###### Abstract  
Currently, the researches on the regenerative braking system (RBS) of the range-extended electric vehicle (R-EEV) are inadequate, especially on the comparison and analysis of the multi-objective optimization (MOO) problem. Actually, the results of the MOO problem should be mutually independent and balanced. With the aim of guaranteeing comprehensive regenerative braking performance (CRBP), a revised regenerative braking control strategy (RRBCS) is introduced, and a method of the MOO algorithm for RRBCS is proposed to balance the braking performance (BP), regenerative braking loss efficiency (RBLE), and battery capacity loss rate (BCLR). Firstly, the models of the main components related to the RBS of the R-EEV for the calculation of optimization objectives are built in MATLAB/Simulink and AVL/Cruise. The BP, RBLE, and BCLR are selected as the optimization objectives. The non-dominated sorting genetic algorithm (NSGA-II) is applied in RRBCS to solve the MOO problem, and a group of the non-inferior Pareto solution sets are obtained. The simulation results show a clear conflict that three optimization objectives cannot be optimal at the same time. Then, we evaluate the performance of the proposed method by taking the individual with the optimal CRBP as the final optimal solution. The comparation among BP, RBLE, BCLR, and CRBP before and after optimization are analyzed and discussed. The results illustrate that characteristic parameters of RRBCS is crucial to optimization objectives. After parameters optimization, regenerative braking torque works early to increase braking energy recovery on low tire-road adhesion condition, and to reduce the battery capacity loss rate at the expense of small braking energy recovery on the medium tire-road adhesion condition. In addition, the results of the sensitivity analysis show that after parameter optimization, RRBCS is proved to perform better road adaptability regarding the distribution of solutions. These results thoroughly validate the proposed approach for multi-objective optimization of RRBCS and have a strong directive to optimize the control strategy parameters of RBS. range-extended electric vehicle; regenerative braking system; multi-objective optimization; regenerative braking control strategy; NSGA-II +
Footnote †: journal: Applied Soft  
Present research mainly focuses on the balance and optimization between braking performance and braking energy recovery of RBS. Literature [5] focuses on the control algorithm of the braking energy regeneration system of an electric bus in a safety-critical driving situation. A sliding-mode controller based on the exponential reaching law for the antilock braking system is developed in the literature [6]. With the aims of regeneration efficiency and braking safety, three different control strategies are studied in [7; 8]. Similar studies are available in the literature [9; 10; 11; 12], which develop the braking torque allocating method to improve braking performance and energy regeneration. In the literature [13], a hierarchical control strategy is proposed, taking battery aging into consideration to ensure vehicle braking safety, recover more energy, and protect components from aging. Cooperative regenerative braking control is proposed in the literature [14] to recover optimal braking energy while guaranteeing the vehicle lateral stability. The longitudinal friction between the road and the tires is estimated and controlled while optimizing regenerative braking in the literature [15]. Moreover, battery is the most sensitive component in the powertrain of R-EEV, so a large regenerative charging current (RCC) can cause damage to the battery and reduce its service life [13]. However, current control strategies pay less attention to the impaction of regenerative braking current (RCC) on the battery state of health and rarely follow this essential characteristic of the multi-objective problem. How to optimize the control parameters of RBCS is mostly derived from the developer's experience.