## 3 Methodology
### Optimal Driving Model  
3.2.1. Multi-Objective Optimisation  
To establish a global optimisation model for the passage of CAEFVs in the WCSSI, a multi-objective optimisation function representing energy consumption, passenger comfort, and passage efficiency is constructed in this study. Moreover, all objectives are normalised to reduce the influence of dimensional discrepancy on optimisation results. Here, the energy-consumption optimisation refers to the fact that CAEFVs are subject not only to power losses such as motors and auxiliary systems but also to the power replenishment from the WCL and regenerative braking systems during the journey. The formulas utilised in this model are provided below:  
\[F_{e}=\frac{\left(E_{Cm}-E_{Re}-E_{C}-E_{\mu}\right)}{E_{\sigma}}, \tag{7}\]  
\[E_{\mu}=\sum_{i=1}^{n}(E_{Cm}(i)-E_{Re}(i)-E_{C}(i))/n, \tag{8}\]  
\[E_{\sigma}=\sqrt{\frac{1}{n}{\sum_{i=1}^{n}}\big{(}E_{Cm}(i)-E_{Re}(i)-E_{C}( i)-E_{\mu}\big{)}^{2}}, \tag{9}\]  
where \(E_{\mu}\) and \(E_{\sigma}\) are the mean and standard deviation of the total electricity consumption during driving, respectively.  
Driving comfort is closely related to changes in the vehicle acceleration, which can be reduced by minimising speed fluctuations during the vehicle control phase [48]. To avoid the influence of the offset of the positive and negative acceleration values on vehicle fluctuations, the vehicle stability during driving can be assessed by integrating the squared acceleration in the CA over time. Therefore, the comfort optimisation objective is expressed as follows:  
\[F_{e}=\frac{\left(\int_{t_{0}}^{t_{f}}a^{2}(t)d_{t}-C_{\mu}\right)}{C_{\sigma }}, \tag{10}\]  
\[C_{\mu}=\sum_{i=1}^{n}\left(\int_{t_{0}(i)}^{t_{f}(i)}a^{2}(t)d_{t}\right)/n, \tag{11}\]  
\[C_{\sigma}=\sqrt{\frac{1}{n}{\sum_{i=1}^{n}}\bigg{(}\int_{t_{0}(i)}^{t_{f}(i )}a^{2}(t)d_{t}-C_{\mu}\bigg{)}^{2}}, \tag{12}\]where \(C_{\mu}\) and \(C_{\sigma}\) are the mean and standard deviation of speed fluctuations during the vehicle movement, respectively.  
Traffic efficiency optimisation is performed to increase the efficiency of traffic movement by reducing the lead time of CAEFVs in the CA. If a vehicle is unable to cross a signalised intersection at its current speed, it is necessary to adjust the vehicle speed collaboratively to avoid the Stop-Go behaviour at the signalised intersection. The following expressions are used for this purpose:  
\[F_{t}=\frac{\Big{(}t_{f}-t_{0}-T_{\mu}\Big{)}}{T_{\sigma}}, \tag{13}\]  
\[T_{\mu}=\sum_{i=1}^{n}\Big{(}t_{f}(i)-t_{0}(i)\Big{)}/n, \tag{14}\]  
\[T_{\sigma}=\sqrt{\frac{1}{n}{\sum_{i=1}^{n}}\Big{(}t_{f}(i)-t_{0}(i)-T_{\mu} \Big{)}^{2}}, \tag{15}\]  
where \(T_{\mu}\) and \(T_{\sigma}\) are the mean and standard deviation of the pass time during travel, respectively.  
Combining Equations (7)-(15), the multi-objective optimisation function considering the communication delay in the connected environment is obtained.  
\[\min_{a(t+t_{d})}F=\omega_{1}F_{e}+\omega_{2}F_{e}+\omega_{3}F_{t} \tag{16}\]  
\[\omega_{1}+\omega_{2}+\omega_{3}=1 \tag{17}\]  
\[0<\omega_{i}<1,i=1,2,3 \tag{18}\]  
Here, \(F\) is the target optimisation value; \(\omega_{1}\), \(\omega_{2}\), and \(\omega_{3}\) are the weighting coefficients indicating differentiated charging needs; and \(t_{d}\) is the communication delay.