Neural algorithms for placement problems

Two improved neural algorithms are presented for solving a placement problem which is a familiar class of NP-hard quadratic assignment problems. Formulation of the problem as a zero-one integer programming leads to an improved form of the Hopfield networks, while a mixed integer programming formulation results in an analogue algorithm similar to the elastic nets. The outermost loop in these algorithms performs an automatically scheduled deterministic annealing. This gives us a natural interpretation of the annealing procedure derived directly from the mathematical programming framework. Experiments reveal that the adaptive elastic net algorithm outperforms the adaptive Hopfield method.