## 2 Literature Review
### Overview of Dandelion Optimizer  
The dandelion optimizer (DO) is a nature-inspired optimization algorithm based on the dispersal process of dandelion seeds. This process models the way dandelion seeds are carried by the wind, allowing them to explore new areas and settle in fertile ground. The DO algorithm translates this natural phenomenon into an optimization framework that balances exploration and exploitation, making it well-suited for solving complex and high-dimensional optimization problems. Rising stage  
In this stage, dandelion seeds (solutions) are dispersed into the air, mimicking the exploration phase. The algorithm introduces randomness through parameters such as the angle \(\theta\), scaling factor \(\lambda\), and a randomly generated vector NEW. The position of each seed is updated as shown in Equation (6):  
\[P(i,j)=P(i,j)+\alpha\cdot v_{x}\cdot v_{y}\cdot(\lambda,0,1)\cdot(\text{NEW}(1, j)-P(i,j)) \tag{6}\]  
where  
* \(\alpha\) is a scaling factor;
* \(v_{x}\) and \(v_{y}\) are velocity components;
* \(\lambda\) is a random scaling factor;
* NEW is a randomly generated vector. This stage allows the algorithm to explore new areas of the search space, mimicking the dispersal of seeds by the wind. Decline stage  
After the seeds have risen, they begin to descend, symbolizing the transition from exploration to exploitation. In this stage, the population is adjusted based on the mean position of the seeds and a random factor \(\beta\), ensuring that seeds settle closer to promising areas, as shown in Equation (7):  
\[P(i,j)=P(i,j)-\beta(i,j)\cdot\alpha\cdot(P_{\text{mean}}(1,j)-\beta(i,j)\cdot \alpha\cdot P(i,j)) \tag{7}\]  
Here, \(P_{\text{mean}}\) represents the mean position of the population, and \(\beta\) is a random factor that controls the descent. This stage refines the search and exploits the best-found solutions. In the final stage, the seeds land and settle into optimal positions. This stage is driven by a Levy flight mechanism, which enhances global exploration by introducing larger, random steps. The position update in the landing stage is given, as shown in Equation (61):  
\[P(i,j)=\text{Elite}(i,j)+\text{Step length}(i,j)\cdot\alpha\cdot(\text{ Elite}(i,j)-P(i,j)\cdot\frac{2l}{\text{Max iter}}) \tag{8}\]  
where  
* Elite(\(i,j\)) represents the best individuals in the population;
* Step length(\(i,j\)) is a step size determined by the Levy flight distribution;
* \(l\) is the current iteration, and Max iter is the maximum number of iterations. This stage ensures thorough exploration of the search space and helps avoid premature convergence. The dandelion optimizer effectively balances exploration and exploitation through its three-stage process. The rising stage emphasizes exploration by allowing the algorithm to search new regions of the search space. The decline and landing stages shift the focus toward exploitation, refining the solutions, and converging toward optimal results. This balance is crucial for solving complex optimization problems, as it prevents the algorithm from becoming trapped in local optima while still ensuring convergence. A key feature of the dandelion optimizer is the incorporation of the Levy flight mechanism in the landing stage. Levy flights introduce randomness with a probability distribution that allows for large, random steps, helping the algorithm escape local optima and explore new areas of the search space. This mechanism is particularly beneficial in high-dimensional and multimodal optimization problems, where the search space is vast and complex.