Particle swarm optimization (2)----standard particle swarm optimization algorithm

In the narrative of the previous section, the only thing that hasn't been introduced is how the random dots (particles) of a function are moving, only that they are updated according to a certain formula. This formula is the position Velocity update formula in the particle swarm algorithm. Here's what this formula is about. In the previous section we evaluated the [0,4] maximum value of the function Y=1-cos (3*x) *exp (-X). Two random points are placed between [0,4], and the coordinates of these points are assumed to be x1=1.5; x2=2.5 here is a scalar, but the problem we often encounter may be a more general case--x for a vector case, such as a two-dimensional case z=2*x1+3*x2² of the situation. Each of our particles is two-dimensional, p1= (x11,x12), p2= (x21,x22), p3= (x31,x32), ... Pn= (XN1,XN2). Here n is the size of the group of particles, the number of particles in the group, and the dimension of each particle is 2. More generally, the dimension of the particle is Q, so that there are n particles in the population, and each particle is q-dimensional.

A group of n particles searches for the space of Q-dimensional (the dimension of each particle). Each particle is expressed as:_{x i}= (_{x i1}, x_i2, x_i3,..., x_iQ), each particle corresponding to the velocity can be expressed as V_i= (v _I1, v_i2, v_i3,...., v_iQ), each particle has two factors to consider when searching:

1. Own search to the historical optimal value P_i,p_i= (P_i1, p_i2,...., P_iQ), i=1,2,3,...., N.

2. All particles search for the optimal value P G_,p_g= (p_G1, p_G2,...., P_gQ), note here P_g Only one.

The position velocity update formula for the particle swarm algorithm is given below:

Here are a few important parameters that need to be remembered, as they will often be used in future lectures:

They are:

is to maintain the original speed of the coefficient, so called inertia weight.

is the particle tracking its own historical optimal value of the weight coefficient, it represents the particle itself, so called "cognition." typically set to 2.

is the weight coefficient of particle tracking group optimal value, it represents the knowledge of the whole group of particles, so it is called "social knowledge", often called "society". typically set to 2.

is a uniformly distributed random number within a [0,1] interval.

Is the time to update the position, in front of the speed of a coefficient, this coefficient we call the constraint factor. typically set to 1.

Such a standard particle swarm algorithm is over.