

Complex Systems Group Department of Theoretical Physics Lund University Sweden 
1. Map the problem onto an energy function, e.g.
where S = {s_{i }; i = 1 ... N} is a set of binary spin variables s_{i} = 0 or s_{i} = 1, representing the elementary choices involved in minimizing E, while the weightsw_{ij} encode the costs and constraints.
2. To find configurations with low E, iterate the
mean field (MF) equations,
where T is a fictitious temperature. V = {v_{i}} is a new set of variables, called the mean field variables and represents the thermal average <s_{i}>_{T}. Each v_{i} is a continuous variable that lies within [0,1], which allows for a probabilistic interpretation. The above, so called, mean field theory equations are solved iteratively, while lowering T.
The above equations only represent one example. More elaborate encodings have been considered, e.g. based on Potts spins allowing for more general basic decisions elements than simple binary ones. A propagator formalism based on Potts neurons has been developed for handling topological complications in e.g. routing problems.
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