Particle swarm optimization (PSO) is a popular optimization algorithm inspired by the social behavior of birds flocking or fish schooling. It was introduced by James Kennedy and Russell Eberhart in 1995 as a method for solving optimization problems in which you need to find the best solution (minimum or maximum) of a function within a certain search space. PSO is particularly known for its simplicity, flexibility, and effectiveness across a range of optimization problems.

Initialization: A swarm of particles (potential solutions) is initialized randomly within the search space. Each particle has a position, a velocity, a best-known position (personal best or pbest), and the swarm as a whole maintains a global best-known position (global best or gbest).

Movement: Each particle moves through the search space according to its velocity, which is influenced by its own personal best position and the global best position. The velocity is adjusted using a combination of the current velocity, a term that encourages the particle to move toward its personal best, and a term that encourages the particle to move toward the global best.

Update: At each iteration, the particles' positions and velocities are updated. After moving, the algorithm checks whether each particle's new position is an improvement over its personal best. If it is, the particle's personal best is updated. Similarly, if any particle's position is an improvement over the current global best, the global best is updated.

Termination: The algorithm continues iterating, updating the positions and velocities of the particles until a stopping condition is met. This could be a certain number of iterations, a time limit, or a desired level of fitness is achieved.

Output: Once the algorithm stops, the global best known position is the solution to the optimization problem.