1. Introduction
Hybrid electric vehicles (HEVs) have a large advantage in energy emission performance compared to internal combustion engines, and their continued voyage is better than that of pure electric vehicles, which can effectively improve transport efficiency. The main part parameters of a hybrid car include the engine, driving motor, transmission as well as main deceleration, and the performance difference of its car’s power, as well as fuel economy, which largely depends on the rationality of the power transfer system [
1]. The main purpose of HEVs is to continuously reduce the emission of cars, so it has a high economic requirement for fuel. In parallel and hybrid HEVs, when the energy of the batteries is insufficient, the batteries will be involved in the conversion problems of their energy efficiency, and then the phenomenon of increased oil consumption of the cars occurs. The diversity of the design of the composition structure of the power system (as well as the state of vehicle driving, individual driver differences, and so on) can cause different degrees of impact on the transformation of the efficiency of HEVs. The current research focus on the energy consumption issues for hybrid cars is mainly on their energy management, i.e., finding the most suitable car operation mode to improve their energy consumption issues. The improvement of engine efficiency can effectively achieve its goal of fuel economy, and improving the efficiency of automotive batteries can, to some extent, ensure a reduction in energy consumption. The adaptive concept is often applied in the battery condition assessment, which can effectively ensure that the state of charge (SOC) can reach the maximum level and, thereby, reduce energy consumption. At the same time, in the process of vehicle planning, its supply chain problem is mostly transformed into a double objective linear programming problem, and the setting of the relevant economic objective functions and conditional parameters is reasonable to achieve the cost minimization of the planned route. The non-dominated genetic algorithm can effectively set constraints and reduce the problem of size constraints in the process of the car’s energy consumption. On the basis of guaranteeing the dynamic performance of vehicles, reducing fuel consumption, elevating the operation efficiency of the vehicles, and improving them, are the most important contents of this current research. The high range of parameter conditions and engineering constraints, as well as the high number of influencing factors, should strengthen the objective optimization of hybrid parameters and the parameter objective design for their performance development needs. The energy consumption parameters of hybrid electric vehicles are highly nonlinear and discontinuous and gradient-based optimization algorithms are often difficult to produce good application results when performing problem-solving [
2,
3]. The NSGA-II algorithm, as a global optimization search algorithm, has a better global search ability, problem-solving ability, and performs parallel processing. The NSGA-II algorithm can effectively determine the evaluation indicators and objective functions for the requirements of the power and fuel economy in the analysis of automobile energy consumption, taking into account factors such as vehicle mass, transmission system quality, and transmission system efficiency, and achieving the construction of multi-objective optimization models for power transmission systems. Additionally, this algorithm can solve the objective function through mutation operation and optimal solution calculation when optimizing speed and accuracy, so it can achieve the minimization of energy consumption on the basis of grasping the vehicle’s power performance. In this study, based on the performance advantages of the non-dominated sorting genetic algorithm (non-dominated sorting genetic algorithm-II generation, NSGA-II), the multi-objective optimization theory and methods are used to transform the energy optimization problem of hybrid electric vehicles into a multi-objective solution problem with the smallest energy consumption. With the help of other scholars for the analysis of automobile energy consumption problems, and with the help of genetic algorithms which focus on the limitations of the algorithm accuracy effect, the research also analyzes the influencing factors that affect the efficiency of automobile energy consumption and purposefully selects the parameters of the power vehicle driveline for optimal selection, in the hopes of better research on automobile energy consumption and the design of related strategies to improve its power and economy.
2. Related Work
In the research of automobile fuel cell engines, the classical Pontryagin minimum principle (PMP) and Dynamic programming (DP) theory can be used to improve the efficiency of fuel application. The practicability of these two theories has been verified by practice. However, this method needs to know the driving conditions so as to judge the actual driving conditions of the vehicle and, finally, apply them to the actual vehicle. In the study of fuel cell engine systems by Fu J et al., adaptive regulation and PMP could manage the engine energy in layers and estimate the future vehicle power demand according to the Energy Management Strategy (EMS). Compared with the global optimization method, the EMS maximized the capacity of vehicle batteries and improved fuel economy [
4]. The optimal power of hybrid electric vehicles can be solved according to the PMP principle. On this basis, Shi et al. introduced a neural network to solve the parameters of power prediction and adopted an adaptive adjustment method to calculate the SOC of the battery. The simulation results showed that the hybrid improved method could evaluate the vehicle speed and had good power prediction ability. While ensuring the economic cost of the vehicle, it also ensured the sustainability of battery charging [
5]. In the study of the battery life of electric vehicles, the way to increase vehicle mileage includes the improvement of energy efficiency. Zhang Q. G. found that the multi-island genetic algorithm (GA) could optimize the parameters of the control strategy in the hybrid electric vehicle, thus improving the accuracy of the model control strategy. The results showed that this method could improve the effective utilization rate of automobile energy. In the energy consumption optimization of hybrid vehicles, it was necessary to focus on the oil pump components in the power system. The efficiency of the oil pump had a significant impact on the efficiency of the hybrid vehicle [
6]. Huang M. and other researchers used the NSGA-II algorithm to adjust the proportion of the oil pump rotor to achieve the adjustment of the oil supply system, thus improving its functional accuracy. The prototype test results showed that the proportion designed by this method is reasonable [
7].
The energy consumption solution of hybrid vehicles can be considered as the solution to multi-objective optimization problems, mainly including mathematical programming and heuristic intelligent algorithm [
8]. The mathematical programming method requires the variables to meet the requirements of continuous differentiability, which leads to the poor universality of the method. Heuristic intelligent algorithms include the genetic algorithm, ant colony algorithm, particle swarm algorithm, etc. These methods have a strong global search ability. It has wide applicability in solving high-latitude nonlinear problems [
9]. S. Kumar et al. used fuzzy mathematics to establish the model and then adopted a genetic algorithm to optimize the parameters of the mathematical model. In the evaluation and prediction of the relationship between parameters and targets, the predicted value of the model was slightly different from the experimental value, indicating that the newly established model had a good prediction performance [
10]. The combination of different heuristic algorithms also has advantages in solving multi-objective optimization problems. Xue B. applied the ant colony algorithm and the GA to wireless power transmission. For the multi-objective optimization of energy transmission and information transmission, this method could optimize both objectives at the same time and had a high efficiency and information transmission capacity [
11]. The vehicle battery system has a strong correlation with EMS. To prolong the life of the vehicle battery system, on the basis of the GA and other methods, Liang J. and others used the PMP principle to optimize the function and constructed the cost function as the objective optimization function. PMP had good performance after optimization and could be used to evaluate the durability and economic cost of the battery [
12]. Dutta J. solved the multi-objective vehicle planning problem with the help of the cluster main path and fully considered the operating costs and fuel consumption to reduce the vehicle’s pollution emissions. The cluster concept and multi-objective model were used to realize the selection of the best planning route and linked customers to the planning route [
13]. The decision information is judged and selected optimally with the help of the strength Pareto evolutionary algorithm and the non-dominated genetic algorithm (NSGA). Yuen T. J. used evolutionary algorithms to achieve multi-objective optimization and adopted constraints to standardize the powertrain design. The non-dominated sequencing genetic algorithm and differential constraint algorithm were used to analyze the motor transmission ratio, motor torque, and wheel pressure ratio. The results showed that this method could complete the convergence in a short time and greatly reduce the energy consumption of vehicles [
14]. Jin L. et al. proposed an improved NSGA-II algorithm to analyze the search problem of motor multi-objective parameters. A redundant mutation operator was used to improve the recognition performance of non-dominant individuals. The rotor clearance, rotor tooth width, and other parameters affecting the motor performance were optimized. The optimization model based on the maximum output shaft torque was established. The experimental results showed that the optimized parameters could shorten the 100-km acceleration time in the background experimental simulation environment. The battery SOC value had good stability and was suitable for the design of the motor system. Electric vehicles had a relatively wide application space due to the advantages of distributed energy storage [
15]. Wei H. proposed to maximize the diversity of the NSGA-II to achieve the relationship between the charge distribution, the charging cost, and the goal optimization and to dynamically adjust the time. The results showed that this method could improve the durability and practicability of electric vehicles, reduce the over-dependence on data, and have high applicability [
16]. Dao D. N. proposed an evolutionary algorithm based on the strength Pareto and multi-objective optimization parameters, which was an innovative combination of the NSGA-III algorithm and SPEA/R algorithm. The benchmark function was the test tool and the suspension system was the simulation environment. The results showed that the algorithm had good applicability and potential in parameter optimization [
17].
In summary, enhancing the research on energy management strategies for fuel cell engines can effectively achieve the estimation of power demand. Many scholars use neural network algorithms, genetic algorithms, and multi-objective algorithms to study the issue of energy consumption. In addition, the NSGA-II algorithm has received more attention due to its advantages in solving the multi-objective parameter problem, but most of the problems focus on solving the parameters and battery cost, and less consideration is given to the factors affecting the automobile’s power. As for how to carry out the analysis of automobile energy consumption problems, D. Shi et.al., in the literature [
7], solve the power prediction, Zhang Q. Y. et.al., in the literature [
8], carry out the control strategy of hybrid cars with the help of the multi-Island GA parameter optimization and Huang M et.al., in the literature [
9] scale the rotor of the oil pumps with the help of NSGA-II algorithm. The research content of the literature is to analyze the impact on the energy consumption and operation efficiency of hybrid cars, different from that, the research translates the energy consumption problems of the cars into multi-objective solution problems and performs efficiency optimal problem-solving from the impact factor evaluation, the control of the power index, and so on, instead of analyzing them only from a single dimension. In the analysis of the objective problem of energy optimization for hybrid electric vehicles, Liang J et al., in Reference [
13], use the principle of PMP for the optimization of the cost objective function and construct the cost function as the objective optimization function. In the literature [
15] Yuen T. J. et.al. combine the Pareto algorithm with the NSGA algorithm to realize the judgment of decision information, Jin L et.al. then implement the improvement of the NSGA-II algorithm with the operation of redundant mutation operators and realize the improvement of the motor multi-objective parameters search efficiency. In the literature [
16], Wei H et.al. performed a charge cost analysis with the NSGA-II algorithm for better dynamic regulation. Most scholars conduct automobile problem analysis with the help of the NSGA-II algorithm, indicating its better application efficacy. Different from other scholars in the NSGA-II algorithm, to improve the research of the concept of the energy impression unit of hybrid cars to conduct the problem, the factor analysis from the nature of its problem, to some extent, reduces the computational effort but also reduces the experimental error caused by the uniformity of the parameter environment. Therefore, combined with the above analysis, the research is based on the advantages of the NSGA-II algorithm to construct the objective problem based on the parameter indicators that affect the power and economy of hybrid electric vehicles, to control the constraints of the parameter conditions, to establish the constraints that meet the practical needs, to use the economy, and power as the criterion goals for the optimal value solution of the problem to achieve its energy consumption optimization effect.
4. Application Evaluation of Hybrid Vehicle Energy Consumption Optimization Strategy Based on NSGA-II Genetic Algorithm
The research analyzes the external feature-fitting data of the selected engine. The external characteristics are analyzed through programming with MATLAB software, and the engine torque and power are analyzed at different engine speeds.
Table 3 presents the specific data.
Table 3 shows that when the engine speed is less than 4000, the corresponding engine matrix shows an overall upward trend. After the rotational speed exceeds 4000, the engine matrix value shows a downward trend and the maximum value reaches 103.3 (r/min). The relevant engine power also increases first and then decreases and the engine speed is 5600 N.m. The change in fuel consumption rate reaches the minimum value of 265.4 when the engine speed is 4200. Then the engine efficiency before and after the improvement of the multi-objective optimization algorithm is statistically analyzed.
Figure 5 shows the specific results.
Figure 5 shows that before applying the multi-objective optimization algorithm, the working efficiency of the engine changes in varying degrees with the increase in working time. The adjustment of working points is large. After algorithm improvement, the working points of the engine are mostly concentrated in the high-value area, which effectively reduces the energy consumption and improves the efficiency by 13.25%.
Figure 6 shows the convergence curve changes before and after the improvement, labeled as population points.
Figure 6 shows that the convergence curve of population evolution under the initial parameters is relatively scattered. When the acceleration time is greater than 15 s, data loss occurs, the population converges to a small region, and the convergence of the Pareto front is poor. The proposed algorithm is in the optimal solution set when the number of iterations reaches 200. The individuals of each group are evenly distributed and can better maintain the edge individuals, achieving satisfactory optimization results. The Pareto optimal solutions obtained correspond to the corresponding points and there is no difference between good and bad. The ADVISOR simulation system is used to simulate the power performance and fuel economy of the engine. It is optimized to analyze the multi-objective optimization control performance of hybrid electric vehicles. The dynamic characteristics of the vehicle can be fitted by optimizing the gear ratio before and after.
Figure 7 shows the relevant dynamic characteristic curve.
Figure 7 shows that the power factor displayed by the different vehicle gears at different speeds is quite different. Specifically, after the improvement, the power factor of the first gear increases by 6.74%, and the power factor of the third gear increases by 14.28%. The dynamic characteristics of gears 1~3 have been greatly improved. The average value of the power factor of the fourth gear, before and after improvement, is 0.48 and 0.45, respectively. There is an average difference range of 2.15% when using the fourth gear in the analysis of the vehicle’s fuel consumption performance. The slope of the fuel consumption curve of the fourth gear at constant speed before the improvement is significantly greater than after the improvement. The maximum fuel consumption reaches 6.45 L/km at 120 km/h. After optimization, the fuel consumption of the fourth gear vehicle at 40 km/h per 100 km decreases by 3.75%. The fuel consumption per 100 km at 80 km/h decreases by 4.92%. The fuel economy has been greatly improved. The results show that this method can improve the power performance of low-grade vehicles and reduce the energy consumption of high-grade vehicles.
Table 4 compares the target data of hybrid electric vehicles before and after the algorithm optimization.
Table 4 shows that the dynamic index and economic index change to a certain extent after the algorithm optimization. Among them, the starting acceleration time and fuel consumption per hundred kilometers have decreased to varying degrees after optimization. The value of mixed fuel consumption at 100 km has changed from 5.41 to 5.21, with a decrease of 1.4%. The maximum climbing gradient of the whole vehicle after improvement is 33.9%. The constant speed fuel consumption of the whole vehicle in different gears has decreased after improvement. The overall performance of the car has been improved. The power factor of direct gear is more than 15%. Therefore, the multi-objective control optimization strategy proposed in the study has good applicability and rationality. We evaluated the vehicle power performance of the NSGA-II genetic algorithm proposed in the study and analyze it from the aspects of climbing ability, acceleration status, and energy consumption. The comparison algorithms are genetic algorithm, particle swarm optimization (PSO), and model predictive adaptive control (MPD) based on the model’s prediction. The results are shown in
Figure 8.
The results in
Figure 8 indicate that, in terms of climbing ability, the performance of the four algorithms from large to small is: NSGA-II > MPD > PSO > GA. Among them, the average number of climbing degrees of the PSO algorithm and the GA is small at different driving speeds, and the overall node fluctuation is more obvious. Although the MPD algorithm performs well and the overall curve changes smoothly, its climbing curve slope is smaller than the NSGA-II proposed in the study. In terms of vehicle acceleration status, the NSGA-II algorithm and MPD algorithm spend less time on acceleration improvements, and the overall performance is relatively stable. When the time is greater than 13.2 s, the NSGA-II algorithm still has a different amplitude of 0.64% compared to the MPD algorithm. In terms of fuel consumption, the proportion of fuel consumption for the four algorithms varies from high to low: GA > PSO > MPD > NSGA-II. The overall fuel consumption of the NSGA-II algorithm proposed in the study is relatively low, and there are fewer fluctuations under power acceleration. The above results indicate that the NSGA-II algorithm can achieve energy consumption optimization while retaining the power of the vehicle and maintaining a relatively stable driving state of the power vehicle.