Simulated Annealing
Simulated annealing is a probabilistic optimization metaheuristic inspired by the controlled cooling of metals. Its trick is to sometimes accept worse solutions to escape local optima, with a probability that falls as it cools. We explain its origin, acceptance criterion, uses and limits.
Simulated annealing is a probabilistic optimization metaheuristic: it searches for a near-optimal solution in huge spaces by occasionally accepting a temporary worsening so as not to get stuck. Its name comes from metallurgy: annealing consists of heating a metal and cooling it slowly so its atoms settle into a low-energy structure. The technique carries that idea over to optimization.
Origin
The modern formulation was proposed by Scott Kirkpatrick, C. Daniel Gelatt and Mario Vecchi in 1983, in the paper “Optimization by Simulated Annealing,” published in the journal Science; Vlado Černý independently arrived at the same method in 1985. It builds on an earlier procedure, the Metropolis algorithm (Metropolis and colleagues, 1953), born in physics to simulate many-particle systems.
How it works
The method starts from a solution and a high “temperature,” and at each step it proposes a neighboring solution. If it improves, it is accepted; if it worsens, it is accepted with a probability that depends on how much it worsens and on the current temperature. That probability has the form exp(−ΔE/T), where ΔE is the worsening and T the temperature. At first, with high T, the system explores freely and escapes local optima; as the temperature falls according to a cooling schedule, worse solutions are accepted less and less and the search concentrates on refining.
What it is used for
It is a classic tool of combinatorial optimization, where the number of possible solutions grows explosively. The canonical example is the traveling salesman problem (finding the shortest route that visits a set of cities), and it has been widely used in integrated-circuit design and in scheduling. Its appeal is its simplicity and that it does not need to know the internal structure of the problem.
Its limits
Simulated annealing is not without drawbacks. Its convergence is slow and its results depend heavily on the cooling schedule: cool too fast and it settles for a mediocre solution; too slow and it takes forever. There are theoretical guarantees that it reaches the optimum, but they require cooling so slow as to be impractical. In 2026 it remains a valid method and a conceptual reference, including its physical counterpart in quantum annealing.
This article was produced with artificial intelligence under human editorial oversight.
