The definition of necessary hidden units in neural networks for combinatorial optimization

Hopfield-type thermodynamic networks composed of functionally homogeneous visible units have been applied to a variety of structurally simple NP-hard optimization problems. A fundamental obstacle to the application of neural networks to difficult problems is that these problems must first be reduced to 0-1 Hamiltonian minimization problems. It has been shown that certain optimization problems cannot be embedded in networks composed entirely of visible units. A method for defining necessary hidden units together with their best features is presented. A knapsack-packing network of O(n) units with standard and conjunctive synapses is derived, and simulation results are presented