# Optimization by Simulated Annealing

@article{Kirkpatrick1983OptimizationBS, title={Optimization by Simulated Annealing}, author={Scott Kirkpatrick and Charles D. Gelatt and Michelle Vecchi}, journal={Science}, year={1983}, volume={220}, pages={671 - 680} }

There is a deep and useful connection between statistical mechanics (the behavior of systems with many degrees of freedom in thermal equilibrium at a finite temperature) and multivariate or combinatorial optimization (finding the minimum of a given function depending on many parameters). A detailed analogy with annealing in solids provides a framework for optimization of the properties of very large and complex systems. This connection to statistical mechanics exposes new information and…

## 39,861 Citations

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Just as Nature manages to cool a macroscopic system into or very close to its ground state in a short period of time even though its number of degrees of freedom is of the order of Avogadro’s number, so does simulated annealing rapidly find a good guess of the solution of the posed problem.

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Simulated annealing (a stochastic algorithm based on the Monte Carlo method) is used to find approximate solutions to complex optimization problems involving frustrated disordered systems.

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For long sequences, the energy minima found with the simulated annealing procedure differ by about a factor of 2 from the conjectured “true” minimum, indicating that the lowest-energy configurations are extremely isolated in configuration space.

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