Particle swarm optimization operates on the basis of the neighborhood principle, which is derived from the study of social network structures. The property that drives particle swarm optimization is social interaction. The individuals (particles) in the swarm learn from each other and based on the acquired knowledge move to better neighbors that are more similar to them. Individuals in the neighborhood communicate with each other.
A swarm is composed of a collection of particles, each particle representing a potential solution. Particles flow through hyperspace, and the position of each particle changes according to its experience and the positions of neighboring particles. The velocity vector drives the optimization process and reflects the information exchanged by society. The following briefly introduces three different particle swarm optimization algorithms, and they have different extensions to social information exchange.
Particle Swarm Optimization Algorithm
1. individual best algorithm
For the individual best algorithm, each individual only compares its current position with its own best position pbest, without using the information of other particles. The specific algorithm is as follows:
(1) Initialize the particle group P(t), so that the position X(t) of each particle P∈P(t) in the hyperspace is random when t=0.
(2) Evaluate the performance f of each particle by its current position.
(3) Compare the current performance of each individual with the best performance it has had so far.
(4) Change the velocity vector of each particle.
(5) Turn back to step (2) and repeat the recursion until convergence.
The farther a particle is from its previously found best solution in the above algorithm, the greater the velocity required to move that particle (individual) back to its best solution. The upper limit of the random value P is a system parameter specified by the user. The larger the upper bound on p, the larger the particle trajectory oscillations. Smaller P values can ensure smooth trajectories of particles.
Particle Swarm Optimization Algorithm
2. global best algorithm
For the global best (global best) algorithm, the global optimization scheme gbest of particle swarms reflects a neighborhood topology called a star (stan). In this structure, each particle can communicate with other particles (individuals), forming a fully connected social network. The social knowledge used to drive each particle's movement includes the best particle position selected from the population, and each particle uses its historical experience based on the best previously found solution.
For the global optimal algorithm, the farther a particle is from the global optimal position and its own optimal solution, the greater the velocity change required to bring the particle back to its optimal solution.
3. local optimal algorithm
The local best (local best) algorithm uses the best plan lbest of particle swarm optimization to reflect a neighborhood topology called ring. Each particle in this structure communicates with its n intermediate neighbors. If n=2, then a particle communicates with its intermediate neighbors as shown in the figure below. Particles are influenced by their neighborhood's optimal position and their own past experience.
Particle Swarm Optimization Algorithm
Step (2) of the above three algorithms detects the performance of each particle. where a function is used to measure how close the corresponding solution is to the optimal solution. In evolutionary computing, this proximity is called a fitness function.
Particle swarm optimization has been used to solve the maximum and minimum values of nonlinear functions, and it has also been successfully applied to neural network training. At this time, each particle represents a weight vector, representing a neural network. Particle swarm optimization has also been successfully applied to the analysis of human tremors for the diagnosis of Parkinson's disease.