## 5 Developed BEA-SSA for Optimal CHS  
Solution encoding: as said earlier, CHs are optimally chosen via the BEA-SSA model. The input solution will be the nodes and the solution length will be 100, from which 10 nodes will be chosen as CH. Proposed BEA-SSA ModelTo augment the performance of the traditionalist SSA model [36], BES [37] is combined with it to form BEA-SSA. Usually, self-improvement in typical optimization schemes [38; 39; 40; 41; 42; 43; 44] outcome in superior accuracy. The following rules are included in BEA-SSA. 1. The producers usually have a significant amount of energy and give foraging locations or guidance to all scavengers. Further, it has the responsibility of locating places with abundant food supplies. The level of energy reserves is determined by an evaluation of the individuals' fitness values. 2. Individual sparrows begin to chirp as alarm messages as they detect the predator. When the alarm value exceeds the safety level, the producers must direct all scavengers to the safe zone. 3. Every sparrow becomes a producer as much as it seeks out larger food sources; however, the proportion of scroungers and producers remains constant in the entire population. 4. The producers would act as the sparrows with the maximum energy. Numerous starving scavengers are inclined to fly toward different locations in search of food to gain energy. 5. Scroungers search for food by following the producer who can supply the healthiest food. Meanwhile, some scavengers might keep a close eye on the producers and fight for food to boost their predation rate. 6. When the sparrows present at the group's edge become aware of the danger, they swiftly move into the safe region to obtain a higher position, but the sparrows in the center of the group arbitrarily walk to be adjacent to others. The sparrows make use of virtual sparrows for searching for food in the simulated experimentation. As per BEA-SSA, the initialization is done using the chaotic map function via a sinusoidal map, as shown in Equation (29), where \(X^{r}\in(0,1)\). \[X^{r+1}=bX_{r}^{2}\sin(\pi X^{r}) \tag{29}\]  
Equation (30) is used to represent the position of sparrows. \[X=\left[ \begin{array}{ccccc}X_{1,1}&X_{1,2}&\ldots&\ldots&X_{1,a}\\ X_{2,1}&X_{2,2}&\ldots&\ldots&X_{2,a}\\ \cdot&\cdot&\cdot&\cdot&\cdot\\ \cdot&\cdot&\cdot&\cdot\\ \cdot&\cdot&\cdot&\cdot\\ X_{s,1}&X_{s,2}&\ldots&\ldots&X_{s,a}\end{array} \right] \tag{30}\]  
In Equation (30), \(s\) points out the sparrow count and \(a\) indicates the optimized variable's dimension. The fitness of the sparrow is symbolized as in Equation (31), where \(F_{X}\) point to the fitness value of the individual. \[F_{X}=\left[ \begin{array}{ccccc}f([X_{1,1}&X_{1,2}&\ldots&\ldots&X_{1,a}])\\ f([X_{2,1}&X_{2,2}&\ldots&\ldots&X_{2,a}])\\ \cdot&\cdot&\cdot&\cdot\\ \cdot&\cdot&\cdot&\cdot\\ f([X_{s,1}&X_{s,2}&\ldots&\ldots&X_{s,a}])\end{array} \right] \tag{31}\]  
The producers with large fitness levels in SSA contain a maximum possibility of attaining food all through the searching phase. The producers are reliable in discovering food and direct the moment of the entire populace; the producers look for foodstuff in more areas compared to scroungers. The locations of producers are updated based on rules (a) and (b) of SSA, as per Equation (32). \[X_{c,d}^{r+1}=\left\{ \begin{array}{ll}X_{c,d}^{r}.\exp\biggl{(}\frac{-c}{ \alpha.it_{\max}}\biggr{)}&\quad if\ C_{2}<st\\ X_{c,d}^{r}+P\cdot M&\quad if\ C_{2}\geq st\end{array} \right. \tag{32}\]  
In Equation (32), \(r\) denotes the present iteration, \(it_{\max}\) refers to maximal iteration, \(\alpha\) indicates arbitrary integer, \(st\) and \(C_{2}\) refer to safety threshold and alarm value, \(P\) denotes random number with normal distribution, and \(M\) Illustrate a matrix of \(1\times d\) with element \(1\). Conversely, the scroungers should pursue rules (d) and (e). As said earlier, various scroungers keep a close eye on producers. Because producers recognize good food, they depart their present position to fight for food.