Initialization of Rider and other algorithmic parameters

The foremost step is the initialization of algorithm which is done using four groups of riders represented as ${\displaystyle V}$, and initializations of its positions are performed in arbitrary manner. The initialization of group is given by,

${\displaystyle S_{l}=\{S_{l}(v,k)\};1\leq v\leq P,1\leq k\leq W}$

(1)

where, ${\displaystyle P}$ signifies count of riders, and ${\displaystyle S_{l}(v,k)}$signifies position of ${\displaystyle v^{th}}$ rider in ${\displaystyle k^{th}}$ size at ${\displaystyle l^{th}}$ time instant.

The count of riders is evaluated with count of riders of each group and is expressed as,

${\textstyle P=B+J+O+A+K}$

(2)

where, ${\displaystyle B}$ signifies bypass rider, ${\displaystyle J}$ represent follower, ${\displaystyle O}$ signifies overtaker, ${\displaystyle A}$ represent attacker, and ${\displaystyle K}$ signifies rag bull rider. Hence, the relation amongst the aforementioned attributes is represented as,

${\textstyle B+J+O+A+K={\frac {P}{5}}}$

(3)

Finding rate of success

After rider group parameters initialization, the rate of success considering each rider is evaluated. The rate of success is computed with distance and is measured between rider location and target and is formulated as,

${\textstyle Successrate={\frac {1}{\|S_{v}-l_{t}\|}}}$

(4)

where,${\displaystyle S_{v}}$ symbolize position of ${\displaystyle v^{th}}$ rider and ${\displaystyle l_{t}}$ indicate target position. To elevate rate of success, distance must be minimized and hence, distance reciprocal offers the success rate of rider.

Determination of leading rider

The rate of success is employed as significant part in discovering leader. The rider that reside in near target location is supposed to contain highest rate of success.

Evaluate the rider’s update position

The position of rider in each group is updated to discover rider at leading position and hence is winner. Thus, the rider update the position using the features of each rider defined on the definition. The update position of each rider is explained below:

The follower has an inclination to update position based on location of leading rider to attain target in quick manner and is expressed as,

${\displaystyle S_{l+1}^{f}(v,o)=S^{G}(G,o)+[cos(\varphi _{v,o}^{l}*S^{G}(G,o)*\partial _{v}^{l})]}$

(5)

where, ${\displaystyle o}$ signifies coordinate selector, ${\displaystyle S^{G}}$ represent leading rider position, ${\displaystyle G}$ indicate leader's index, ${\displaystyle \varphi _{v,o}^{l}}$signifies angle of steering considering ${\displaystyle v^{th}}$ rider in ${\displaystyle o^{th}}$coordinate, and ${\displaystyle \partial _{v}^{l}}$ represent distance.

The overtaker's update position is utilized to elevate rate of success by discovering overtaker position and is represented as,

${\displaystyle S_{l+1}^{o}(v,o)=S_{l}(v,o)+[D_{l}^{*}{\bigl (}v{\bigr )}*S^{G}(G,o)]}$

(6)

where, ${\displaystyle D_{l}^{*}{\bigl (}v{\bigr )}}$signifies direction indicator.

The attacker contains an inclination to confiscate the leaders position by following the leader's update process and is expressed as,

${\displaystyle S_{l+1}^{a}(v,\rho )=S^{G}(G,\rho )+[cos\varphi _{v,\rho }^{l}*S^{G}(G,\rho )]+\partial _{v}^{l}}$

(7)

Here, the update rule of bypass riders is exhibited wherein standard bypass rider is expressed as,

${\displaystyle S_{l+1}^{b}(v,\rho )=\lambda [S_{l}(\chi ,\rho )*\delta (\rho )+S_{l}(\xi ,\rho )*[1-\delta (\rho )]]}$

(8)

where, ${\displaystyle \lambda }$ signifies random number, ${\displaystyle \chi }$ symbolize random number between 1 and ${\displaystyle P}$ , ${\displaystyle \xi }$ indicate a random number ranging between 1 and ${\displaystyle P}$ and ${\displaystyle \delta }$ represent random number between 0 and 1.

Finding success rate

After executing process of update, the rate of success considering each rider is computed.

Update of Rider parameter

The parameter of rider's update is important to discover an effective solution. Moreover, the steering angle, gears are updated with activity counter, and are updated with success rate.

Off time of rider

The procedure is iterated repeatedly till ${\displaystyle L_{OFF}}$ wherein, leader is discovered. After race completion, the leading rider is considered as winner.

algorithm rider-optimization is
    input: Arbitrary rider position ${\displaystyle S_{l}}$,
           iteration ${\displaystyle l}$,
           maximum iteration ${\displaystyle L}$
    output: Leading rider ${\displaystyle S^{G}}$

    Initialize solution set
    Initialize other parameter of rider.
    Find rate of success using equation (4)

    while ${\displaystyle l<L_{OFF}}$
        for ${\displaystyle v=1toP}$
            Update position of follower using equation (5)
            Update position of overtaker with equation (6)
            Update position of attacker with equation (7)
            Update position of bypass rider with equation (8)
            Rank the riders based on success rate using equation (4)
            Select the rider with  high success rate
            Update rider parameters
            Return ${\displaystyle S^{G}}$
            ${\displaystyle l=l+1}$