## 4 Privacy-Preserving Optimization Based on Advanced CH Selection (P2O-ACH)
### Conventional ROA  
Generally, rider optimization algorithm (ROA) is developed based on the concept of the riders being grouped to achieve the target. Here, bypass rider, follower, overtaker, and attacker are considered groups of riders. All the riders are arranged and then divided into groups according to this order. Each group produces their performance separately to achieve their goal. This algorithm pursues a sequential process in a step-by-step manner. At the initial stage, parameter initialization of riders and groups take place. In the ROA method, the determined groups are together represented as T and it randomly takes their position. Hence, the mathematical expression for the process of their group initialization is given below. \[G^{t}=\left\{G^{t}(S_{a},S_{b})\right\};1\leq S_{a}\leq NR_{t};1\leq S_{b}\leq DI _{t} \tag{8}\]  
In Equation (8), \(NR_{t}\) denotes the number of riders present in the race concerning time, \(DI_{t}\) denotes represents the dimension concerning time t. The position of the riders is denoted as \(G^{t}(S_{a},S_{b})\). The notation represents the total number of riders such as bypass rider, follower, overtaker, as well as attacker are BR, F, O, and AT, where (T = BR + F + O + AT). The parameters that are considered are steering angle, acceleration, gear, as well as the brake, and they are installed in each group of riders. The mathematical expression for the calculation of steering angle (\(SA^{t}\)) is given below. \[SA^{t}=\left\{SA^{t}_{S_{a},S_{b}}\right\};1\leq S_{a}\leq NR_{t};1\leq S_{b} \leq DI_{t} \tag{9}\]  
In Equation (9), the steering angle of the current rider is denoted as \(SA^{t}_{S_{a},S_{b}}\) and the beginning stage of the steering angle is shown in Equation (10). \[SA^{t=0}_{S_{a},S_{b}}=\begin{cases}\theta_{a};&\quad\quad\quad\quad\quad\quad \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quadcentralized in nature and use the idea of an arbitrary search in all directions that reflects in the improvement of the success rate. The major parameter which is considered for the measure of the success rate is distance. The mathematical expression for the calculation of distance (\(CR_{dis}\)) is given below.  
\[CR_{dis}=\frac{S_{a}+D_{v}}{S_{a}-D_{v}} \tag{11}\]  
In Equation (11), \(S_{a}\) denoted the location of the current rider and \(D_{v}\) denotes the location of the destination. To increase the success, the rate of the process of leader identification is preceded. The major principle behind the process of leader selection is that the leader that is chosen has the minimum distance (high success rate) from the destination and the leaders are dynamic in nature, varying according to speed, position, and time. Now, the position update takes place according to the groups of riders. At the initial stage, the position update of the bypass rider is mathematically expressed below. \[G_{t+1}^{BR_{j}}(S_{a},S_{b})=\gamma\big{[}G^{t}(\eta,S_{b})\times\mu(S_{b})+G ^{t}(\epsilon,S_{b})\times[1-\mu(S_{b})]\big{]} \tag{12}\]  
In Equation (12), \(\gamma\) denotes an arbitrary number which lies between 0 and 1, \(\eta\) denotes a random value which ranges from 1 to T, \(\epsilon\) a random value which ranges from 1 to T, \(\mu\) represents an arbitrary value ranging between 0 and 1 of size 1 \(\times\) D. Secondly, the position update of the follower rider is mathematically expressed below. \[G_{t+1}^{F}(S_{a},S_{b})=G^{L_{index}}(L_{index},c)+\left[\cos\big{(}SA_{S_{a},S_{b}}^{t=0}\big{)}\times G^{L_{index}}(L_{index},c)\times d_{S_{a}}^{t}\right] \tag{13}\]  
In Equation (13), \(G^{L_{index}}\) denoted the leader location, \(L_{index}\) denoted the leader index, \(SA_{S_{a},S_{b}}^{t=0}\) denotes the current rider steering angle, and \(d_{S_{a}}^{t}\) denotes the additional distance needed to cover the current rider.