▶Energy difference
A proposed move is immediately accepted if it lowers the objective; otherwise it faces a probabilistic test.
Simulated Annealing
Escaping local optima through controlled randomness
Simulated annealing adapts the Metropolis idea for optimization. Early randomness permits uphill moves; cooling gradually focuses the search near low-energy solutions.
watchone idea
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The essential idea: temperature balances global exploration early with local refinement late.
One Concept · One Example
What to notice
- Better moves are always accepted.
- Worse moves may be accepted when temperature is high.
- The cooling schedule controls exploration and convergence.
Optimization with a temperature
Thermal acceptance
High temperature makes uphill moves plausible. As temperature approaches zero, the search becomes increasingly selective.
Can randomness escape the nearest minimum?
Start from x = 4 on a multimodal objective. Compare greedy hill climbing with simulated annealing under different cooling schedules.
hot explorationcool refinementhill-climbing result
Controlled stochasticity can escape local optima and balance exploration with exploitation in a non-convex landscape.