# Freeway Traffic Congestion Reduction and Environment Regulation via Model Predictive Control
## 2 Literature Review  
Model predictive control (MPC) is a new control algorithm that was proposed in the late 1970s. It is a control algorithm based on model prediction [3]. When a traffic light is placed at the on-ramp of a freeway, a ramp metering is set-up. The traffic light turns over between the red and the green phase. The number of vehicles that enters the freeway through the on-ramp is controlled by the variation of the timing of the red and the green phases. In order to keep the traffic density below the critical density, the inflow of vehicles onto the freeway is limited by the ramp metering set-up. Then, the traffic breakdown and congestion is avoided. A waiting queue of vehicles is formed at the on-ramp whenever the traffic demand is larger than the number of cars allowed to enter the freeway [4]. MPC is a commonly-used method in freeway control [5; 6]. It is usually solved through resilient back propagation [7] and sequence quadratic programming [8]. MPC is quite often designed for linear or linearized system with linear constraints in order to solve optimization problem easily. However, the on-line optimization problem in MPC with the characteristics of non-linearity, non-convex and complicated constraints is considered in some existed research recently. For example, the authors of [2; 9], introduce genetic algorithm (GA) into MPC to realize on-line optimization. In order to acquire better performance for freeway control, some studies use multiple indicators for evaluation. These performance indicators are considered as objectives in optimization. Some of them are conflicts with each other [10; 11]. However, most of the papers adopt weighted sum methods to transfer the multi-objective problem into single-objective problem [12; 13]. However, it performs worse in solving multi-objective problems. Moreover, repeated experiments are necessary to determine proper weighs. Thus, the authors of [14] adopt a fast and elitist multi-objective genetic algorithm (NSGA-II) [15], which is verified as an effective algorithm to alleviate congestions. Considering that the essence of the on-line optimization problem in MPC at each control is a dynamic multi-objective problem, a new solution needs to be provided by the controller in each control step. Therefore, static multi-objective optimization algorithms, such as NSGA-II, cannot rapidly respond to the change of environment. Thus, dynamic multi-objective optimization algorithm is used to realize on-line optimization in model predictive control at each control step. As for dynamic multi-objective optimization algorithm (DMOAs), it is important to maintain or increase population diversity to search for new Pareto front in the current environment. It spends a long time to be converged. Prediction is an effective strategy to shorten the time of convergence [16]. It tracks the changed Pareto front through historical individuals to provide guidance direction in evolution, which also increases the diversity of population. The authors of [17] first employ prediction models in economics, such as AR and VAR. But the premise is that historical data have statistical characteristics. The authors of [18] then propose four general methods, RND, VAR, PRE and V&P. They are easier to operate than AR and VAR. However, the performance of distribution they considered and the historical information they offered are limited. The authors of [19; 20] design a strategy called clustering prediction. The individual elements of prediction are replaced with centers of clustering, which are regarded as the representatives of the Pareto front. But the performance is related to the method of clustering. We will discuss model predictive control method based on dynamic multi-objective optimization algorithm in the next section. Traditional, the minimum reference deviation, minimum variation or cost of some parameters, minimum control action is used as the multiple objectives in model predictive control, and the multiple objectives are combined as a single objective problem by the weight sum method.