Deterministic Annealing and Nonlinear Assignment

Details Deterministic Annealing and Nonlinear Assignment Deterministic Annealing and Nonlinear Assignment

2001-05-16

arxiv.org/abs/cond-mat/0105321v1

Physics

Condensed Matter

Disordered Systems and Neural Networks

15 pages, 3 figures

Scientific paper

For combinatorial optimization problems that can be formulated as Ising or Potts spin systems, the Mean Field (MF) approximation yields a versatile and simple ANN heuristic, Deterministic Annealing. For assignment problems the situation is more complex -- the natural analog of the MF approximation lacks the simplicity present in the Potts and Ising cases. In this article the difficulties associated with this issue are investigated, and the options for solving them discussed. Improvements to existing Potts-based MF-inspired heuristics are suggested, and the possibilities for defining a proper variational approach are scrutinized.

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