## 1 Introduction
In the HiL implementation stage, exerted road load on wheels can be manipulated in a real-time manner by introducing an input driving cycle to the physical testbed to examine operating conditions as if in a real driving environment. The main objective of HiL implementation is to experimentally test and verify the feasibility, accuracy, high dynamic response, scalability, and reliability merits of a designed control algorithm to guarantee its real-world applicability. The HiL test ensures savings in design cost and time by reducing the total development cycle of vehicle calibration as it indicates how an EMS control unit, and consequently the plant's components, will communicate and behave in a real vehicle. In other words, it provides a validation method for development engineers for the safety and precision of the control system before an actual rule vehicle is available. Hence, once an EMS is designed and verified in a closed-loop manner through HiL, it can ideally be transmitted to a vehicle-in-the-loop (ViL) testbed without design modifications, expecting that the proposed strategy can represent identical features. Considering the discussed phases, Figure 1 recapitulates the chronological design steps known as the \"V\" development process [7]. Although the effectiveness of various EMS algorithms has been extensively reported in previously performed studies, many have been limited to an early EMS design stage (i.e., MiL) of the studied topologies. There has been a tremendous interest in the development of these virtually tested models mainly based on optimization-based (OB) and rule-based (RB) techniques, but in the absence of real-time implementation. Instead, the main outcomes have compared the validity and competency of approaches in addressing the non-linearities/multimodalities of non-convex objectives such as fuel consumption enhancement and battery charge-sustaining in a fully software-based way. For example, in [9], objectives such as battery charge-sustaining and improving fuel economy were considered using a RB EMS, and power distribution through the vehicle components were investigated. In another study [10], different RB strategies were compared in terms of fuel consumption improvements, and the computational costs of the RB EMSs were evaluated through a comparison for a use-case of parallel HEV topology in [11]. In another study [12], the battery state of charge (SoC) control, power flow, and fuel consumption were evaluated through a RB power split method considering the engine operating points. The SoC pattern evolutions were investigated in [13] using a RB supervisory control approach, and in [14], a driving cycle recognition method was employed to improve fuel efficiency. [PERSON] et al. [15] performed an optimization of the control strategy parameters for a series HEV topology to minimize the fuel consumption. In that study, different OB techniques were compared for optimal EMS design in a MATLAB/Simulink(r) environment where the results indicated the superiority of genetic algorithm (GA) compared to DIRECT and thermostatic (On/Off) methods. In another study, [PERSON] and [PERSON] [16] proposed an OB EMS of HEVs by aggregating the constraints into the objective function. In that study, penalty functions were used to weed out the infeasible solutions and minimize fuel consumption and emissions. [PERSON] et al. [17] used GA in a PSAT environment for powertrain optimization of a parallel HEV topology to improve the overall fuel economy. [PERSON] [18] for HEVs and [PERSON] et al. [19] for plug-in HEVs classified and overviewed control strategies including various RB and OB methods, leading to future trends in the field. The equivalent consumption minimization strategy (ECMS) was incorporated into driving cycle prediction, performing horizon optimizations, and pattern recognition concepts in [20; 21] to provide efficient power splitting.