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Mean field variational framework for integer optimization
A principled method to obtain approximate solutions of general constrained
integer optimization problems is introduced. The approach is based on the
calculation of a mean field probability distribution for the decision variables
which is consistent with the objective function and the constraints. The
original discrete task is in this way transformed into a continuous variational
problem. In the context of particular problem classes at small and medium
sizes, the mean field results are comparable to those of standard specialized
methods, while at large sized instances is capable to find feasible solutions
in computation times for which standard approaches can't find any valuable
result. The mean field variational framework remains valid for widely diverse
problem structures so it represents a promising paradigm for large dimensional
nonlinear combinatorial optimization tasks