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. [PERSON] et al.