# Multi-Objective Optimization for Plug-In 4 WD Hybrid Electric Vehicle Powertrain
## 1 Introduction  
Owing to regulations on fuel economy and emissions become more and more stringent, the development of electrified vehicles in recent years have been a surging trend [1; 2]. Plug-in hybrid electric vehicles (PHEVs), which achieve a longer all-electric range compared to conventional hybrid electric vehicles and have no driver range anxiety compared to pure battery electric vehicles, become an important research direction in the field of electric vehicles [3; 4]. The parameters of PHEV's powertrain have a significant impact on the electric energy consumption, fuel consumption and dynamic performance of the vehicle. Therefore, parameter optimization of the powertrain is the basis of the vehicle development. The research on PHEV's parameter optimization has gone through the following process. In the initial stage, scholars did not realize the problem that powertrain parameters and control strategy parameters coupled and affected vehicles' performance together. Therefore, the parameter optimization during this stage is mainly focused on independent optimization of powertrain parameters, instead of joint optimizing the parameters of powertrain and control strategy [5; 6]. With the in-depth research, attention has been paid to the coupling problemof powertrain parameters and control strategy parameters. Then, simultaneously optimization of powertrain parameters and control strategy parameters begins to appear in some literature [7; 8; 9]. Actually, literatures [5; 6; 7; 8; 9] take parameter optimization as a single objective optimization problem, the parameters of PHEV are optimized to only improve the economy of the vehicle. However, the objectives of vehicle economy, power system cost, emission and power performance usually conflict with each other. The optimization only considering the vehicle economy will result in achieving optimal economic performance at the expense of other objectives that conflict with it. Therefore, in recent years, multi-objective optimization has been applied to optimize PHEV's parameters. In reference [10], energy storage system costs and fuel economy are considered as the objective functions for hybrid electric vehicle's battery size optimization. Reference [11] presents a multi-objective optimization methodology for vehicles design considering the parameters for design and macro level operating strategy. Reference [12] applies multi-objective algorithms (minimization of the couples cost and fuel, cost and LCA (life cycle impact) CO\({}_{\text{2 eq}}\), fuel and LCA CO\({}_{\text{2 eq}}\)) to perform the powertrain components optimization. Reference [13] takes powertrain cost, fuel consumption and emission as multi-objectives to optimize the parameters of powertrain and control parameters simultaneously. In [14], the usage cost, acceleration performance and mode discrimination of the whole vehicle under a new European driving cycle (NEDC) are considered as the optimization objectives to optimize the transmission system of a new hybrid power system. Reference [15] aims at minimizing the cost of the power supply and the energy flow of batteries, and adopts the convex optimization algorithm to optimize the power supply's parameters and energy management strategy. Multi-objective optimization and its applications have been an important area of research for over two decades now [16]. The key of solving the multi-objective optimization problem is how to get the Pareto solution set. Traditional algorithms for solving multi-objective optimization problems include the linear weighting method [17], constraint method [18], mini-max method [19], goal programming method [20] and goal satisfaction method [21]. In order to get the Pareto solution set, these methods need to run many times, which reduces the efficiency of the algorithm. Evolutionary algorithms are a group-based global optimization algorithm that simulate the evolution process of natural organisms [22].