## 3 Proposed RBAVO-DE for GS
### Boosting Positions via the AVO Algorithm
#### 3.3.4 Phase of Exploitation  
In this phase, \(|F_{i}^{g}|\) is less than 1. The proposed AVO algorithm's efficacy is evaluated in two sub-phases that comprise the exploitation phase. Each of these sub-phases uses two different strategies. For each internal sub-phase, the appropriate strategy is chosen using two predefined parameters: \(P_{2}\) for the first sub-phase and \(P_{3}\) for the second, with values ranging from 0 to 1. These two internal sub-phases are explained as follows:  
* **First sub-phase of exploitation:** This sub-phase applies two different strategies when \(|F_{i}^{g}|\) is less than 1 and greater than or equal to 0.5. The selection of one of these two strategies is made using a random value \(rand_{P_{2}}\) within the range \([0,1]\) and a specified parameter \(P_{2}\). The initial strategy of this sub-phase is called **siege fight**, which involves sufficiently powerful and somewhat satiated cultures. More robust and healthier cultures try not to share food with others because they convene around a single food source. By swarming near the healthy cultures and engaging in small fights, the weaker cultures try to take food from them. Conversely, the second strategy is called **rotational flight**; it creates a spiral movement between a superior culture and the others. The following illustrates the strategies for the first exploitation sub-phase: \[X_{i}^{g+1}=\left\{ \begin{array}{ll}D_{i}^{g}\times(F_{i}^{g}+rand)-d_{i}^{g },&\text{if }rand_{P_{2}}\leq P_{2},\\ R^{g}-(S_{1}^{g}+S_{2}^{g}),&\text{if }rand_{P_{2}}>P_{2},\end{array} \right\}\text{if }1>|F_{i}^{g}| \geq 0.5,\] (9) \[d_{i}^{g}=R^{g}-X_{i}^{g},\] (10) \[S_{1}^{g}=R^{g}\times\left(\frac{rand\times X_{i}^{g}}{2\pi}\right)\times \cos(X_{i}^{g}),\] (11)\[S_{2}^{g}=R^{g}\times\left(\frac{rand\times X_{i}^{g}}{2\pi}\right)\times\sin(X_{ i}^{g}). \tag{12}\]  
where the vulture's next updated position at the next \((g+1)^{th}\) iteration is denoted by \(X_{i}^{g+1}\), \(D_{i}^{g}\) is defined using Equation (8), and \(rand\) is an arbitrary value between 0 and 1. The distance \(d_{t}^{g}\) between the vulture and one of the best two vultures is estimated using Equation (10); \(R^{g}\) denotes the appropriate best vulture in the current \(g^{th}\) iteration, which is computed using Equation (2); \(S_{1}^{g}\) and \(S_{2}^{g}\) are computed employing Equations (11) and (12), respectively; and \(X_{i}^{g}\) denotes the current position at the \(g^{th}\) iteration. * **Second sub-phase of exploitation:** This sub-phase is carried out when \(|F_{i}^{g}|\) is less than 0.5. Various vulture species gather around the food supply and engage in many sieges and brawls during this sub-phase. This sub-phase employs two different strategies. A predefined parameter \(P_{3}\) and an arbitrary value \(rand_{P_{3}}\), with values ranging from 0 to 1, are used to decide which of these two strategies to use. This sub-phase's initial strategy is called **assemble vultures around the food source**. In this strategy, different kinds of vultures search for food and may compete near a single source. The second strategy is known as **hostile siegeg fight**. In this strategy, the vultures become more aggressive and try to plunder the leftover food from the healthy vultures by flocking around them in different ways. The healthy vultures, on the other hand, deteriorate and are unable to fend off the other vultures. The following illustrates the strategies for the second exploitation sub-phase: \[X_{i}^{g+1}=\left\{ \begin{array}{ll}\frac{A_{1}^{g}+A_{2}^{g}}{2},&\text{ if }rand_{P_{3}}\leq P_{3},\\ R^{g}-|d_{t}^{g}|\times F_{i}^{g}\times Levy_{d},&\text{ if }rand_{P_{3}}>P_{3}, \end{array}