization process of DOPs. Therefore, obvious improvements in the evolution efficiency and search performance of the algorithm can be obtained through reusing these reserved solutions when detecting a similar dynamic environment. At present, robust dynamic optimization methods have been adopted by many researchers to solve DOPs, mainly including dynamic single-objective methods [16] and static multi-objective robust optimization methods [17]. However, research on robust dynamic multi-objective optimization methods is still limited. Hence, it is necessary to extend the research on robust dynamic multi-objective optimization algorithms extensively. While dealing with DOPs, the major challenge is to determine the distribution of Pareto fronts because of the irregular Pareto optimal front distribution nature. This is due to the fact that the robust dynamic solution sets, which constitute the Pareto optimal front, often change with the environment during the robust dynamic optimization process. Therefore, the research on the exploration of Pareto fronts will be reviewed below. In paper [18], it is pointed out that clustering methods can help multi-objective optimization algorithms describe the Pareto front, detect the distribution of the solutions over the objective space, track the Pareto front continuously and guide search directions by the use of cluster centers, thereby leading to an increase in population diversity and convergence speed. The k-means method, proposed in paper [19], is one of the most widely used clustering algorithms which belongs to hard clustering. The principle of hard clustering is to divide data points into specific clusters, and the corresponding relationship between data points and clusters is unique. In paper [20], the k-means clustering algorithm was used to determine the irregular Pareto front shapes in a multi-objective optimization algorithm. By dividing the population into several cluster sets, the overall structure of the Pareto front can be discovered, which makes the population evolve in different cluster centers, thereby improving the diversity and convergence speed of the NSGA-II algorithm. However, the number of initial cluster centers in the k-means method needs to be determined by empirical methods. Moreover, random generation of initial cluster centers may lead to unstable clustering results. It is proposed in paper [21] that fuzzy clustering is one of the most widely used soft clustering algorithms which can accurately describe the mediation of the data samples. Among the fuzzy clustering methods, the fuzzy c-means clustering method, which combines traditional clustering algorithms with fuzzy theory, can provide more flexible clustering results [22]. Considering the large dimension of the objective spaces in the multi-objective optimization problems, in most cases, the solutions contained in the Pareto front are difficult to classify into a specific cluster center. Therefore, in this case, it is not reasonable to use hard clustering methods to divide the solutions into a specific cluster. Accordingly, it might be a better choice to use soft clustering methods instead to divide the samples into each cluster center according to a certain proportion. However, there are still two issues which need to be remedied.