## 3 Material and Methods
### Methodology
#### 3.2.2 Individual Random Search
```
1:Initialize each FP position
2:Initialize each Tree position
3:while termination condition not satisfied:
4:\(FP_{current}\) choose two another random FP; \(FP_{1}\) and \(FP_{2}\). 5: Repeat until \(FP_{1}\
eq FP_{2}\). 6: Get position of FP; \(X_{1}=FP_{1}\) position, \(X_{2}=FP_{2}\) position. 7:\(FP_{1}\) as aggressor, \(FP_{2}\) as defender. 8:\(X_{new}=X_{1}+(X_{2}-X_{1})*1.2\)
9: Update new position. 10: Calculate distance between FP and nearest Tree; \(d_{tree}=d(X_{new}-X_{tree})\). 11:if\(d_{tree}\leq 3\) (\(T_{nearest}\) found):
12:if FP carry poll of \(T_{poll}\
eq T_{nearest}\):
13: Pollination. 14:endif
15: FP carry poll of \(T_{nearest}\); \(T_{poll}=T_{nearest}\)
16:endif
17:endwhile
```

**Algorithm 5** DAG. ## 4 Results

The experiment results using the metaheuristic algorithm method from the three different techniques vary depending on the method's behavior. Figure 7 represents the results of these variations by showing the average tree pollination. The time is represented on the x-axis, which ranges from 0 to 20 min. The first minute represented on the graph indicates that the average pollination happened between 0:00 and 0:59. Figure 7a indicates that DAG pollinated more trees at the first minute with an average value of 3.8. Levy comes in second with an average value of 2.35, followed by Idle-CSA 2.2, Idle-Cuckco, and Idle-Jaya with the same average score of 0.95. All simulations demonstrate a substantial difference in results when using the swarm algorithm, i.e., Idle-Jaya, Idle-CSA, and Idle-Cuckco, compared to searches that do not use swarm behavior approaches such as Levy flight and DAG; the average percentage results. Swarm search algorithms such as Idle-Jaya, Idle-CSA, and Idle-Cuckco need some time to pollinate more trees, but Levy flight and DAG require less time to pollinate more trees. This simulation indicates that the swarm method in pollination here requires a longer period of time since these algorithms are meant to work together in the search. However, if using multi-agent system search and individual random search method, more trees are pollinated in a not too long time period since the range of each FP is different. The FP acts independently without the need to stay together. In other words, in using SI algorithms,

Figure 6: Rules for playing the Defender Aggressor Game. we could observe that the FP swarm all close to the same tree, where they can obtain all nectar but will not cross-pollinate before reaching another tree. Once the first FP arrives at the other tree, the tree becomes pollinated and the nectar will not be available to other FP anymore. Figure 7: The average results from all simulation. (**a**) Experiment I. (**b**) Experiment II. (**c**) Experiment III. Aside from the average tree pollination results shown above, this simulation also shows how much nectar FP collects during a tree search. The average results are shown in Table 2. The average amount of nectar collected from all simulations also shows that Levy flight and DAG collect more nectar, even though the values of other Idle-SI are not significantly different from the results. According to [PERSON] and the researchers of [32], the Gini index is the single best measure of inequality. The Gini index is a well-known concentration index established by [PERSON] [33] more than a century ago to measure the level of inequality in income distribution and wealth distribution. The Gini index is used here to describe whether FP nectar intake is spread throughout the FP population in a impartial and balanced manner, contrary to a situation where few FP pick most of the nectar alone. The Gini index values for the FP are shown in Table 3. The Gini index from all experiments revealed that FP distributed nectar equally because zero represents the Gini index of perfect equality. All values are the same, whereas 1 expresses maximal inequality among FP. However, an advantage of DAG against other algorithms is notable here.