Particle swarm algorithm (1)----particle swarm optimization

First, the history of particle swarm algorithm

Particle swarm algorithm originates from complex adaptive system (Complex adaptive System,cas). CAS theory was formally proposed in 1994, and members in CAs are called principals. For example, the study of bird systems, each bird in this system is called the subject. Subject has adaptability, it can communicate with environment and other subject, and change its structure and behavior according to the process of communication "learning" or "accumulating experience". The evolution or evolution of the whole system includes: the emergence of new levels (the birth of a bird), the emergence of differentiation and diversity (birds in a flock of birds into many small groups), and the emergence of new themes (the bird finds new food in the process of finding food).

Therefore, the main body of CAS system has 4 basic characteristics (these characteristics are the basis of the development and change of particle swarm algorithm):

First of all, the subject is active and active.

Subject and environment and other subjects interact and interact with each other, which is the main motive force for the development and change of the system.

The influence of the environment is macroscopic, the influence between the main body is microcosmic, the macroscopic and microcosmic should combine organically.

Finally, the whole system may also be affected by some random factors.

Particle swarm optimization (PSO) is the study of a CAS system-bird colony social system.

Particle swarm algorithm (particle Swarm optimization, PSO) was first proposed by Eberhart and Kennedy in 1995, and its basic concept stems from the study of bird swarm foraging behavior. Imagine a scene where a flock of birds are randomly searching for food, and there is only one piece of food in the area, and all birds don't know where the food is, but they know how far away the food is. So what's the best strategy for finding food? The simplest and most effective thing is to search the surrounding area of the bird nearest to the food.

The PSO algorithm can be used to solve the optimization problem, which is inspired by the behavioral characteristics of the biological population. In PSO, the potential solution of each optimization problem can be imagined as a point on the D-dimensional search space, which we call "the particle" (particle), and all particles have an adaptive value determined by the objective function (Fitness value), Each particle also has a velocity that determines the direction and distance of their flight, and the particles then follow the current optimal particle to search in the solution space. Reynolds's study of bird swarm flight found. The bird simply tracks its limited number of neighbors, but the overall result is that the whole flock seems to be under a central control. The complex global behavior is caused by the interaction of simple rules.

Second, the specific expression of particle swarm algorithm

It's a long, long, long time, and those are the voices of research workers writing papers, but the history of PSO is as it says. The following popular interpretation of the PSO algorithm.

PSO algorithm is to simulate a group of birds in search of food process, each bird is the particle in the PSO, that is, we need to solve the problem of possible solutions, these birds in the search for food in the process, constantly changing their position and speed in the Air flight. We can also observe that the birds in the process of finding food, began the birds are more dispersed, gradually these birds converge into a group, this group of high and Low, suddenly left and right, until finally found food. This process transforms us into a mathematical problem. Find the maximum value for the [0,4] of the function Y=1-cos (3*x) *exp (-X). The graph of the function is as follows: