# Artificial Flora (AF) Optimization Algorithm
## 2 Artificial Flora Algorithm
### Artificial Flora Algorithm Theory  
The artificial flora algorithm consists of four basic elements: original plant, offspring plant, plant location, and propagation distance. Original plants refer to the plants that are ready to spread seeds. Offspring plants are the seeds of original plants, and they cannot spread seeds in that moment. Plant location is the location of a plant. Propagation distance refers to how far a seed can spread. There are three major behavioral patterns: evolution behavior, spreading behavior, and select behavior [41; 42; 43]. Evolution behavior means there is a probability that the plant will evolve to adapt to the environment behavior [44; 45; 46]. Spreading behavior refers to the movement of seeds, and seeds can move through autochory or allochory. Select behavior means that flora may survive or become extinct due to the environment. The aforementioned social behaviors can be simplified by some idealized rules as follows:  
**Rule 1:**: Because of a sudden change in the environment or some kind of artificial action, a species may be randomly distributed in a region where there is no such species and then become the most primitive original plant. **Rule 2:**: Plants will evolve to adapt to the new environment as the environment changes. Therefore, the propagation distance of offspring plants is not a complete inheritance to the parent plant but rather evolves on the basis of the distance of the previous generation of plants. In addition, in the ideal case, the offspring can only learn from the nearest two generations. **Rule 3:**: In the ideal case, when the original plant spreads seeds around autonomously, the range is a circle whose radius is the maximum propagation distance. Offspring plants can be distributed anywhere in the circle (include the circumference). **Rule 4:**: Environmental factors such as climate and temperature vary from one position to another, so plants have different probability of survival. The probability of survival is related to the fitness of plant in the position, fitness refers to how well plants can adapt to the environment. That is, fitness is the survival probability of a plant in the position. The higher the fitness, the greater the probability of survival is. However, inter-specific competition may cause plant with high fitness to die. **Rule 5:**: The further the distance from the original plants, the lower the probability of survival because the difference between the current environment and the previous environment will be greater as the offspring plan farther from the original plant in the same generation. **Rule 6:**: When seeds spread by an external way, the spread distance cannot exceed the maximum limit area because of constraints such as the range of animal activity. Figure 1 illustrates the process of migration and reproduction. The details are as follows:  
1. According to **Rule 1**, there was no such species in the region, due to sudden environmental changes or some kind of artificial action, original plants were spread over a random location in the region, as the \(\Diamond(x1)\) shows in Figure 1.
2. According to **Rule 3**, original plants spread seeds in the propagation range. In Figure 1, Distance\({}_{1}\) is the propagation distance of \(\Diamond(x1)\), offspring can be located in anywhere within the blue circle, and the offspring is shown as \(\Diamond(a1a2a3)\) in Figure 1.
3. The number of \(\Diamond\) stand for the fitness. The higher the number, the higher the offspring's fitness. It can be seen from the Figure 1 that if the offspring is closer to the original plant, the fitness is higher: fitness\((a1)>\) fitness\((a2)>\) fitness\((a3)\). This matches **Rule 5**. 4. According to **Rule 4**, only some of the offspring plant survive because the fitness is different. As shown in Figure 1, the solid line indicates a living plant and the dotted line indicates that the plant is not living.