Particle swarm Algorithm (3)----standard particle swarm algorithm (partial version)

In the global version of the standard particle swarm algorithm, the speed of each particle is updated according to two factors, the two factors are: 1. Particle own historical optimal value P_i. 2. The global optimal value of particle population p_g. If you change the particle velocity update formula, let the velocity of each particle update according to the following two factors, a. Particle own historical optimal value P_I. B. The optimal value of the particle in the neighborhood of the particle pn_K. the rest remains the same as the global version of the standard particle swarm algorithm, which becomes the local version of the particle swarm algorithm.

In general, the neighborhood of a particle I increases gradually with the increase of the number of iterations, begins the first iteration, its neighborhood is 0, as the number of iterations is linearly larger, the last neighborhood expands to the whole particle swarm, then it becomes the global version of the particle swarm algorithm. It is proved by practice that the global version of particle swarm algorithm converges fast, but it is easy to fall into local optimum. The local version of particle swarm algorithm converges slowly, but it is difficult to get into the local optimal. Most of the PSO algorithms are focused on convergence speed and getting rid of local optimum. In fact, these two aspects are contradictory. See how the better compromise is.

According to the different methods of the neighborhood, the local particle swarm optimization algorithm has many different implementations.

The first method: according to the number of particles to take the neighborhood of particles, there are four kinds of: 1, Ring 2, Random ring 3, Wheel-shape Method 4, Random wheel shape.

1 Ring 2 random ring

3 Wheel-shaped 4 random wheel shape

Because there is an algorithm that is implemented in the loop, a little bit of the loop is illustrated here: with particle 1 as an example, when the neighborhood is 0, the neighborhood is itself, when the neighborhood is 1 o'clock, the neighborhood is 2, 8, when the neighborhood is 2 o'clock, the neighborhood is 2,3,7,8 ..., and so on, until the neighborhood is 4, this time , the neighborhood extends to the entire example group. According to the literature (foreign literature), the use of wheel-shaped topology, PSO effect is very good.

The second method: the neighborhood of particles is taken by the Euclidean distance of the particles

In the first method, the particle's neighborhood is obtained according to the number of the particle, but the particles may not be adjacent to the actual position, so Suganthan proposes a partition scheme based on space distance, in which the distance between each particle and the other particles in the group is computed. Record the maximum distance between any 2 particles as DM. For each particle follow | | X_a-x_b| | /DM calculates a ratio. which | | X_a-x_b| | is the distance from the current particle A to B. The selection threshold Frac varies according to the number of iterations. When another particle b satisfies | | X_a-x_b| | /dm<frac, it is considered that B becomes the adjacent area of the current particle.

This method has been tested and obtained good application effect, but it is not used frequently because it is computationally large and requires a lot of storage space to calculate the distance between all the particles.