Particle Swarm Optimization

Function:

Particles: 20

Inertia (w): 0.5

Cognitive (c1): 1.5

Social (c2): 1.5

Speed: 100ms

Iteration: 0

Best Fitness: Infinity

Best Position: (0.00, 0.00)

Particle Swarm Optimization (PSO)

PSO is a computational method that optimizes a problem by iteratively improving candidate solutions (particles) with regard to a given measure of quality (fitness function).

Velocity Update:

v_i(t+1) = w \cdot v_i(t) + c_1 \cdot r_1 \cdot (p_i - x_i(t)) + c_2 \cdot r_2 \cdot (g - x_i(t))

Position Update:

x_i(t+1) = x_i(t) + v_i(t+1)

Parameters:

$w$ - inertia weight (momentum)
$c_1$ - cognitive coefficient (personal best attraction)
$c_2$ - social coefficient (global best attraction)
$r_1, r_2$ - random numbers [0,1]
$x_i$ - particle position
$v_i$ - particle velocity
$p_i$ - particle's best known position
$g$ - swarm's best known position