# Multi-Objective Optimization for Plug-In 4 WD Hybrid Electric Vehicle Powertrain
## 1 Introduction
The evolutionary algorithm has achieved great success in solving power system's multi-objective optimization problems [16; 23; 24; 25], e.g., a strength Pareto evolutionary algorithm is used to solve the multi-objective reactive power price clearing problem [23]; a novel-efficient evolutionary-based multi-objective optimization approach is proposed to solve multi-objective optimal power flow problems [16; 24] and the multi-objective strength Pareto evolutionary algorithm 2+ has been employed to solve the congestion management problem [25]. Therefore, it has become an important method for solving multi-objective optimization problems. Parameter optimization of PHEVs is related to the energy management strategy, and energy management strategies need to be developed before parameter optimization. At present, the research on the energy management strategy for PHEVs mainly focuses on the development of the advanced optimization algorithm, such as the algorithm based on the minimum equivalent fuel consumption [26; 27; 28; 29], the dynamic programming algorithm [30; 31; 32], stochastic dynamic programming [33], the algorithm based on convex optimization [2; 34] and the model predictive control algorithm [35; 36; 37; 38]. Although the above-mentioned optimization algorithm can obtain the local or global optimum, it is difficult to apply to real vehicle control for hardly knowing the driving cycles beforehand or the large amount of calculation. However, the rule control strategy based on the charge depleting-charge sustain (CD-CS) mode does not need to know the driving cycles beforehand, and the calculation is small, so it is widely used in the real vehicle control of PHEVs. As a summary of the entire literature review, in order to complete the plug-in 4 WD HEV's parameter optimization well, the simultaneous optimization for the main parameters of powertrain and control strategy is necessary, multi-objective optimization should be taken into account and the rule control strategy based on the CD-CS mode for plug-in 4 WD HEVs should be developed. However, there is still a large shortage for plug-in 4 WD HEV's parameter optimization. Firstly, it is still challenging to select reasonably multi-objective functions, which can evaluate the optimal performance of plug-in 4 WD HEV well. Secondly, although the evolutionary algorithm has achieved great success in solving power system's multi-objective optimization problems, it rarely applies to solve plug-in 4 WD HEV's multi-objective parameter optimization problems. Finally, the rule control strategy based on the CD-CS mode for plug-in 2 WD hybrid electric vehicles is mature, but there is little literature on the rule control strategy based on the CD-CS mode for plug-in 4 WD HEVs. To address the challenges summarized above, in this study, the energy management strategy based on the CD-CS mode for plug-in 4 WD HEV is developed. Then, the reasonably multi-objective functions, which are composed of electric energy consumption under the CD stage, fuel consumption under the CS stage and acceleration time from 0-120 km/h, are established. Finally, the evolutionary based NSGA-II (non-dominated sorting genetic algorithms-II) approach is selected to simultaneously optimize the parameters of the powertrain and control strategy. The outline of this paper is as follows. The structure and dynamic model of the powertrain are provided in Section 2. The energy management strategy based on the CD-CS mode is developed in Section 3. Mathematical model of multi-objective optimization is built in Section 4. Optimization algorithm is proposed in Section 5. Optimization results are discussed in Section 6. Finally, conclusions are summarized in Section 7.