PSO

Question 1

What is Particle Swarm Optimization (PSO)?

Answer 1

A population-based stochastic optimization technique inspired by social behavior like bird flocking or fish schooling. (ACO & PSO Slides, p26)
A metaheuristic.
Each “particle” (candidate solution) “flies” through the multi-dimensional search space. (ACO & PSO Slides, p26)
Particles adjust their paths based on their own experience and the experience of other particles in the swarm.

Question 2

What properties does each particle have?

Answer 2

Position (x_i): Its current location in the search space (representing a candidate solution).
Velocity (v_i): The speed and direction of its movement.
Fitness Value: The quality of its current position, evaluated by an objective function.
Personal Best (pbest_i or p_i): The best position it has found so far.
(Each particle also knows the Global Best (gbest or g): The best position found so far by any particle in the entire swarm.)

Question 3

How do particles move/update their state?

Answer 3

Particles move through the search space.
Their movement (velocity and position update) is influenced by:
Their current velocity (inertia).
Their own personal best (pbest) position found so far (cognitive component - individual experience).
The global best (gbest) position found by any particle in the swarm (social component - collective experience).

Question 4

PSO: What are the main components of a particle’s velocity update?

Answer 4

v_i(t+1) = wv_i(t) + c1r1(pbest_i - x_i(t)) + c2r2*(gbest - x_i(t))

Question 5

How does a particle update its position?

Answer 5

x_i(t+1) = x_i(t) + v_i(t+1)
The new position is the old position plus the newly calculated velocity.
(ACO & PSO Slides, p29)

Question 6

PSO: Key parameters?

Answer 6

Swarm Size: Number of particles.
Inertia Weight (w): Controls the impact of the previous velocity.
Cognitive Coefficient (c1): Weight of the particle’s pbest.
Social Coefficient (c2): Weight of the swarm’s gbest.
r1, r2: Random numbers (0-1) introduce stochasticity.

Question 7

What kind of optimization problems is PSO well-suited for?

Answer 7

Problems with continuous and differentiable functions (though it can be adapted for discrete problems).
It does not require knowledge of the gradient (unlike gradient descent).
Can handle complex, non-linear, multi-modal search spaces.