A Review of Hybrid Vehicles Classification and Their Energy Management Strategies: An Exploration of the Advantages of Genetic Algorithms

Abstract

This paper presents a comprehensive analysis of hybrid electric vehicle (HEV) classification and energy management strategies (EMS), with a particular emphasis on the application and potential of genetic algorithms (GAs) in optimizing energy management strategies for hybrid electric vehicles. Initially, the paper categorizes hybrid electric vehicles based on mixing rates and power source configurations, elucidating the operational principles and the range of applicability for different hybrid electric vehicle types. Following this, the two primary categories of energy management strategies—rule-based and optimization-based—are introduced, emphasizing their significance in enhancing energy efficiency and performance, while also acknowledging their inherent limitations. Furthermore, the advantages of utilizing genetic algorithms in optimizing energy management systems for hybrid vehicles are underscored. As a global optimization technique, genetic algorithms are capable of effectively addressing complex multi-objective problems by circumventing local optima and identifying the global optimal solution. The adaptability and versatility of genetic algorithms allow them to conduct real-time optimization across diverse driving conditions. Genetic algorithms play a pivotal role in hybrid vehicle energy management and exhibit a promising future. When combined with other optimization techniques, genetic algorithms can augment the optimization potential for tackling complex tasks. Nonetheless, the advancement of this technique is confronted with challenges such as cost, battery longevity, and charging infrastructure, which significantly influence its widespread adoption and application.

1. Introduction

With the rapid global development of science and technology, the total global consumption of fossil energy has continued to rise, a trend that has not only exacerbated the energy crisis but also triggered a series of serious environmental problems. Among them, the transportation sector, as one of the major consumers of fossil energy, has a particularly significant impact. According to the U.S. Energy Information Administration in 2014, the transportation sector accounted for 55% of total global energy consumption. The automotive industry, as a core component of the transportation sector, plays a crucial role in the world’s economic growth. However, as most vehicles rely on internal combustion engines (ICEs) for their operation, ICEs emit a variety of harmful gases such as CO₂, NO₂, NO, and CO during fuel combustion [1]. According to studies, the transportation sector contributes 25–30% of global greenhouse gas emissions, leading to environmental degradation, such as the greenhouse effect, and negative impacts on human health [2]. Figure 1 depicts recent energy usage within industries. Considering energy saving and environmental protection, society has put forward the demand for clean, efficient, and sustainable vehicles in urban traffic. Renewable energy-powered electric vehicles have a significant role to play in improving air quality and protecting the health of the population, as their emissions are only natural by-products rather than exhaust gases [3]. However, their limited range, inadequate charging infrastructure, and long charging time highlight their shortcomings [4]. In order to further improve driving performance and experience, effective solutions should be actively sought to complement the efforts to build a more efficient, convenient, and environmentally friendly transportation system.

A hybrid electric vehicle (HEV) utilizes two or more power sources [6]. By merging the benefits of traditional ICEs with electric motors, HEVs effectively address the shortcomings of both ICE vehicles and electric vehicles (EVs) by integrating the engine and electric motor in their design [7]. Through a sophisticated energy management system, it coordinates the energy distribution between the engine and the battery/electrical unit to ensure that the engine operates in a highly efficient, low-energy-consumption operating range, while utilizing the regenerative braking function of the electric motor to maximize energy recovery. This significantly alleviates the technical challenges of limited battery energy storage and low range faced by pure EVs. In urban traffic, HEVs minimize frequent starts and stops through their unique operating mechanism, reducing idle time and demonstrating superior fuel economy and environmental performance compared to traditional internal combustion engine vehicles. In addition, HEVs are designed with a variety of structures that can be achieved by fine-tuning the conventional vehicle’s structure, thereby reducing the complexity and difficulty of design. Compared to conventional vehicles, HEVs significantly reduce the weight and cost of key components such as the engine through rational structural configurations while ensuring no loss in driving performance and service life. This design not only retains the advantages of traditional vehicles, but also integrates the energy-saving characteristics of pure EVs, realizing the perfect integration of the advantages of the two models. HEVs present a new solution for the sustainable development of the automotive industry by significantly improving energy-saving and emission reduction performance. This is achieved through optimization, complementing, coordination, and cooperation between different energy sources. By integrating these diverse power sources effectively, HEVs not only ensure enhanced vehicle dynamics, but also maintain high standards of safety and comfort. Ultimately, the holistic approach of managing multiple energy sources in HEVs addresses the overarching goals of sustainability in the automotive sector.

Various types of HEVs exist, and regardless of their specific type, they all constitute highly complex nonlinear systems [8]. These systems necessitate particularly rigorous control strategies due to their inherent complexity. Consequently, Energy Management Strategies (EMS) have emerged as a pivotal research area within the field of HEVs. Researchers have focused extensively on developing and optimizing EMS to ensure efficient energy utilization and to enhance the overall performance of HEVs. Investigating the effects of energy price fluctuations on optimal control strategies and designing optimal control strategies that can cope with such uncertainties are crucial for improving the reliability, control, economy, and emission performance of HEVs. In large cities, electricity and oil prices fluctuate significantly, and peak and valley prices vary greatly, making it difficult to achieve optimal control with fixed-price EMS. As a result, the control methodology of EMS is in urgent need of innovation and optimization [9]. EMSs are generally categorized into two types: rule-based and optimization-based strategies [10]. The former strategy, which is a real-time control approach used in production vehicles, demands substantial time and effort for design and calibration [11,12,13]. Despite its practical application, it operates heuristically and often falls short of ensuring optimal performance [14]. In contrast, the latter methods achieve optimization by minimizing an infinite- or finite-horizon function of the fuel or battery state-of-charge (SOC) over time. The commonly used optimization methods include dynamic programming (DP) [15,16], equivalent consumption minimization strategy (ECMS) [17,18,19,20], Pontryagin’s minimum principle (PMP) [21,22], and receding horizon optimization [23,24]. Recently, reinforcement learning and neural networks have gained popularity for optimizing control strategies in diverse driving scenarios [25,26,27,28,29,30]. For hybrid power systems, key performance factors include system efficiency, economic indicators, and protection measures [31]. The control performance is primarily indicated by the dynamic response and steady-state characteristics [32]. Additionally, protective measures are essential to ensure the system’s stable operation and extended service life. These measures primarily aim to reduce current fluctuations and control the depth of charging and discharging [33,34]. Therefore, when formulating EMSs for HEVs, we should not limit ourselves to only optimizing the energy consumption of the system, but should comprehensively consider the impacts of the above aspects. By selecting the optimal HPS method and formulating the corresponding control strategy, we are expected to further improve the overall performance of HEVs and promote their widespread popularity in practical applications.

Since the 1960s and 1970s, artificial intelligence technology and biological evolution mechanisms have been incorporated into optimization methods [35,36]. This development has led to the creation of modern optimization techniques that differ significantly from traditional ones [32]. Genetic Algorithms (GAs) in the field of evolutionary computation have attained substantial recognition as a premier optimization technique, attributed to their remarkable global search capabilities and comparatively low algorithmic complexity. Utilizing the foundational principles of natural selection and genetics, GAs enable swift global convergence and effectively discern optimal solutions within intricate problem spaces. By employing adaptive probabilistic iterative search mechanisms, these algorithms exhibit a profound capability to traverse vast and multifaceted search spaces with efficacy. Wieczorek et al. (2017) employed the GA search technique to optimize the coefficients of the gamma function utilized in the EMS of an electric vehicle hybrid energy storage system in real-time. The results indicated that, compared to the rule-based strategy and the battery-only system, the strategy incorporating GAs and the strategy with fixed coefficients achieved a 40% reduction in the RMS current rate during the New European Driving Cycle without exceeding the nominal maximum current rate [37]. Wang et al. (2022) optimized a fuzzy-controlled energy storage system for an electric vehicle hybrid energy storage system through the application of a GA management strategy. The results demonstrated that the energy economy was enhanced by 2.6%, 2.4%, and 3.3% at ambient temperatures of 10 °C, 25 °C, and 40 °C, respectively [38]. Wang et al. (2023) utilized GAs to optimize the fuzzy logic control parameters, including the center of the subordinate function and the width of the fuel cell. The results indicated that the equivalent hydrogen consumption was reduced by 16.55% when compared to the GA-optimized fuzzy EMS, and by 40.50% when compared to the conventional fuzzy EMS. This significantly improved the total fuel economy of the fuel cell vehicle [39]. Mazouzi et al. (2024) optimized the fuzzy logic EMS parameters of the fuel cell HEV using GA. The simulation results validated the effectiveness of the proposed strategy, which involved a four-stage optimization process, including the adjustment of the affiliation function. This led to a substantial improvement in the fitness function, with fuel utilization increased by 28.5% and inefficient operation reduced by 13%, compared to the original EMS and thermostat strategy [40].

Furthermore, hybrid genetic algorithms (HGAs) demonstrate superior performance in addressing multi-objective, nonlinear optimization problems. This is primarily attributed to their enhanced time efficiency, which stems from the utilization of particle swarms. These swarms mitigate the computationally intensive task of generating and refining candidate solution populations, thereby diminishing the likelihood of premature convergence. Additionally, HGAs incorporating a population intelligence mechanism or local search strategy effectively mitigate the limitations associated with local optima and premature convergence. This hybrid optimization strategy not only expedites convergence but also yields a more robust solution. For instance, Tinós et al. (2018) introduced a hybrid genetic algorithm leveraging NKCV2 and PX to achieve efficient clustering with O(N) complexity. Experimental results indicate an 18.6% improvement in clustering purity compared to traditional genetic algorithms, a 41% enhancement in efficiency relative to DBSCAN, and a one-third reduction in parameter sensitivity compared to DP. This algorithm innovatively addresses challenges such as clustering arbitrary shapes, automatically determining cluster counts, and ensuring noise robustness. Theoretical validation of the local search strategy reveals a 37% acceleration in convergence, offering a novel approach for clustering complex data [41]. Akopov et al. (2025) proposed a multi-intelligence hybrid genetic algorithm (MA-HCAGA) that innovatively combines binary-coded genetic operators, bi-objective discrete particle swarm optimization, and fuzzy clustering techniques. The algorithm effectively addresses the bi-objective optimization challenge of maximizing vehicle flow and minimizing network complexity in reconfigurable multi-layer road networks. This is achieved by orchestrating intelligence interactions through finite state machines. Experimental findings demonstrate that the method selects the optimal topology along the Pareto front and substantially enhances road network capacity [42].

Previous research has demonstrated that the global search capability of GAs facilitates the development of an efficient methodology through the identification of optimal solutions within a complex parameter space for energy management. Furthermore, the algorithm exhibits particular suitability for addressing multi-objective optimization problems. The algorithm simultaneously takes into account multiple performance metrics, such as power, fuel economy, and emission performance, enabling it to achieve multi-objective optimization. This comprehensive optimization capability not only enhances the robustness of energy management systems for hybrid vehicles, but also offers promising applications for improving energy efficiency and vehicle performance.

This paper presents a novel review that focuses on the following aspects:

• A comprehensive review and analysis of the classification of hybrid vehicles and their associated EMSs. This section presents the structural features, operating principles, and performance advantages and disadvantages of each type of hybrid vehicle, based on their classification. This provides readers with a clear understanding of the basic classification of hybrid vehicles.
• The paper will delve into the classification and application of EMSs. The EMS is the cornerstone of hybrid vehicle technology, determining the power performance, fuel economy, and emission levels of the vehicle. This paper compiles and examines the main categories of contemporary energy management technologies, including rule-based and optimization-based approaches. Furthermore, the paper presents the advantages, disadvantages, and applications of these different approaches.
• The paper focuses specifically on the optimization effectiveness of GA-based EMSs. As a review, the paper provides an overview of the potential and current status of GA applications in optimization, offering readers a comprehensive perspective on the research dynamics and trends in the field. The objective of this paper is to provide readers with a comprehensive understanding of the classification methods and energy management techniques of hybrid vehicles, while also serving as a reference and inspiration for further research and applications in related fields.

2. Classification of HEVs

As of 2025, traditional internal combustion engine vehicles (ICEVs) continue to dominate global automobile ownership, while the market share of new energy vehicles (NEVs), encompassing pure electric vehicles (PEVs) and HEVs, is experiencing rapid growth. According to data from China’s Ministry of Public Security, the NEV fleet in China is projected to reach 31.4 million units by the end of 2024, constituting 8.9% of the total automobile fleet. Among these, battery electric vehicles (BEVs) account for 70.3% (approximately 22.09 million units), while plug-in hybrid electric vehicles (PHEVs) and other NEV models account for the remaining 29.7%. Simultaneously, traditional fuel vehicles (TFVs) still constitute a significant portion of the global fleet, accounting for 91.1%. However, this proportion is gradually decreasing due to policy incentives and technological advancements. Hybrid vehicles (HEVs and PHEVs) are gaining prominence in new car sales, with global hybrid sales exceeding those of pure electric vehicles for the first time in 2024. In the Chinese market, the share of plug-in hybrids has reached 70%. Globally, the ownership of internal combustion engine vehicles (ICEVs) is expected to remain high in the short term due to the large existing stock. However, the penetration rate of NEVs is anticipated to accelerate significantly after 2030.

2.1. HEV Classification by Hybridization Rate

The ratio of the power generated by an electric motor in a HEV to the total power used by the vehicle’s hybridization is known as the degree of hybridization [43]. Automotive cars can be categorized as Micro, Mild, Full, or Plug-in Hybrid based on the level of hybridization [44].

Micro HEVs: The hybridization level of micro HEVs is less than 5%. In micro HEVs, the engine is turned off when the driver applies the brake pedal, and the vehicle is started again by the electric motor, which takes the shape of a tiny integrated alternator/starter. The ICE powers the car after it is moving [45]. Using a micro HEV system results in an approximate 5–10% boost in fuel economy. The BMW 1 and 3 series, the Fiat 500, the SMART car, the Peugeot Citroen C3, the Ford Focus and Transit, and the Mercedes-Benz A-class are a few examples of micro HEVs that are now in use.

Mild HEVs: The degree of hybridization in mild HEVs is less than 20%. The mild HEV and micro HEV are extremely similar; however, the mild HEV may provide power assistance during vehicle propulsion due to the larger integrated alternator/starter motor and batteries, which offer higher electric motor power outputs ranging from 7 to 12 kW/150 V [5]. Because mild HEVs have a larger electric motor, they may save more fuel by using regenerative braking and torque assistance. In real-world driving, mild hybrid vehicles often result in a 20–25% boost in fuel efficiency when compared to non-hybrid vehicles [45]. The power performance of MHEVs is heavily dependent on engine performance, as they do not use high-voltage batteries and their batteries and motors are relatively low-powered [46], which makes them cost-effective and allows them to be brought to market quickly compared to battery electric and hydrogen fuel cell vehicles, which improves average fuel economy across the fleet [47]. As illustrations of commercially available mild-HEVs, the Honda Civic, Honda Accord, the 2009 Saturn Vue, and the GMC Sierra 1500 truck stand out among numerous options. The distinction between micro and mild HEVs primarily lies in their ability to deliver torque to the vehicle. Specifically, micro HEVs lack the capacity to do so, as the electric motor in these vehicles is primarily utilized for enabling start–stop functionality and powering accessories, rather than directly contributing to torque output.

Full HEVs: FHEV is a system that carries both an internal combustion engine and a high-voltage electric motor as dual power sources, along with the following features: (1) independent drive is possible in pure electric mode; (2) the electric motor and internal combustion engine can work together; (3) it is capable of regenerative braking energy recovery; (4) no external charging required. Full HEVs exhibit a hybridization level that surpasses 50%, indicating a significant integration of electric propulsion components. Full HEVs incorporate significantly larger batteries and more robust electric motors compared to their micro and mild hybrid counterparts. However, this enhanced level of hybridization often results in a higher cost of ownership [48]. In the design of this type of HEV, a dual power path is incorporated for the ICE and the electric motor, thereby enabling both independent and coordinated modes of operation [5]. The full hybrid system is capable of more than just using the generator to start and stop the engine. It can also absorb some energy during braking and deceleration, run the engine at a constant speed while driving, and adjust the amount of energy it produces based on how much is needed to charge the generator or drive the wheels. The electric motor can help drive the wheels while the automobile is accelerating or under high load, boosting the engine’s power output and improving the overall performance of the vehicle. The electric motor can help drive the wheels while the automobile is accelerating or under high load, boosting the engine’s power output and improving the overall performance of the vehicle. In addition to producing no emissions at the time of use, FHEVs in pure electric mode are perfect for removing localized pollutants in urban areas while preserving the ability to travel great distances inside the city when utilizing an ICE [49]. However, this benefit comes at the expense of complexity and expense [50]. Contrary to conventional vehicles, including MHEVs, which harness the engine’s power to operate auxiliary components like water pumps, fuel pumps, and air conditioning (A/C) compressors, and utilize combustion’s waste heat for cabin heating, FHEVs necessitate the operation of these systems entirely on electric power [51,52]. Full hybrids are best suited to the stop-and-start driving patterns found in cities [53]. Compared to micro and mild hybrids, FHEVs have considerably smaller engines and demand more advanced energy management systems. When compared to non-HEVs, FHEVs typically have fuel efficiency gains of 40–45%. The Chevrolet Tahoe Hybrid, Toyota Prius and Camry Hybrid, Ford C-Max, Honda CR-Z, and Kia Optima Hybrid are a few examples of FHEVs now on the road [45].

PHEV: Plug-in HEVs (PHEVs), which offer lower emissions and better fuel efficiency than traditional fossil fuel-powered cars, have become a popular substitute. Unlike conventional HEVs (HEVs), plug-in hybrids can be recharged directly from the grid, resulting in additional all-electric range and further reducing engine fuel consumption [54]. PHEVs can run on electricity for long periods of time thanks to high-capacity electrical components. PHEV, as a multiple power source system, uses ICE and lithium-ion battery packs, supercapacitors, etc., to provide power [55]. In typical applications, the ICE serves as the primary power source, while energy storage mechanisms, including batteries and supercapacitors, function as secondary or supplementary sources, either independently or in conjunction, to facilitate the propulsion of the vehicle [56]. In order to maximize fuel efficiency and prolong battery life, PHEVs require appropriate energy allocation between the two sources [57]. In the current market, two variations of PHEV exist: extended-range electric vehicles and hybrid PHEVs. The extended-range PHEVs typically adopt a series arrangement, where the gasoline engine primarily generates electricity for the electric motor to propel the vehicle until the batteries are depleted, at which point the engine activates. Conversely, in hybrid PHEVs, the engine is predominantly employed to directly provide power to the vehicle. In terms of the torque source for the drive wheels, the operational modes of PHEVs are categorized as centralized drive and distributed drive [58]. Presently, the majority of PHEVs favor centralized drive systems due to their advanced level of technological maturity [59]. The Chevy Tahoe Hybrid, Toyota Prius and Camry Hybrid, Ford C-Max, Honda CR-Z, and Kia Optima Hybrid are a few examples of fully electric vehicles currently on the road [45]. PHEVs that are selling the best in 2018 include the Mitsubishi Outlander, BYD Tang, and BYD Qin [60]. The comparison of the above four types of HEV is shown in

Table 1. Comparison of micro, mild, full and plug-in HEVs.

Function or Component Parameters	Types of HEV
	Micro	Mild	Full	Plug-In
Idle Stop/Start	●	●	●	●
Electric Torque Assistance		●	●	●
Energy Recuperation		●	●	●
Electric Drive			●	●
Battery Charging			●	●
Battery Charging (from Grid)				●
Battery Voltage (V)	12	48–160	200–300	300–400
Electric Machine Power (kW)	2–3	10–15	30–50	60–100
EV Mode Range (km)	0	0	5–10	>10
CO2 Estimated Benefit	5–6%	7–12%	15–20%	>20%

[44].

HEVs combine the benefits of a gasoline engine and an electric motor to provide better fuel economy or more power than conventional vehicles. Most hybrids use several advanced technologies [61]:

◆

Braking Regenerative: During coasting or braking, regenerative braking restores energy normally lost.

◆

Drive/Assist Electric Motor: In order to help the engine accelerate, move, or hill climb, the electric motor provides power. This enables the use of a smaller, more efficient engine.

◆

Stop/Start Automatic: When the car comes to a halt, the engine automatically shuts off and restarts when the accelerator is pressed. It minimizes wasted energy from idling.

The key to achieving these benefits is the ability to coordinate real-time control strategies for onboard power supplies to maximize fuel economy and reduce emissions.

2.2. HEV Powertrain Configuration

HEVs come in many different configurations and sizes, but they all have the same goal: to achieve the best possible fuel economy and the lowest possible tailpipe emissions. According to powertrain configuration, hybrid vehicles can be categorized as series, parallel, and power split [44].

2.2.1. Series Hybrid Powertrain

Series HEVs are composed of a generator, engine, rectifier, battery, traction motor, mechanical transmission, etc. In series HEVs, the ICE is connected to a generator, which provides power to either run the electric motor or charge the battery. Typically, the electric motor operates the vehicle independently, drawing the necessary power from both the generator and the battery. This configuration allows the electric motor to receive power directly from the generator or from the battery, facilitating electric all-wheel drive capability when the motor, generator, and battery are appropriately mounted on both the front and rear axles. Figure 2 illustrates the series HEV configuration.

In this configuration, the electric motor alone provides the traction to drive the vehicle [62]. Because there is no mechanical coupling between the ICE and the drive axle, the ICE can function independently of the vehicle’s power demands and near its peak efficiency, thereby significantly reducing fuel consumption. Traction motors offer a broader operating range and greater efficiency compared to ICEs. Consequently, the transmission, essential in conventional vehicles, may not be required in a tandem HEV.

In series HEVs, mechanical energy needs to be converted into electrical energy and then electrical energy into mechanical energy, which can be less efficient overall because of the need for two energy conversions. In order to replace the ICE for traction purposes in series HEVs, a sufficiently powerful drive motor is necessary. Consequently, the battery capacity and the generator size must be substantial enough to support this motor. This requirement leads to increased costs for the battery and its components, ultimately restricting the commercial application of series HEVs primarily to heavy-duty vehicles [63]. Kim et al. (2019) [64] introduced a hybrid powertrain design framework for a heavy-duty multi-purpose vehicle, considering various driving conditions. The gasoline equivalent fuel economy of the series hybrid powertrain was 53% higher than conventional diesel powertrain for the target drive cycle. Few hybrid vehicles on the market utilize the series configuration. Despite the limited adoption, several automobile manufacturers, including Mitsubishi, Volvo, and BMW, have explored this technology. A notable example is the BMW i3, which offers an optional gasoline-powered range-extender auxiliary power unit [44]. Some of the more common series hybrids on the market are the Nissan Kizashi, Swiss auto REX VW Polo, and the Volvo S90.

2.2.2. Parallel Hybrid Powertrain

In parallel HEVs, the ICE and MG (Motor/Generator) are both directly connected to the output shaft to provide drive. The ICE connection is termed the mechanical path, while the MG connection is known as the electrical path [65]. Since the two power sources operate in different modes, parallel HEVs allow the electric motor and ICE to provide power to drive the vehicle in parallel, so the ICE and the electric motor can be driven separately or jointly, as illustrated in Figure 3. Under certain operational conditions, the vehicle can be operated by either the motor or the ICE alone when the battery’s state of charge is high. Some of the torque from the ICE will be redirected to turn the MG, which will be utilized as a generator to recharge the battery pack, in order to prolong the battery life when the SOC of the battery is at a lower level. In the state of charge, the drive power required for the exercise of the vehicle can only be provided by the ICE alone [66]. The MG functions as a generator during low power demand and as a motor during high power demand, keeping the ICE operating in the high-efficiency range and thereby reducing fuel consumption. Furthermore, parallel hybrids require transmissions to align high engine speeds with low vehicle speeds [44].

In parallel HEVs, the ICE serves as the primary drivetrain source, while the electric motor functions as a secondary source to increase traction power through control strategies that can successfully reduce fuel consumption [67]. In contrast to the series HEV, the parallel hybrid vehicle arrangement uses a larger ICE with a comparatively smaller and less powerful electric motor [45]. However, both the mechanical and electrical energy of a parallel HEV can be used to directly propel the vehicle, resulting in increased driveline efficiency compared to a series configuration under most operating conditions [61]. Although this approach increases performance and efficiency, it has drawbacks. The parallel design is more complicated than the series configuration, and the transmission and driveline are more costly [68]. Anselma et al. (2019) [69] evaluated the potential for reducing CO₂ emissions, drivability, and total cost of ownership of different parallel HEV architectures in comparison to conventional layouts. Although parallel HEVs have higher procurement costs, they can be effectively recovered over the life of the vehicle. Al-Samari et al. (2017) [70] studied and simulated a parallel hybrid vehicle using Autonomie software and concluded that the fuel economy increased by 68%, emissions decreased by 40%, and engine efficiency increased by 12% during the real driving cycle. There are many applications of parallel hybrid technology in the market, such as Volkswagen Passat Hybrid [71], Hyundai Sonata Hybrid, BYD Qin, Honda’s Insight, Civic, Accord, and the Chevrolet Malibu Hybrid in parallel configuration [68]. Parallel HEVs are unsuitable for typical city driving with frequent stop-and-go traffic, as the constant starting and stopping significantly drains the battery. The charging mechanism is not available when the vehicle is not moving, and the ICE is unable to drive the generator to charge the batteries when the SOC is at a low battery level, which forces the engine to produce power in the area of low efficiency.

2.2.3. Power-Split Powertrain

Power-split HEV vehicles consist of two MGs and a driveshaft together by one or more planetary gear sets (PGS) coupled to an ICE [72,73], as illustrated in Figure 4. The PG set, also known as the power-split device (PSD), is the central component of the power-split hybrid system [44]. In power-split hybrid vehicles, the PSD divides the power generated by the ICE and transmits it through both mechanical and electrical transfer paths to the output shaft. Functionally similar to a continuously variable transmission, the PSD synchronizes the speed of the ICE with that of the vehicle. This synchronization is crucial because it allows the ICE speed and torque to be entirely decoupled from the speed and torque of the system’s output shaft. Consequently, this decoupling enables the optimization of the engine’s operating point, leading to improved fuel efficiency. The electric motor can also recover kinetic energy and turn off the engine for purely electric driving under certain operating conditions. This design allows the ICE to operate at high efficiency regardless of vehicle speed. Therefore, PSD is also known as electronic CVT in power-split hybrid vehicles [74]. Power can be transferred from the driveshaft via an electrical or mechanical path thanks to the PSD [75]. In the electrical path, the PSD works similarly to series HEVs. The power split hybrid vehicle integrates the benefits of both series and parallel hybrid vehicles, effectively addressing the size constraints of series hybrids and the frequent stopping and starting issues associated with parallel hybrids. First, part of the ICE power is converted into electricity through a generator. This electricity can then be utilized to drive the electric motor or to charge the battery. In the mechanical path, the PSD functions similarly to PHEVs, allowing the ICE to generate power flow directly to the drive shaft to propel the vehicle. The ICE and the battery can supply power to the vehicle independently or in conjunction, and the battery can be charged by the engine simultaneously. Essentially, this configuration extends the all-electric range of a hybrid vehicle, providing a versatile and efficient propulsion system [66].

Power-split HEVs are based on planetary displacements as energy distribution components, which couple the electric motor with the engine for optimal energy matching. The goal of the control logic is to continuously operate the engine in the high-efficiency range. Kabalan et al. (2019) [76] have previously observed that the efficacy of a power split hybrid powertrain system is contingent upon its specific design, which is influenced by several factors. These include the count of PGS as well as the variety, quantity, and installation position of the transmission actuators, also known as clutches or brakes. Depending on the number of PGS, power split configurations are differentiated into two distinct modalities: a single-mode configuration and a multi-mode configuration. In the single mode, there exists only one PGS, while the multi-mode configuration incorporates two or more PGS [68].

The single-mode power-split hybrid system configuration encompasses two distinct subtypes of power distribution arrangements: namely, input-split schemes and output-split schemes.

(1) In the input-split configuration, the engine and generator are respectively coupled to two distinct central shafts of the planetary gear sets, while the electric motor is linked to the output central shaft [77]. The earliest power-splitting systems were developed by Thompson Ramo Wooldridge Inc. in the 1960s. Today, the Toyota Prius is the best-selling hybrid system globally. Ford Motor Company employs a similar input split concept in its Fusion Hybrid and C-Max models [44].

(2) In the output-split configuration, the engine and generator are firmly attached to the input central shaft of the planetary gear set, whereas the electric motor is linked to a separate central shaft within the planetary gear set [77]. The output-split powertrain may perform poorly at low vehicle speeds compared to the input-split configuration [78].

Yang et al. (2019) [79] introduced a single planetary gear-based dual-mode hybrid powertrain, which incorporates both input and output split. To assess its efficacy, they benchmarked this novel configuration against two established power-split designs, the THS-P610 and Volt-II, following comprehensive optimization. This hybrid powertrain enabled the vehicle to operate in either pure electric, series hybrid, or parallel hybrid modes when the power-split operation was not engaged.

(3) Multi-mode power distribution hybrid system configurations are combinations of more than two power distribution schemes [80,81], allowing for complex power distribution methods [80]. The compound split is a multi-mode power distribution hybrid powertrain configuration subtype with no configuration between the MG and the output shaft or engine [44]. The Lexus HS 250 h, Lexus RX 400 h, Toyota Camry and Honda, Lexus GS 450 h, and Lexus LS 600 h utilize the compound-split configuration [68].

Gu et al. (2020) [82] proposed a systematic approach for designing, analyzing, evaluating, and screening the 2-PG multi-mode power-split hybrid powertrain system configuration. Additionally, they took into account all possible 2-PG configurations, power component connection locations, actuator counts, and combinations of various operating modes. Zhang et al. (2019) [83] investigated the optimization of a composite power distribution configuration in the PHEV bus to reduce fuel consumption and battery degradation. They explored potential composite power distribution configurations with two planetary gear sets. Multi-mode optimization addressed driveline issues, with composite power-split configurations performing better in terms of fuel economy, acceleration, and motor size.

In recent years, the development of planetary gear hybrid powertrain (PGHT) systems has been mainly aimed at the fuel economy of HEVs. Wang et al. (2021) [84] introduced the Torsional Vibration Considered for PHEVs, with the objective of achieving desirable energy economy and ride comfort. Contributing work to the PGHT includes Tang et al. (2021) [85] and Bao et al. (2022) [86]. Power-split HEVs offer better performance compared to series and shunt HEVs, but they also lead to complex structures, increased integration and control difficulties, and increased costs.

The differences in the inherent characteristics of engine and motor operating efficiency, frequency response characteristics, torque characteristics, etc., result in EMSs that play a decisive role in the overall vehicle performance improvement of HEVs. However, different types of powertrain configurations of HEVs determine the selection of different algorithms and optimization potentials [87], but all of them aim to improve energy utilization efficiency, reduce energy consumption and environmental pollution, and enhance vehicle performance and driving experience. Through rational energy management, hybrid vehicles are able to choose the optimal energy source and distribution method in different driving scenarios to achieve more efficient and environmentally friendly energy utilization.

3. Energy Management Strategies for HEVs

The control strategy’s primary objectives are to reduce hazardous emissions and fuel consumption while also maximizing vehicle performance to satisfy the driver’s need for power. To achieve the desired control objectives and consequently strike a balance between fuel economy and emission minimization, it is imperative to first comprehensively grasp the operational principles and unique traits of various power sources. Furthermore, a rational exploitation of the respective merits of these power sources, along with the implementation of effective control strategies, is crucial in achieving the desired outcomes. The optimal control algorithms of EMSs have been studied from a variety of angles by experts and scholars both domestically and internationally. Based on a substantial body of existing literature, this paper describes and summarizes the energy management issues of HEVs from a variety of angles. Zhang et al. (2020) [88] conducted a thorough evaluation, categorization, and comparative analysis of energy management techniques for HEVs, offering an insightful glimpse into the current standing of this research domain. HEV EMSs are categorized into two groups based on their various control methods: rule-based control strategies and optimization-based control strategies. Figure 5 illustrates this division.

3.1. Rule-Based Control Strategies

Rule-based EMSs typically rely on predefined operating modes that are formulated either through human expertise, mathematical frameworks, or computational models. These approaches often function without the necessity of prior knowledge about the specific driving cycle [68]. These strategies have simple control methods that are easy to implement and were therefore first used for the control of HEVs. They mainly consist of two forms: one is a deterministic rule-based control method, where the motor or engine operating state is divided into modes according to different torque, speed, and SOC conditions (e.g., accelerator pedal, brake pedal commands) or their efficiency Map diagrams, and rules are formulated for switching control. Another control strategy relies on FL, which is particularly advantageous for HEVs due to their multivariable, nonlinear, and time-varying characteristics. By leveraging the strengths of fuzzy control, this strategy establishes state variables and the affiliation functions of state variable change rates. These affiliation functions are then used to formulate fuzzy control rules that govern energy distribution and SOC.

Torreglosa et al. [90] (2020) focused on the application of rule-based strategies in commercial HEVs, emphasizing the continued reliance on these strategies despite the evolution of new energy management systems. Conversely, Rana et al. (2020) [91] devised a rule-driven algorithm to assess fuel efficiency, battery SOC, and potential energy savings for series HEVs. Additionally, Hwang (2020) [92] employed an ECMS in order to optimize the fuel consumption of an Advanced Hybrid Powertrain-II (AHS-II). The findings revealed that, with regard to the electric motor’s efficiency, the discrepancy between the ECMS and the rule-based baseline control strategy was negligible. K et al. (2021) [93] discussed how rule-based control strategies can be continuously improved to incorporate more predictive, cognitive, and artificial intelligence tools for real-time applications. Won (2021) [94] developed a rule-based topology simulation tool for HEVs, emphasizing the continued relevance and applicability of rule-based strategies in HEVs. Together, these studies demonstrate the continued relevance and evolution of rule-based control strategies for HEVs and the continued development and implementation of novel energy management systems.

3.1.1. Deterministic Rule-Based Control Strategy

The design of these rules integrates multiple factors, including fuel economy, emissions data, ICE operating diagrams, power flow within the driveline, and driving experience. To facilitate precise power allocation between the ICE and the electric traction motor, these rules are executed through a look-up table mechanism [68]. The central idea is to coordinate the electric motor’s activity to move the engine’s operating point, allowing the engine to run as much as possible in its high-efficiency zone. The engine’s operating zone is defined through in-depth theoretical analysis as well as rich engineering experience; for example, we can delineate the engine’s high-efficiency operating zone based on its static operating efficiency curve Map diagram. In these rules, we pre-set a series of logic rules based on engine mapping and motor efficiency mapping to reasonably allocate power. At the same time, these guidelines also take into account the motor’s efficiency in addition to other elements like the engine and battery SOC [88]. These control rules are designed to be both simple and practical, and can be easily implemented online to achieve precise control of the engine and motor for the purpose of optimizing fuel economy and reducing emissions. Rule-based EMSs achieve power distribution through predefined deterministic logic with the core objective of optimizing engine operating points and coordinating motor assistance.

Table 2. Key Implementation Rules for Rule-Based EMSs.

Rule Category	Design Basis	Implementation Method	Representative Studies
Load-Zone Partitioning Rules	Division of engine efficiency map into high/medium/low-efficiency zones	Matching demanded power with optimal load zones	Wu et al. (2004) [95]
Mode Shift Rules	Co-optimization of gear ratio and SOC	Decoupling engine speed through multi-mode transmissions	Gu et al. (2020) [82]
Dynamic Compensation Rules	Rate of change in accelerator pedal position	Predictive adjustment of motor compensation power	Xiang et al. (2017) [96]
Expert Knowledge-Integrated Rules	Encoding engineering experience into DRL reward functions	Embedding rule constraints in DDPG algorithms	Lian et al. (2020) [97]

summarizes typical control rules and their design rationale.

Dextreit et al. (2013) [98] introduced a methodology for rulemaking that primarily involves segmenting the engine’s operational domain into distinct zones of high, medium, and medium–low loads. This approach integrates the driver’s throttle pedal position and its rate of change to assess the instantaneous power demand, thus facilitating the determination of the appropriate operational mode. Min et al. (2011) [99] explored the design of a multi-mode electronic variable transmission, focusing on the transmission structure and utilizing multiple planetary wheel systems to achieve varying operational modes. By effectively managing the switch between these modes, they aimed to maintain the engine’s operation in the zone of optimal efficiency and minimal energy consumption. This approach was implemented by considering the decoupling ratio of the engine, ensuring its consistent performance in the high-efficiency region throughout the entire working process. Lian et al. [97] (2020) introduced an energy management framework that leverages expert knowledge within the deep deterministic policy gradient (DDPG) algorithm, thereby enhancing the optimization and training efficiency of deep reinforcement learning (DRL)-based strategies. Lee et al. (2020) [100] compared reinforcement learning-based strategies with DP-based control approaches, highlighting similarities in control frameworks. Sun et al. (2020) [101] developed a semi-rule-based decision-making strategy for heavy intelligent vehicles using the DDPG algorithm. Furthermore, Tang et al. (2021) [102] investigated double DRL-based energy management in parallel HEVs. Conversely, Hu et al. (2022) [103] proposed an adaptive hierarchical approach that integrates DDPG and heuristic domain knowledge for HEVs. Huang et al. (2022) [104] developed a rule-based control strategy for power distribution in a parallel HEV based on driver demand. These studies demonstrate the effectiveness of deterministic rule-based control strategies in optimizing energy management for HEVs, showcasing improvements in energy consumption costs, comfort maintenance, and fuel efficiency.

The rule-based deterministic approach, which relies on engineering expertise, operational mode segmentation, and static energy efficiency maps, offers straightforward comprehension and implementation. However, its inability to adapt to fluctuating operating conditions and dynamic demands poses challenges in achieving optimal control. In order to optimize the performance and adapt to the working conditions in real time, fuzzy control began to be integrated into the rule-based control.

3.1.2. Fuzzy Rule-Based Control Strategy

FL control theory incorporates fuzzy set theory, which extends traditional TRUE and FALSE set theory, and FL, which extends traditional logic of how a system determines its output. Within FL, the veracity of a statement is expressed not as an absolute, but as a matter of varying degrees, rendering it remarkably resilient and responsive in real-time scenarios. Considering the HEV’s energy management system, which comprises numerous subsystems exhibiting nonlinear and time-varying properties, the implementation of FL rules for management control emerges as a viable and effective alternative. FL can directly translate the designer’s experience into control rules, providing a powerful tool for intelligent control. With FL, rule-based behavior is recognized and expert knowledge can be encoded into a rule base, which in turn can be used in the decision-making process [105]. The primary advantage of FL is its adaptability and flexibility, which significantly enhances control freedom. The nonlinear structure of FL is particularly suitable for managing complex systems, such as energy management systems for HEVs. Consequently, implementing FL for the control of these energy management systems not only enhances the overall performance of the vehicle but also serves as a practical solution. Figure 6 illustrates a schematic diagram of a typical FL control strategy.

Huynh et al. (2020) [106] proposed an intelligent regenerative braking strategy for power-split HEVs, utilizing FL and rule-based control to design braking torque controllers. Similarly, Dao et al. (2020) [107] introduced a fuzzy approach grounded in optimization techniques for a hybrid construction excavator. This strategy seamlessly integrates FL control and a rule-based algorithm, enabling an efficient allocation of power across diverse energy sources. Chen et al. (2020) [108] introduced a nonlinear model predictive control (MPC) for heavy-duty HEVs, which outperformed rule-based control strategies and showed similar results to offline global optimization strategies. This suggests that nonlinear MPC may offer advantages over traditional rule-based strategies in certain applications. Sarvaiya et al. (2021) [109] conducted a comprehensive evaluation comparing hybrid vehicle EMSs, revealing a significant 25% enhancement in fuel economy when employing an ECMS compared to traditional rule-based methods. This indicates the potential for optimization-based strategies to enhance vehicle performance and efficiency. Luo et al. (2021) [110] proposed a fuzzy control strategy for parallel HEVs, combining fuzzy control with rule-based strategies to optimize engine and motor output torque. Jia et al. (2022) [111] presented a master–slave electro-hydraulic HEV with a rule-based control strategy for managing energy distribution and switching operating modes. This hybrid approach may offer improved energy control and efficiency in hybrid vehicles. Bai et al. (2023) [112] explored the potential of hybrid electric propulsion systems (HEPS) in reducing energy consumption and emissions in unmanned aerial vehicles (UAVs). Given the limitations of conventional EMS in maintaining SOC during engine failure, they proposed the FL-ECMS method. This approach achieved a noteworthy reduction of at least 18.6% in fuel consumption and CO₂ emissions for HEPS-equipped UAVs. Furthermore, it effectively addressed the challenge of conventional EMS in sustaining the battery SOC within the required level in the event of engine malfunction. In conclusion, the above literature shows that rule-based FL control strategies can play an important role in optimizing energy management and improving the performance of HEVs, especially when combined with other optimization techniques such as nonlinear MPC or FL optimization.

Figure 6. Schematic diagram of a typical fuzzy logic control strategy [113].

Figure 6. Schematic diagram of a typical fuzzy logic control strategy [113].

The rule-based FL, known for its strong robustness and reasonability, is particularly suitable for controlling complex hybrid nonlinear systems due to its independence from the accuracy of the system model. However, despite its advantages, this approach still relies on empirical rules to achieve precise control effects, which means it cannot always ensure control optimization. Consequently, it is often integrated with other intelligent control algorithms to enhance overall control performance. To achieve a globally optimal control outcome, recent research increasingly focuses on exploring optimization-based energy management control strategies.

3.2. Optimization-Based Control Strategy

The central goal of an optimization-based control strategy is to minimize a cost function by precisely tuning various parameters to achieve a specific control effect. When it comes to HEVs, the cost function is not defined by a single criterion, but rather is determined comprehensively based on a set of constraints and optimization objectives [113], including factors that are closely related to the application, such as emission levels, fuel consumption rate, and torque output [68]. This diversified evaluation system ensures that the control strategy is able to consider various key factors affecting HEV performance in a comprehensive and balanced manner. The global optimal solution, as a desired control state, is usually obtained by executing exhaustive optimization algorithms under specific, fixed design conditions. However, although this global optimization method can provide a theoretically optimal solution, it does not directly involve real-time energy management and thus may have some limitations in practical applications. To make up for these deficiencies, instantaneous cost function-based real-time control solutions have been created. In order to accomplish more precise and timely energy management, this technique can modify the control parameters in real time based on the system variables at the moment, such as vehicle speed, battery status, and load condition. This real-time capability enhances energy efficiency and allows HEVs to maintain stable performance under diverse and complex conditions. Based on the distinctive characteristics and application scenarios of optimization strategies, researchers can broadly categorize them into two primary types: global optimization and real-time optimization. Global optimization methods predominantly utilize static data tables or historical datasets to achieve the global optimum in energy usage under specific operating conditions. Although this method is complicated to calculate, it can provide a more accurate global optimal solution and provide theoretical support for the energy management of HEVs. The real-time optimization method, on the other hand, pays more attention to online control based on the real-time state or current parameters of the vehicle to ensure that the local or instantaneous optimal energy management effect can be achieved at any moment. This method is less computationally intensive, but it can respond to changes in vehicle state in real time and improve the adaptability and flexibility of HEVs.

3.2.1. Global Optimization

Among the most notable EMSs, those rooted in global optimization encompass the DP control approach, the stochastic dynamic programming (SDP) methodology, the linear programming (LP) technique, the PMP control method, as well as hybrid strategies that incorporate various intelligent control methods. These global optimization-based energy management techniques predominantly oversee the allocation of energy for a designated duty cycle, wherein the vehicular fuel economy is inherently reliant on the particular duty cycle, thereby posing certain inherent constraints.

(a) Dynamic Programming.

The optimization challenge in the decision-making process is solved mathematically by the dynamic planning-based energy management approach. Bellman first developed this technique in the 1950s. It entails breaking down a complicated problem into several tiers of single-step optimization decisions [114]. The basic principle of DP is illustrated in Figure 7. It involves optimizing the process by finding the lowest-cost path from A to F. Although it can achieve global optimization under specific conditions, it is challenging to apply directly to real-time vehicle control due to the necessity of predicting cyclic conditions and the ‘dimensionality catastrophe’ from high computational demands [113]. However, it remains valuable for finding the optimal solution within the model’s predictive control range, offering a crucial reference for energy management, optimizing energy efficiency, and enhancing system performance [115].

Patil et al. (2013) [116] proposed a new DP method that utilizes an inverse simulation model to evaluate state constraints, avoiding demand interpolation and improving planning accuracy. Murphey et al. (2012) [117] developed an energy management system based on machine learning for online training of neural networks for predicting traffic congestion and road types, which improves the energy management efficiency of hybrid vehicles. Wang et al. (2019) [118] presented a Receding Horizon Control technique based on DP for multi-mode HEV power splitting and mode selection. Lee et al. [100] (2020) compared reinforcement learning with DP control approaches for energy management in HEVs. Zhu et al. (2020) [119] developed a DP strategy for simultaneous identification and control in series HEVs to balance conflicting objectives. Kasture (2020) [120] compared DP with GAs for power management in a parallel plug-in HEV. Zhang et al. (2020) [121] mainly solved the optimization problem of energy allocation for power-split hybrid vehicles using dynamic planning, which improved the transmission efficiency and thus the performance and fuel economy of the vehicle. Inuzuka et al. (2020) [122] applied DP to solve the energy management problem in an HEV with three driving modes. Maino et al. (2021) [123] investigated optimal mesh discretization in DP for HEVs, aiming to enhance both calculation times and accuracy. Zhu et al. (2021) [124] proposed an iterative DP algorithm for transient powertrain control in HEVs. Zhou et al. (2021) [125] consider parallel HEVs and propose a dual EMS that combines long-term DP and short-term online optimization. Long-term planning calculates the SOC trajectory by DP and generates an intelligent SOC reference model with neural networks. For short-term optimization, a deep neural network is constructed to predict speed, and energy management is achieved by MPC and neighborhood search techniques. Bae et al. (2022) [126] employed a deterministic DP approach to study energy-optimal regulatory control strategies for parallel HEVs. This method aims to maximize energy efficiency and offers an accurate and reliable optimization path for regulatory control systems. Anselma (2022) [127] highlighted DP as the optimal energy management approach for HEVs with constraints on battery SOC, SOH, and smooth driving. Liu et al. (2023) [128] put forward a DP-based MPC approach integrated with a speed anticipation model, effectively augmenting the economic efficiency of HEVs through refined energy management. This strategy addresses the challenge posed by traditional methods in precisely forecasting future power demands and maintaining the SOC within the prescribed range. Han et al. (2024) [129] addressed a multi-stack fuel cell system (FCS) for a distributed fuel cell hybrid electric tracked vehicle; they reconstructed the DP algorithm rules and proposed a multi-objective hierarchical EMS to ensure the efficient operation of the system and prolong the life of the FCS, which solved the problem of aging consistency and performance optimization of the multi-stack FCS that is difficult to meet by the conventional EMS. These studies demonstrate the effectiveness of DP in addressing various challenges in HEV control and energy management.

(b) Stochastic Dynamic Programming.

Stochastic optimization is a technique for describing and resolving optimization issues using random variables. In the framework of DP, when the form of the probability function of a state or a decision is known, this approach is called SDP [68]. The principle of SDP posits that a sequence of values can be represented as a Markov chain. It estimates the driver’s power demand by generating a state transfer matrix graph [88]. The characteristics of Markov chains allow us to project future states from the present and identify the best control variables at that projected point in time. Markov chains are utilized in a dynamic planning algorithm to develop the SDP algorithm because of their predictive capabilities for cyclic conditions. This innovation effectively removes the dependence of conventional dynamic planning algorithms on particular driving conditions [113]. However, addressing the stochastic optimal control problem necessitates the utilization of high-performance computational techniques to guarantee both the precision and efficiency of the derived solutions.

Leroy et al. (2012) [130] suggested treating the driving cycle as a stochastic process and utilizing SDP for optimal energy management of HEV powertrains. Ko et al. (2014) [131] proposed an SDP algorithm where the cost function incorporates weighted fuel consumption, emissions, and battery power. The optimal solution for the LP is determined using an offline iterative method. Lee et al. (2015) [132] proposed an HEV energy management method based on SDP, which firstly expresses the power demand through a Markov process to obtain uncertain working condition information, forming an infinite optimization problem, and then optimizes the power allocation Map graph based on SDP to obtain an optimal control law, which realizes real-time control and improves the fuel economy. Zeng et al. (2015) [133] framed the HEV energy management challenge as a Markov decision process with a finite horizon, which they then addressed by applying the method of SDP. Liu et al. (2018) [134] focused on regenerative braking strategies for HEVs using cluster-based SDP. Jiao et al. (2018) [135] created a stochastic optimal adaptive equivalency factor-based real-time energy management approach for HEVs. Li et al. (2019) [136] investigated real-time HEVs with traffic information recognition based on adaptive ECMS and SDP. Lee et al. (2020) [100] conducted a comparative analysis of EMSs for HEVs, examining reinforcement learning, deterministic DP, and SDP. Aubeck et al. (2020) [137] introduced a novel energy optimization method for autonomous vehicle HEVs using a stochastic optimization technique, specifically employing Particle Filters within a routine of SDP to efficiently solve power split trajectories. Ulmer (2020) [138] discussed the combination of online and offline approximate DP methods for stochastic dynamic vehicle routing problems, showcasing improved performance and reduced computational time. Yang et al. (2022) [139] proposed an SDP-based energy management method for HEVs. This method dynamically adjusted energy allocation, adapted to uncertainties, and met complex constraints during real-world driving. Overall, the integration of SDP techniques into energy optimization and control strategies for hybrid vehicles demonstrates the effectiveness of these methods in dealing with uncertainty and optimizing the decision-making process.

(c) Pontryagin’s Minimum Principle.

PMP, alternatively known as the Principle of Greatest Value, was introduced in the mid-1950s by Soviet scholar Pontryagin and his contemporaries. This principle later evolved into a pivotal component of modern control theory, superseding the classical variational method and facilitating the resolution of optimal control challenges [140]. The principle applies to solving optimal control problems in both continuous and discrete forms of controlled systems. PMP is a specific instance of the Euler–Lagrange variational equation, offering necessary conditions for finding an optimal solution. However, the sufficient conditions are met by Hamilton’s equation [68]. Under specific assumptions, the optimal trajectory obtained by the PMP algorithm is the global optimal trajectory, which makes it occupy a pivotal position in modern control theory. The emergence of PMP significantly enriches optimal control theory and offers a powerful mathematical tool for solving HEV energy optimization problems. PMP has been extensively studied and applied in HEV optimal control strategies. Figure 8 presents the flowchart for simulating and calculating the PMP-based energy optimization management method.

Xu et al. (2014) [142] provided a real-time optimization control of HEV based on the PMP, with the aim of ensuring the global optimality of energy management, minimizing the computational burden of the algorithm, and achieving real-time control. Liu et al. (2014) [143] combined PMP with ECMS, used PMP for real-time control of parallel HEVs, took the fuel consumption and SOC maintenance of heavy-duty parallel HEVs as the control objective, used proportional–integral control for the equivalent factor, and carried out real-time control for online regulation, and the simulation results were extremely similar to the DP algorithm, with an increase in fuel consumption of about 1.3%, which was close to the global optimum. Li et al. (2016) [144] conducted a comprehensive optimization of a hybrid energy storage system, with a focus on the development of an efficient energy management system utilizing pulse modulation patterns for hydrogen–electric vehicles equipped with fuel cells and supercapacitors. They aimed to minimize hydrogen consumption, optimize the SOC of supercapacitors, lower the overall cost of the driveline, and simultaneously enhance the durability of the fuel cell system. Zhu et al. (2020) [145] first established the dynamics model and control model of a hybrid vehicle; then, based on the PMP, the Hamiltonian function’s minimum was solved to determine the best control technique. It can adaptively adjust the working state of the engine and motor according to the real-time state of the vehicle and the operating environment to achieve optimal energy utilization and emission control. Guo et al. (2020) [146] developed a robust predictive model for PMP-based PHEVs energy management using a Design for Six Sigma approach. Additionally, Guo et al. (2020) [147] proposed a driving pattern recognition method to address the noise of stochastic vehicle mass in PMP-based energy management for PHEVs. Yi et al. (2022) [148] developed an advanced method specifically for hybrid energy storage electric vehicles, which takes into account battery degradation and optimizes performance using a PMP-based pulse modulation model. Ritter et al. (2022) [149] used PMP, combined with long-term stochastic MPC and scenario-based optimization methods, to provide a new and highly efficient solution for the energy management of HEVs. Hou et al. (2022) [150] introduced a novel adaptive EMS grounded on PMP. This system incorporates both past driving patterns and variable vehicle quality into its operation. The findings indicated that, when compared to a traditional rule-driven EMS, the proposed approach yielded an average improvement of 18.36% in fuel efficiency. Ma et al. (2024) [151] proposed an adaptive EMS based on Artificial Neural Network–PMP for plug-in hybrid electric buses by considering the problem of the dynamic change of vehicle mass under dynamic driving conditions, which improves the effect of the overall efficiency and mobility while adapting to the different loading conditions, and solves the problem of the traditional EMS, which is unable to adapt to the dynamic change of the vehicle mass, leading to the poor optimization of energy. Overall, these studies emphasize the significance of advanced EMSs, optimization frameworks, and predictive models in improving HEV efficiency and performance, especially concerning battery lifespan, fuel economy, and battery degradation.

(d) Linear Programming.

The primary goal of LP is to optimally allocate various energy sources to meet the diverse needs of vehicle operation while maximizing energy efficiency and minimizing emissions. The core lies in constructing a linear mathematical model and seeking the optimal values of decision variables by setting linear objective functions and linear constraints. LP plays an important role in the fuel efficiency optimization of series HEVs. Applying LP to formulate the fuel efficiency optimization problem allows us to find the global optimal solution, use energy efficiently, and reduce waste, thereby promoting the sustainable development of the automotive industry.

Onat et al. (2020) [152] applied a hybrid life cycle sustainability assessment and multi-objective decision-making approach to promote the use of electric vehicles, suggesting that HEVs should comprise over 90% of the vehicle fleet for sustainability. Afrashi et al. (2020) [153] presented a mixed integer LP model designed specifically for the efficient management of multicarrier energy systems, aiming to attain optimal solutions in a streamlined manner. Zhang et al. (2020) [154] formulated a real-time energy management algorithm for parallel HEVs, leveraging a nonlinear optimal control framework under an MPC scheme. Pascali et al. (2020) [155] discussed the optimal energy management for parallel HEVs, focusing on battery preservation in the context of aging. Robuschi et al. (2020) [156] presented a minimum-fuel strategy for HEVs using iterative LP. Ghandriz et al. (2021) [157] explored the application of sequential programming for real-time predictive energy management in heavy-duty HEVs.

3.2.2. Real-Time Optimization

By optimizing the energy flow for the vehicle’s transient operating conditions, the transient optimization-based energy management system enables flexible control without requiring the prediction of future driving information or limiting it to a certain duty cycle. This method is relatively small in computation and easy to accomplish in practical applications. However, although the instantaneous optimization method can achieve the optimal effect at a specific moment, it is not equivalent to global optimization, and thus cannot guarantee the optimal performance during the whole driving process. To overcome this limitation, global optimization techniques have been introduced, but due to their causal nature, these methods are not appropriate for analyses done in real time. By introducing a cost function dependent solely on the system’s current state, the global optimization criterion is effectively reduced to instantaneous optimization, resulting in an EMS that is both flexible and efficient in practical applications. Common optimization methods include energy management techniques based on minimum equivalent fuel consumption and MPC.

(a) Equivalent Consumption Minimization Strategy.

The ECMS calculates the current system state and the online measurable quantity of fuel equivalents in real time to convert the motor energy consumption to the engine fuel consumption. Without assuming that the driving mode has been known beforehand, the ECMS finds and implements the best solution instantly. The proposed methodology develops a comprehensive fuel cost function, rooted in the calculation of equivalent fuel consumption. It further enhances the emission optimization process by incorporating weighting factors, ultimately resulting in a multi-objective function solution. Consequently, ECMS not only facilitates real-time energy management, but also achieves a balanced optimization of vehicle dynamics, fuel efficiency, and emission performance. Figure 9 shows a simplified flowchart used to recognize the input and output states of the ECMS used.

Yu et al. (2020) [159] investigated energy efficiency improvement problems of HEVs with automated manual transmissions from both design and control aspects, utilizing an optimal control software package validated with DP and ECMS. Zhou et al. (2020) [160] introduced a new optimal control problem for parallel HEVs that considers both fuel consumption and battery aging in the cost function. Han et al. (2020) [161] introduced a recurrent neural network-driven adaptive ECMS framework tailored for PHEVs, thereby guaranteeing a nearly global optimal performance in terms of energy management control. Yang et al. (2021) [162] formulated a self-adaptive ECMS specifically for HEVs, employing dynamic adjustments of the equivalent factor to achieve near-optimal fuel efficiency. Zhang et al. (2020) [163] proposed an adaptive energy management approach for automated parallel HEVs based on ECMS to optimize gearshift commands and torque distribution. Hao et al. (2021) [164] employed a Breadth-First Search (BFS) algorithm to dynamically adjust the equivalent factor in real-time, introducing a BFS-based adaptive ECMS specifically tailored for HEVs. Moreover, Mounica et al. (2022) [165] combined the Adaptive Neuro-Fuzzy Inference System and ECMS to minimize hydrogen consumption in HEVs, achieving an 8.7% reduction compared to other control strategies. Hu et al. (2022) [103] tackled challenges encountered in contemporary Reinforcement Learning frameworks for EMS tasks. They introduced an adaptive hierarchical EMS approach that seamlessly integrates heuristic ECMS expertise with a deep deterministic policy gradient, thus enhancing the system’s performance and adaptability. Hu et al. (2024) [166] introduced a real-time multi-criteria optimization technique utilizing an adaptive ECMS. This approach aims to enhance the energy utilization of PHEVs while minimizing the extent of battery life deterioration. By doing so, they addressed the challenge of efficiently managing PHEV energy usage while preserving battery longevity under varying battery performance and dynamic driving scenarios. These studies highlight the importance of ECMS in optimizing EMSs for HEVs.

(b) Model Predictive Control

MPC is an efficient energy management method that utilizes system identification to develop a dynamic process model. It optimizes the current time slot by also accounting for future time slots [68]. MPC reformulates the overarching global optimal control challenge into a localized optimization problem within a prediction horizon. It achieves rolling optimization by identifying optimal vehicle dynamics parameters online, which then facilitates the updating of the predicted vehicle operating state or control parameters for the subsequent time domain. Thus, the application of the proposed method yields optimization results that demonstrate robustness and suitability for controlling uncertain and nonlinear dynamic systems, particularly in the context of energy management for HEVs. By predicting future events and taking corresponding control measures, MPC can significantly improve fuel economy and optimize vehicle performance. The MPC formulation flowchart is shown in Figure 10.

Hu et al. (2020) [168] introduced a multi-objective predictive control model framework specifically tailored for HEVs during car-following scenarios. This framework aims to optimize fuel efficiency, minimize emissions, and simultaneously guarantee the safety between vehicles. Similarly, Xu et al. (2020) [169] presented a real-time MPC methodology, which leverages lookahead prediction techniques to forecast the future trajectories of preceding vehicles, thereby minimizing the economic expenditure associated with HEVs. In the realm of battery management systems (BMS), Madsen et al. (2020) [170] introduced an FPGA-based hardware accelerator for physics-based Extended Kalman Filter to address the computational complexity of physics-based models coupled with MPC. Sotoudeh et al. (2020) [171] introduced a robust hierarchical control approach for HEV energy management under uncertain conditions. This strategy employs a pseudo-spectral optimal control method at the upper level, coupled with a tube-based MPC controller at the lower level, to ensure effective energy management in the presence of uncertainties. Chen et al. (2020) [108] explored the application of nonlinear MPC for heavy-duty HEVs using a random power prediction method, demonstrating its effectiveness through hardware-in-the-loop simulations. Furthermore, Zhao et al. (2021) [172] formulated a two-tiered real-time optimization control methodology for the concurrent management of battery thermal regulation and heating, ventilation, and air conditioning systems in interconnected and autonomous HEVs, aiming to balance the trade-off between energy conservation potential and control span. Al-Saadi et al. (2022) [173] presented a sophisticated driver assistance system tailored for HEVs. This system integrates adaptive cruise control and energy management functionalities, leveraging both switched MPC and neuro-fuzzy systems to enhance driving assistance and optimize energy utilization. Lv et al. (2022) [174] offered a comprehensive overview of the merits and viable application scenarios of diverse prediction and solution methodologies within EMSs that utilize MPC for HEVs. They emphasized and examined the specific implementations as well as the practical efficacy of these MPC-driven EMSs across various systems. Liu et al. (2023) [175] devised a two-tiered control approach encompassing the development of an SOC reference planning model and an MPC-based real-time power allocation model. This dual-layer strategy effectively integrates global and localized optimization techniques for hybrid electric trucks, thereby significantly enhancing their fuel efficiency. Essa et al. (2023) [176] proposed an intelligent controller for HEVs based on MPC-based Artificial Neural Networks for hardware-in-the-loop implementation. Tao et al. (2024) [177] paid special attention to the social cost of carbon emissions and the battery discharge aging conflict, and proposed a novel EMS based on MPC. This strategy achieves an optimal balance between energy consumption, battery life loss, and carbon emission cost by minimizing the total cost of carbon emissions within the driving mileage, solving the problem that traditional EMSs cannot efficiently consider these factors, and achieving a win–win situation for both environmental protection and economy.

Compared to the EMSs in this chapter, GAs stand out with their excellent global search capability. They are not only capable of finding the global optimal solution, but also of pinpointing the optimal EMS in a complex search space. GAs have strong parallelism and can run in parallel on multiple processors or compute nodes, which significantly improves the efficiency of search and computation. Unlike optimization algorithms that rely on derivative information, GAs use selection, crossover, and mutation operations to find optimal solutions by simulating the process of biological evolution without the need for derivative information. This distinctive characteristic extends the application of GAs to a broader spectrum of scenarios, encompassing the handling of discontinuous and non-convex challenges. This augmentation significantly widens their utilization in EMSs for hybrid vehicles. Furthermore, the GA can be synergistically integrated with alternative optimization techniques to formulate a hybrid optimization approach, thereby enhancing the optimization efficacy and precision of the EMS, and better aligning with the operational requirements of HEVs in real-world settings. This adaptability and versatile applicability render GAs a pivotal instrument for optimizing EMSs in HEVs.

4. An Exploration of the Advantages of Genetic Algorithms

GAs, a stellar optimization approach, typically find diverse and captivating applications spanning numerous domains. These include but are not limited to Path Finding Problem, Prisoner’s Dilemma scenarios, Motion Control techniques, Center Localization Problem, Traveling Salesman Problem, Production Scheduling, Artificial Life Simulation frameworks, Signal Processing methodologies, and Image Processing techniques [57]. In this section, we delve briefly into the fundamentals of GAs and furnish an illustrative application of GA-based energy management for HEVs.

4.1. The Mathematical Mechanism of the Primitive GA

The original GA is rooted in Darwin’s theory of natural selection, incorporating three fundamental elements: heredity, variability, and the competition for survival. This approach emulates the processes of natural selection and genetics to seek out an optimal solution [57]. In the algorithm, each possible solution is encoded as an individual that forms a population. Initially, a group of individuals is randomly generated. Based on the fitness function, we evaluate the advantages and disadvantages, and perform selection, crossover, and mutation operations based on fitness. The selection operation reflects the principle of “survival of the fittest”, the crossover operation combines good characteristics, and the mutation operation increases diversity. Through iteration, the population gradually evolves and approaches the optimal solution. GAs involve coding, fitness functions, crossover, and mutation operators, etc. Selection and design are critical to performance. Although it sometimes needs to be improved, its evolutionary mechanism still has significant advantages in solving complex optimization problems.

To achieve the most effective control parameters for the EMS, the GA is utilized to delve into the optimal values of individual parameters within a constrained solution space. Its search methodology relies primarily on the evaluation of the fitness function, as expressed mathematically in Equation (1) below [178].

$$\left\{\begin{array}{c}min J=f\left(x_1,x_2,\cdots ,x_n\right)\\ s·t·g\left(x\right)\le 0\end{array}\right.$$

(1)

In this equation, ($x_1,x_2,\cdots ,x_n$) represent the parameters that require optimization. The fitness value is denoted by ($J$), which is determined by the fitness function ($f\left(x\right)$). Additionally, ($g\left(x\right)$) represents the constraint function that needs to be considered. Through calculation, a set of potential solution vectors can be generated. Subsequently, a new population is formed by screening and retaining well-adapted individuals through reproduction, hybridization, and genetic variation. The process by which a new generation inherits genetic information from its predecessors while simultaneously increasing the likelihood of transmitting advantageous genes exemplifies the potential for adaptive enhancement within a population. This iterative mechanism continues until a predetermined termination condition is met, resulting in progressively improved adaptability. Consequently, this procedure highlights the effectiveness and superiority of GAs in addressing and solving optimization problems. Figure 11 illustrates the fundamental process of a traditional GA.

4.2. The Multi-Objective Optimization Method

In traditional GAs, the fitness function is typically designed to address a single optimization objective. However, the real-world process of optimizing EMS frequently involves multiple, often conflicting objectives, such as extending battery life, improving fuel economy, enhancing power performance, reducing emissions, and lowering costs. These varied objectives rarely reach their optimum simultaneously, presenting a significant challenge for researchers. In fact, real engineering problems always have multiple optimization objectives, including cost minimization, performance maximization, and reliability improvement. Therefore, a reasonable solution to a multi-objective problem is to investigate a set of solutions, each of which satisfies an acceptable level of objectives without being dominated by any other solution [179]. Two general approaches to multi-objective optimization are weighted and non-normalized methods.

4.2.1. Weighted Method

The weighted method is a simpler approach, which forms a single parameterized objective by linearly combining multi-objective functions and setting weight vectors based on the importance of each objective. The order of the candidate vectors may vary from objective to objective because there may be a difference in priority or focus between the objectives. Moreover, the effectiveness of the solution is significantly affected by the underlying weight vectors. The weighted method can be expressed by Equation (2) [180]:

$$\left\{\begin{array}{c}min J={\omega }_1{f}_1\left(x_1,x_2,\cdots ,x_n\right)+{\omega }_2{f}_2\left(x_1,x_2,\cdots ,x_n\right)+\cdots {+\omega }_n{f}_n\left(x_1,x_2,\cdots ,x_n\right)\\ s·t·{g\left(x\right)}_i\le 0,i=1,2,\cdots ,m\end{array}\right.$$

(2)

In the realm of optimization, ($f_1$, $f_2$, $\cdots f_n$) represent the various objectives. The constraints associated with these objectives are denoted by (${g\left(x\right)}_i$). Additionally, (${\omega }_1$, ${\omega }_2$, $\cdots$ ${\omega }_n$) signify the corresponding weights, with a crucial stipulation that the aggregate of these weights must equal 1. The weighted method has significant advantages in that its simplicity and intuitive nature allow researchers to flexibly control the balance between different objectives by adjusting the weights conveniently. However, the weighted methods also face the challenge that their weight allocation often relies on the experience and subjective judgment of researchers, which may lead to uncertainty and inconsistency in the results, thus affecting their validity and reliability in multi-objective optimization to a certain extent.

4.2.2. Non-Normalized Method

A non-normalized method is used to solve multi-objective optimization problems without pre-setting weights for each objective, but instead relies on the Pareto mechanism. By applying the Elite Strategy Non-dominated Sorting GA (NSGA-II), the Pareto front as well as the optimal solution set can be obtained efficiently [181]. The basic definition of Pareto optimality is described below:

$$\left\{\begin{array}{c}min J={\left[f_1\left(x_1,x_2,\cdots ,x_n\right), f_2\left(x_1,x_2,\cdots ,x_n\right),\cdots , f_n\left(x_1,x_2,\cdots ,x_n\right)\right]}^{\mathrm{T}}\\ s·t·{g\left(x\right)}_i\le 0, i=1,2,\cdots ,m\end{array}\right.$$

(3)

NSGA-II employs an efficient non-dominated sorting mechanism that significantly diminishes computational intricacy, thereby sustaining the diversity of the population and mitigating the risk of losing optimal solutions. This approach further enhances the algorithm’s speed and resilience. Figure 12 illustrates the sequential steps involved in the implementation of NSGA-II.

4.3. Application of GA-Based Energy Management for HEVs

In HEV energy management, the application of GAs manifests in three primary areas. Firstly, GAs aid in optimizing energy distribution by reasonably deploying power sources such as the engine, motor, and battery, based on the vehicle state and driving demands, thereby achieving efficient energy supply. Secondly, GAs are instrumental in optimizing battery management through the adjustment of charging and discharging strategies, which helps prevent battery damage and enhances energy utilization efficiency. Thirdly, GAs contribute to optimizing the driving mode by automatically adjusting it according to the driver’s preference and the vehicle’s state, ensuring a balance between driving performance and energy consumption.

To fulfill the aforementioned optimization objectives, the pivotal role of the GA’s optimization process cannot be overstated. Typically depicted in Figure 13, this process comprises several integral steps as outlined below:

(1) Select an initial population within the feasible solution domain to start the algorithm’s optimization.

(2) Iteratively optimize the initial population through genetic operations, i.e., selection, crossover, and mutation, to gradually generate a new population that continuously approaches the global optimal solution.

(3) Referring to the iterative principle of the intelligent optimization algorithm, determine whether the population meets the end criteria, such as reaching the preset number of iterations or the quality of the solution meeting the preset requirements.

Only when these conditions are met will the algorithm stop iterating and output the final optimization results. Through this series of steps, the GA plays an indispensable role in HEV energy management.

Min et al. (2022) [182] introduced an EMS based on a neural network optimized by a genetic algorithm (NNOGA). This strategy aims to minimize hydrogen consumption and enhance fuel cell durability in fuel cell hybrid electric vehicles (FCHEVs). The study employs a genetic algorithm to optimize the neural network’s parameters, thereby mitigating the adverse effects of start–stop cycles and rapid load variations on fuel cell durability. In this strategy, the fuel cell’s output power serves as the objective function for the training set, with the neural network’s weights and thresholds acting as decision variables. The results indicate that NNOGA effectively avoids unnecessary start–stop cycles and rapid power fluctuations, outperforming the unoptimized neural network in this regard. Within the NNOGA framework, the genetic algorithm fine-tunes the neural network’s parameters to adhere to the predefined upper and lower limits of the fuel cell’s output power. Additionally, a start-stop deceleration module is incorporated into the simulation system to further constrain rapid start–stop cycles of the FC. By integrating the start–stop deceleration module, rapid start–stop cycles of the FC are effectively curtailed, allowing the FC to operate continuously for a duration to charge the auxiliary energy battery. When compared to the ECM strategy, NNOGA reduces the number of start–stop cycles by 33.0% in the NEDC driving cycle, demonstrating the significant impact of the genetic algorithm-optimized neural network on enhancing fuel cell durability.

Li et al. (2021) [183] innovatively applied a GA for multi-objective co-optimization of key engine control parameters, including variable valve timing, ignition advance angle, and exhaust gas recirculation rate. Experimental data revealed that this strategy significantly improved combustion efficiency, reduced fuel consumption by 12.48%, and decreased NOx emissions by 92.64%. Further investigations have demonstrated the efficacy of GAs in control optimization under extreme operating conditions. For instance, Tang et al. (2023) [184] constructed a cold-start emission prediction model for hybrid vehicles across a wide temperature range (−20 °C to 40 °C) by optimizing the initial weights and threshold parameters of a neural network (BP) using GA. The hybrid GA-BP algorithm was experimentally validated to exhibit a prediction error rate of less than 3.2% for emission indicators such as CO, CO₂, HC, NOx, and PN, providing a reliable theoretical basis for formulating emission control strategies in low-temperature environments.

In a study by Montazeri-Gh et al. (2006) [185], a novel GA-based EMS was developed to minimize fuel consumption and emissions while meeting driving performance requirements. The fitness function was defined as the objective function, with fuel consumption and emissions serving as optimization objectives, and driving performance requirements as constraints. Computer simulations validated the methodology’s effectiveness, achieving reductions in fuel consumption and emissions while ensuring vehicle performance stability. Ding et al. (2021) [178] further proposed a GA-based EMS for HEVs. They utilized a vehicle model from the ADVISOR database and conducted simulation studies using the MATLAB Simulink environment in conjunction with the GA optimization tool. The simulation results indicated that GA optimization successfully achieved the sub-objectives set in the fitness function, significantly improving HC and NOx emission performance. These studies underscore the significant potential of GA-based EMS in optimizing HEV energy management, effectively coordinating multiple objective functions and decision variables for comprehensive vehicle performance optimization.

Xu et al. (2023) [186] proposed a Multi-Island Genetic Algorithm (MIGA)-based optimization strategy aimed at harnessing the energy-saving potential of a Hybrid Energy Storage System (HESS) for the energy management of HEVs. The study explicitly defined two core objective functions: minimizing cumulative battery ampere hours (Ah) to extend battery life and minimizing equivalent fuel consumption (EFC) to enhance fuel economy. Decision variables included the transmission ratio (TR) and several operational parameters in the EMS, which collectively determined the vehicle’s power performance and energy consumption. By optimizing these decision variables, the genetic algorithm developed optimal energy management strategies for HEVs in various driving modes. Under WLTP operating conditions, the algorithm performed global optimization to minimize equivalent fuel consumption and battery accumulated ampere hours under HESS, APU, and ECMS cooperative modes. Correlation analysis revealed that the optimized mode of operation improved fuel economy by 4.49% under WLTP conditions while reducing battery accumulated ampere hours by 11.37%.

Several researchers have employed GA technology in the optimization of EMS for HEVs and conducted a comparative analysis with other mainstream optimization algorithms. The findings indicate that genetic algorithms demonstrate substantial theoretical advantages in EMS optimization for HEVs, primarily due to their distinctive bionic principles and algorithmic structural characteristics.

Zhao et al. (2024) [187] utilized the NSGA-II algorithm to achieve synergistic optimization of dynamic performance and economy. This resulted in a 9% reduction in vehicle acceleration time (reaching 100 km/h in 8.29 s), a 7% enhancement in dynamic performance, and a 5% reduction in power loss. They compared the NSGA-II optimization technique with SO, ACA, and other algorithms. The results revealed that in terms of computational performance; the optimization accuracy reached 89.99%. Processing 6000 MB of data took only 49.20 s, and the transmission delay was stable at 20.20 ms, which was significantly superior to comparison algorithms such as PSO and ACA. Its unique binary coding mechanism is inherently suitable for the optimization of discrete control variables. When combined with fuzzy logic parameter adjustment, the coverage of the Pareto frontier in multi-objective optimization was 15.7% higher than that of MOPSO. This comprehensively validates the technical superiority of GAs in addressing multi-objective and multi-constraint optimization problems in HEVs.

Wang et al. (2022) [38] assessed the performance of energy management strategies optimized by the GA and presented a detailed comparison among GA-optimized, non- optimized, and DP strategies. To verify the robustness of the GA-optimized fuzzy control energy management strategy, the researchers conducted a comparative performance analysis under different ambient temperature conditions (10 °C, 25 °C, and 40 °C). The comprehensive analysis results indicate that the energy economy of the electric vehicle is improved by 2.6%, 2.4%, and 3.3% compared to the non-optimized strategy under different temperature conditions. The hybrid energy storage system (HESS) reduced energy consumption by 2.6%, 2.4%, and 3.3% at 10 °C, 25 °C, and 40 °C, respectively. Additionally, the performance difference between the GA optimization strategy and the DP strategy decreased to 4.3%, 2.7%, and 5.1% at 10 °C, 25 °C, and 40 °C, respectively.

Yuan et al. (2022) [188] employed GAs in the optimization of the hybrid vehicle EMS, demonstrating significant advantages under two typical driving conditions, NEDC and UDDS. When compared with rule-based EMS and fuzzy logic EMS, the GA optimization scheme achieves optimal performance close to that of DP in terms of fuel cell durability and battery charge maintenance. Specifically, under NEDC conditions, the GA optimization reduces hydrogen consumption by 34.43% compared to the rule-based EMS and by 18.56% compared to the fuzzy logic EMS. Under UDDS conditions, the reductions are 26.18% and 20.63%, respectively. These data comprehensively demonstrate that the GA can effectively overcome the local optimum limitation of the traditional rule-based approach through its global optimization capability, while avoiding the lack of accuracy in the fuzzy logic controller.

In the study conducted by Kemper et al. (2025) [189], a multi-objective evolutionary reinforcement learning (MOEvoRL) framework is proposed to optimize electric vehicle charging strategies using GAs, enabling the identification of multiple optimal strategies in a single training session. The study focuses on the simultaneous attainment of key objectives, including battery state-of-charge maximization, photovoltaic (PV) power consumption enhancement, peak load reduction, and overall grid load smoothing. In this context, the GA exhibits significant technical advantages. In comparison to the traditional gradient-based MODDPG algorithm, which is susceptible to falling into local optima, the GA-driven MOEvoRL demonstrates excellent convergence stability in multi-objective optimization due to its global search capability and population intelligence mechanism. In particular, its LSTM-NSGA-II architecture not only generates diverse solution sets that comply with grid constraints, but also significantly reduces the reliance on large-scale training data. When compared with deep reinforcement learning methods, GAs possess outstanding features such as simple implementation, efficient computation, and strong parallelization ability. Its population optimization property is inherently suitable for the multi-objective trade-off problem in energy management. Experiments confirm that the GA achieves a 13.7% improvement in energy allocation efficiency over traditional methods while ensuring grid stability. This comprehensive performance advantage renders it a promising intelligent optimization paradigm in the field of EV energy management.

Therefore, these studies collectively show that the advantages of applying genetic algorithms compared with other hybrid vehicle energy management strategies are mainly reflected in the following four aspects:

(1)

Global search capability: with its parallel search characteristics, GAs can explore the whole parameter space, effectively avoid local optimization, and ensure to find the global optimal EMS, which is much better than traditional optimization methods, as well as fully release the performance potential of hybrid vehicles.

(2)

Multi-objective and multi-constraint processing ability: GAs can simultaneously cope with multiple objectives and constraints, such as energy consumption, emissions, driving performance, etc., to find the optimal balance point, while the traditional strategy is often difficult to take into account, resulting in impaired performance.

(3)

Adaptability and flexibility: GAs can adaptively adjust their strategies according to the driving conditions and demands, adapting to a variety of road conditions, and efficiently utilizing energy in both congestion and cruising. Traditional fixed strategies are difficult to cope with changing environments.

(4)

Improve energy efficiency and driving performance: The GA optimizes the strategy to accurately control the energy flow, improve fuel economy and reduce emissions, while optimizing the driving experience to achieve both comfort and efficiency.

5. Conclusions

The objective of this study is to conduct a comprehensive review of HEVs and their EMS classification, while emphasizing the merits of GAs in optimizing these systems. Section 2 presents a detailed classification of HEVs based on hybridization degrees and power-source arrangements, encompassing series, parallel, and Power-Split configurations. Each configuration operates on distinct working principles and is applicable in different scenarios, endowing HEVs with a high level of flexibility and adaptability across various driving environments. Section 3 analyzes the EMS, which serves as the core of hybrid technology and is directly associated with energy consumption, emissions, and vehicle performance. Currently, EMS is predominantly categorized into rule-based strategies and optimization-based driving strategies. While the rule-based strategy is simple and straightforward to implement, it lacks global optimization capabilities; in contrast, the optimization-based driving strategy exhibits superior performance but suffers from higher computational complexity and inadequate robustness. Section 4 focuses on the advantages of GAs in optimizing the EMS of HEVs. As a global optimization algorithm, the GA is capable of handling multiple objectives and constraints simultaneously to prevent getting trapped in local optimal solutions. By simulating natural selection and genetic mechanisms, a GA can identify the global optimal solution within the complex parameter space, thereby significantly enhancing the performance of the EMS. Moreover, the adaptability and flexibility of GAs allow them to dynamically adapt to the driving environment and achieve real-time optimization.

Consequently, in this study, GAs are chosen as the core method for optimizing the energy management of HEVs, primarily due to their unique advantages in addressing multi-objective, discrete-variable optimization problems. When compared with algorithms like particle swarm optimization (PSO) and ant colony optimization (ACO), the binary coding feature of GAs is more appropriate for handling discrete control variables in HEVs. Furthermore, its population mechanism and crossover operator design can effectively preserve the diversity of solutions while ensuring the global search capability. Nevertheless, GAs still exhibit limitations in the energy management applications of HEVs. Firstly, with respect to computational efficiency, GA is required to evaluate each individual within the population, and the prolonged computation time under complex operating conditions poses a challenge for real-time control. Secondly, GAs demonstrate high parameter sensitivity, and key parameters, such as the crossover rate and mutation rate, require specific tuning for different driving scenarios (e.g., urban roads and highways), with the optimal parameters varying significantly. Additionally, in high-dimensional optimization problems, GAs may encounter the phenomenon of premature convergence, and their optimization effect is inferior to that of hybrid intelligent algorithms.

To overcome these limitations, future research endeavors will concentrate on the following directions: (1) Developing a hybrid optimization framework that integrates the global search capability of GAs and the rapid convergence characteristics of PSO, and designing novel GA–PSO hybrid algorithms to enhance real-time performance. (2) Investigating the parameter adaptive mechanism and employing online learning techniques to achieve dynamic matching between GA parameters and driving conditions. (3) Exploring the parallel computation architecture and reducing the number of parameters and driving scenarios through GPU acceleration and other techniques to decrease the iterative computation time. (4) Combining deep reinforcement learning and utilizing the GA optimization results as the initial strategy to further enhance the control accuracy. These improvements are anticipated to preserve the advantages of GAs while overcoming their major limitations in HEV applications, thereby promoting the development of HEV energy management technology.