Particle Swarm Optimization in MATLAB

Explore the history and model of particle swarm optimization, a simple yet powerful swarm intelligence algorithm introduced by Kennedy and Eberhart in 1995, using cooperative learning to locate global minima.

Explore how particle swarm optimization uses a swarm of candidate solutions with positions and velocities, guided by personal best and global best, via inertia, cognitive, and social components.

Explore implementing particle swarm optimization in MATLAB by defining a sphere cost function in a five-variable space with bounds [-10, 10], organizing the approach into problem definition, initialization, and iterations.

Set PSO parameters in MATLAB by fixing max iterations to 100 and swarm size to 50, then define inertia W and acceleration coefficients C1 and C2, with C2 = 2.

Initialize a particle swarm in MATLAB by creating a population of 50 particles with position, velocity, cost, and personal best. Establish the global best and initialize positions uniformly for evaluation.

Implement the PSO main loop by updating each particle’s velocity and position with inertia, cognitive, and social components, and updating personal and global bests from cost evaluations with inertia damping.

Finalize the optimization process by plotting the best costs versus iterations and illustrating convergence toward the origin, with Matlab code adapted for educational purposes and broader optimization use.

Convert the particle swarm optimization script into a reusable MATLAB function that accepts a problem structure and parameters, enabling calls with or without iteration display for any minimization problem.

Apply lower and upper bounds to particle positions and velocity in MATLAB PSO, clamping positions within bounds and capping velocities to keep all particles inside the defined limits.

Explore the constriction coefficient in particle swarm optimization implemented in Matlab, including setting the inertia weight and the cognitive and social acceleration coefficients per Kennedy and 2000.