Simulated Annealing

Simulated Annealing (SA) is a probabilistic optimization algorithm inspired by the physical annealing process in metallurgy — accepting both improving and worsening moves (with decreasing probability as "temperature" drops) to escape local optima and find near-global optimal process conditions.

How Simulated Annealing Works

• Initial Solution: Start with a random or heuristic process recipe.
• Perturbation: Randomly modify one or more parameters (neighbor solution).
• Acceptance: Accept always if better. Accept worse solutions with probability $P = e^{-\Delta E / T}$.
• Cooling: Gradually reduce temperature $T$ according to a cooling schedule -> convergence.

Why It Matters

• Escape Local Optima: The probability of accepting worse solutions allows SA to escape local minima early in the search.
• Simple Implementation: Easy to implement — no gradient, population, or complex operators needed.
• Scheduling: SA is effective for combinatorial optimization (fab scheduling, layout optimization) where the search space is discrete.

Simulated Annealing is controlled randomness with cooling — gradually transitioning from exploratory to exploitative search to find near-global optima.