PSO Algorithms Optimization

What PSO is Particle Swarm Optimization is a population-based, stochastic optimization method inspired by flocking/swarming behavior. It se

Common PSO variants you’ll see in MATLAB work

1. Inertia-weight PSOUses www (often decreased over time) to shift from exploration → exploitation.
2. Constriction-factor PSO (Clerc-Kennedy)Uses a stability factor to control velocity and avoid explosion.
3. Local-best (lbest) PSOUses neighborhood best instead of global best; can reduce premature convergence.
4. Hybrid PSOPSO combined with local search (e.g., fmincon / fminunc) for refinement.
5. Binary PSO / Discrete PSOFor feature selection, scheduling, combinatorial problems.

Handling constraints (typical approaches in MATLAB)

• Bound constraints: clamp positions to bounds or reflect velocities.
• General constraints:
• penalty functions added to objective
• feasibility rules (prefer feasible solutions)
• hybridize with constrained solvers (PSO for global search, fmincon for local feasible refinement)

MATLAB implementation options

1) Built-in (recommended if you have Global Optimization Toolbox)

MATLAB provides particleswarm for bound-constrained optimization:

• you define objective function
• specify number of variables and bounds
• tune options like swarm size, max iterations, tolerances

Good for: continuous variables, black-box objectives, engineering tuning problems.2) Custom PSO code (common in research/teaching)

You manually code:

• initialization
• pbest/gbest tracking
• velocity/position updates
• boundary handling
• stopping criteria

Good for: custom constraints, discrete variants, hybrid PSO, novel research modifications.

Key tuning parameters (rule-of-thumb)

• Swarm size: 20–100 (higher for harder/high-dimensional problems)
• Max iterations: depends on budget; often 100–1000
• www: ~0.9 down to ~0.4 (linearly decreasing is common)
• c1,c2c_1, c_2c1​,c2​: often around 1.5–2.5 each (balance matters)
• Velocity limits: helps stability; prevents particles from overshooting

Strengths and weaknesses

Strengths

• No gradients required
• Works well on nonlinear/multi-modal landscapes
• Easy to parallelize (MATLAB supports parallel objective evaluation in many setups)

Weaknesses

• Can converge prematurely (esp. high c2c_2c2​, low diversity)
• Scaling to very high dimensions can be tough
• Needs parameter tuning; performance depends on settings and constraint handling

Typical MATLAB workflow

1. Define objective: f = @(x) ...
2. Define bounds: lb, ub
3. Choose PSO approach: particleswarm or custom
4. Set options: swarm size, iterations, stopping tolerances
5. Run optimization
6. Validate solution + sensitivity checks (rerun with different seeds)