1.1 Algorithm source
The Sparrow Search Algorithm (SSA) is a new type of swarm intelligence optimization algorithm, which was proposed in 2020 and is mainly inspired by the foraging behavior and anti-predation behavior of sparrows. Its journal is: A novel swarm intelligence optimization approach: sparrow search algorithm https://www.tandfonline.com/doi/full/10.1080/21642583.2019.1708830
1.2 Characteristics of bird populations
Sparrows are generally gregarious birds and come in many species. They are found in most parts of the world and prefer to live where humans live. Furthermore, they are omnivorous birds that feed mainly on the seeds of grains or weeds. As we all know, sparrows are common resident birds. Compared to many other small birds, house sparrows are very intelligent and have a strong memory.
Research has shown that individuals monitor the behavior of others in a group. At the same time, aggressors in flocks wanting to increase their own predation rates are used to compete for food resources from high-intake mates .
Individual energy reserves may play an important role when sparrows choose different foraging strategies, with sparrows with low energy reserves searching more. It is worth mentioning that birds located on the outskirts of the population are more vulnerable to predators and are constantly trying to gain a better position. Note that animals in the center may move closer to their neighbors to minimize their danger zone. We also know that all sparrows display a natural instinct to be curious about all things, and at the same time they are always on the alert.
2. Six principles
Before explaining the mathematical model, six rules are given in the original text:
1. In the whole population, explorers usually have high energy reserves and are responsible for searching for food-rich areas, providing all followers with areas and directions for foraging. In the algorithm, the level of energy reserve is closely related to the individual fitness value of the sparrow.
2. Once the sparrow finds a natural enemy, it will make a chirp as an alarm signal. When the alarm value is greater than the safe value, the explorer will guide the followers to other safe areas for food.
3. The identity of the sparrow is defined in the algorithm according to whether it can find better food. Although the identity of the sparrow may change at any time, the proportion of explorers and followers in the population remains unchanged.
4. Sparrows with higher energy reserves will act as explorers. In order to gain more energy, it is possible for followers with lower energy to fly elsewhere to forage.
5. During the foraging process, followers can always follow the explorers with higher energy reserves to forage. In order to increase their predation rate, some individuals eat from the bowl and look into the pot. They may monitor the explorers and compete for more food resources.
6. When the natural enemy poses a certain threat, the sparrows at the edge of the group will quickly move to a safe area in order to obtain a better position, while the sparrows at the middle of the group will move randomly.
3 mathematical models
During each iteration, the finder's location updates are described as follows :
Among them, Xij is the individual position of the sparrow, i is the current iteration number, itermax is the maximum iteration number; α is a random number in [0,1]; R 2 ( R 2 ∈ [0,1]) , ST ( ST ∈ [ 0.5,1]) are warning value and safety value respectively; Q is a random number obeying normal distribution; L is a 1×d matrix, in which each element is 1.
When R 2 < ST , it means that there are no natural enemies around, and the explorer can conduct a global search. If R 2 ≥ ST it means that some sparrows have found the predator, and all sparrows should take related actions. As mentioned earlier, during the foraging process, some followers will always monitor the explorer. Once the explorers find better food, they will immediately leave their current position to compete for food. The food is immediately available if they win the competition, and the follower's position is updated as follows:
Among them, Xp is the position of the optimal explorer, Xworst is the current global worst position; n is the population size. A is a 1×d matrix, each element has a random amplitude of 1 or -1,and A += A T( AA T)-1,when i > n/ 2, this indicates that the fitness value is low The i - th joiner has no food and is very hungry. At this time, he needs to fly to other places for food to obtain more energy.
When aware of danger, sparrow populations engage in anti-predation behavior:
