An overview of mean field theory in combinatorial optimization problems

In the last three decades, there has been significant interest in using mean field theory of statistical physics for combinatorial optimization. This has led to the development of powerful optimization techniques such as neural networks (NNs), simulated annealing (SA), and mean field annealing (MFA). MFA replaces the stochastic nature of SA with a set of deterministic equations named as mean field equations. The mean field equations depend on the energy function of the NNs and are solved at each temperature during the annealing process of SA. MFA advances to the optimal solution in a fundamentally different way than stochastic methods. The use of mean field techniques for the combinatorial optimization problems are reviewed in this study.