## 5 Co-Optimization of Eco-Driving Strategy and EMSs for HEV/PHEVs
### Single-Vehicle Scenarios
Moreover, more specific HEV-related references can be seen in Table 1.  
\begin{table}
\begin{tabular}{l l l l l l l} \hline \hline
**Classification** & **Reference** & **Modelling Approach** & **Application** & **Verification** & **Achievements** \\ \hline \multirow{8}{*}{Single-Vehicle Scenario} & [67] & – & Bi-level MPC & \multirow{2}{*}{HEV} & \multirow{2}{*}{Simulation} & – & Improve energy efficacy and \\  & & – & C/GMRES & & & computational speed \\  & – & FMF & & & & \\ \cline{1-1}  & & & CLOSA & & & & \\ \cline{1-1}  & & & Cometic Algorithm & HEV & Simulation & – & Reduce fuel consumption and passing \\ \cline{1-1}  & & & Co-optimization & & & & \\ \cline{1-1}  & [70] & – & Trigonometric speed profile & & & & \\ \cline{1-1}  & & MILP & & & & \\ \cline{1-1}  & & & Trigonometric speed profile & & & & \\ \cline{  
The studies mentioned above focus on the intersection as a specific scenario and determine the constraints based on the real-time state of the signalized intersection. However, there is another way of considering the signalized intersection scenario that includes their possible encounters in the uncertainty of future traffic information. One such approach was proposed by [83], who used a novel statistical traffic model to generate stochastic driving behavior and formulate the EMS of HEVs as a bi-level hierarchical optimization problem. This formulation led to an effective upper-level problem that could be solved online as a global optimization using a low-dimension deterministic DP and could be optimized offline using Stochastic Dynamic Programming (SDP), which is embedded with stochastic traffic behavior in the lower level. Simulation results showed reasonable over-consumption compared to deterministic optimization and manageable computational times for both offline and online parts. Another recent work by [84] proposed an adaptive co-optimization method of speed planning and EMS with dynamic probabilistic constraints. The proposed composite sequence generation model enabled dynamic probabilistic constraints by forecasting the upcoming speed distribution of the preceding vehicle. This was based on the probability relationship among future speed sequence, historical speed sequence, and macroscopic traffic state of downstream road segments. By accounting for both large-scale and small-scale traffic disruptions, this method enhanced prediction accuracy by around 10% when compared to purely sequence-based models. Additionally, the distribution divergence was reduced by over 57%. Simulation results indicated a 14.81% increase in driving safety and relatively high energy efficiency compared to existing co-optimization methods under the same car-following conditions. * Cooperative Optimization for PHEVs: Compared to the cooperative optimization of hybrid electric vehicles (HEVs), PHEVs have an additional feature, which allows for the depletion of the battery for electric propulsion and recharging of the battery pack. This makes the Energy Management Systems (EMS) for PHEVs more complex, since the State of Charge (SOC) planning aims for battery depletion during a trip [85]. To tackle this challenge, typical work such as [70] integrated an eco-driving assistance system with the co-optimization of vehicle dynamics and powertrain operations. In this approach, the vehicle dynamic optimization was approximated using the trigonometric speed profile, and the powertrain operation optimization was formulated as a nonlinear constrained optimization problem, which was solved using Mixed-Integer Nonlinear Programming (MINP). The performance of the proposed system was evaluated at different automation levels and achieved an average of 24% fuel savings under typical urban driving conditions. [PERSON]. [72; 73] developed an ecological adaptive cruise controller (ECO-ACC) for  
Figure 8: The Scenario of single-vehicle cooperative optimization logic based on V2I information. PHEVs by considering deterministic traffic SPaT information over the entire route.