## 3 Material and Methods
### Methodology
#### 3.2.2 Individual Random Search  
Individual random search refers to an individual who conducts random investigations by themselves without referring to other FP location. **Method 4:** Levy Flight  
Levy flight is well known for solving diffuseness, scaling, and transmission problems related to optimization. According to numerous studies, researchers find that the Levy technique is universal and many innovations have evolved to boost Levy flight efficiency [27]. Levy flight is essentially a random walk, with the arbitrary stride length drawn from the Levy distribution which has infinite variance and infinite mean. According to [PERSON] and [PERSON]'s research [28], the fruit flies influenced the Levy flight style's intermittent free-scale search pattern or _Drosophila melanogaster_ exploring their environment with a succession of straight flight routes interspersed by 90\({}^{\circ}\) sudden twists. A random walk generates Levy flights with a stride length drawn from the stable levy distribution, as shown in Algorithm 4. A simple power-law formula is then described using the Levy probability distribution. Here, \(0<\beta\leq 2\) is the Index of Levy distribution [29]. \[Levy(s)\sim|S|^{-1-\beta} \tag{4}\]```
1:Initialize each FP position
2:Initialize each Tree position
3:Set \(\beta\). 4:Set list sigma value; \(list\_sigma\). 5:Set reach of step; \(reach\). 6:while termination condition not satisfied:
7:if\(0.5<\beta<1.95\):
8: Calculate index; \(i=(\beta/0.05)-1\). 9: Get sigma, \(\sigma=list\_sigma[i]\). 10: Choose random value; \(r_{1},r_{2}\). 11: Calculate normal distribution 1; \(nd_{1}=\sqrt{log(r_{1})*(-2)}*cos(2\pi r_{2})*\sigma\)
12: Calculate normal distribution 2; \(nd_{2}=\sqrt{log(r_{1})*(-2)}*cos(2\pi r_{2})\)
13: Calculate random Levy; \(levy=nd_{1}/|nd_{2}|^{(1/\beta)}\)
14:endif
15: Calculate new position; \(X_{new}=levy*reach*0.1\)
16: Update new position. 17: Calculate distance between FP and nearest Tree; \(d_{tree}=d(X_{new}-X_{tree})\). 18:if\(d_{tree}\leq 3\) (\(T_{nearest}\) found):
19:if FP carry poll of \(T_{poll}\
eq T_{nearest}\):
20: Pollination. 21:endif
22: FP carry poll of \(T_{nearest}\); \(T_{poll}=T_{nearest}\)
23:endif
24:endwhile
```

**Algorithm 4** Individual Levy Flight. #### 3.2.3 Multi-Agent System

A multi-agent system (MAS) is a system consisting of multiple interacting computing components known as agents. MAS appears to be a natural metaphor for understanding and building various types of what we can call an artificial social system. The concept of MAS is not reliant on a single application domain, but it seems to be prevalent across various application domains [30]. MAS is commonly used to model self-organizing systems and emerging behavior but has not been applied much to random searches and the immediate solution of optimization problems in a generic way. Since not tied to the direct evaluation of fitness functions, the Pollination Problem also offers MAS the prospect of an application. **Method 5:** Defender-Aggressor-Game (DAG)

We used a basic participation game inspired the Defender-Aggressor-Game (DAG) in which each player chooses two other players at random. Assume that the selected players are player A and player B, as shown in Figure 6. Everyone in this game seeks to position themselves so that their A (the player's \"Defender\") is always between them and their particular B (the player's \"Aggressor\"). Everyone in this game tries to place herself with A and B in the same concurrent manner. This simple rule maintains the stable dynamics and keeps all agents moving around randomly, with a low chance that the pattern stabilizes to a line-like arrangement of all players [31]. It is stated in the Algorithm 5 that in order to obtain a new position, the position must be multiplied by the safety factor of 1.2. The safety factor is the parameter value that has been determined to move far enough behind the defender but not too far. A value above 1 but close to 1 is a common choice.