Cooling rate

As explained in Optimization Algorithms: AI techniques for design, planning, and control problems

A cooling rate is a parameter controlling how quickly the temperature decreases in an annealing schedule.

Cooling rate controls how quickly temperature decreases during simulated annealing. It is part of the annealing schedule, alongside starting temperature, iterations at each temperature, and final temperature. section 5.2.4

Cooling rate shapes the balance between exploration and exploitation:

• Cooling too quickly can prevent the system from reaching an ordered, low-energy state; in optimization, it can limit search quality. section 5.2.1
• Cooling gradually helps simulated annealing avoid suboptimal local minima while moving from broad exploration toward focused search. section 5.2.1
• Common schedules include linear cooling, where temperature decreases by a fixed pattern over pseudo-time; the schedule remains tunable. section 5.2.4

A practical starting-temperature heuristic

When objective-function changes are unknown, begin at a very high temperature, reduce it quickly until roughly 50%–60% of inferior moves are accepted, then use that temperature for slower cooling. section 5.2.4

Figure 5.8 Different SA cooling schedules

Compare how different cooling schedules decrease temperature over the annealing process. section 5.2.4

How Optimization Algorithms: AI techniques for design, planning, and control problems covers it

How deep it goes

Defines cooling as a tunable schedule, gives a practical acceptance-rate heuristic, and names linear cooling among common schedules.

Examples

Uses physical crystallization, rapid-versus-gradual cooling, linear schedules, and a 50%–60% inferior-move acceptance heuristic.

What it assumes

Assumes basic optimization terms such as objective function and local minimum while relating them to temperature and physical annealing.

What you can do after

Apply it via simulated annealing by choosing a cooling schedule and calibrating its starting temperature from move-acceptance behavior.

How it connects

Connects cooling rate with simulated annealing, temperature, objective functions, exploration, exploitation, and local minima.

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