A Neural Net with Self-Inhibiting Units for the N-Queens Problem

Suggested here is a neural net algorithm for the n-queens problem. The net is basically a Hopfield net but with one major difference: every unit is allowed to inhibit itself. This distinctive characteristic enables the net to escape efficiently from all local minima. The net’s dynamics then can be described as a travel in paths of low-level energy spaces until it finds a solution (global minimum). The paper explains why standard Hopfield nets have failed to solve the queens problem and proofs that the self-inhibiting net (NQ2 algorithm in the text) never stabilizes in local minima and relaxes when it falls into a global minimum are provided. The experimental results supported by theoretical explanation indicate that the net never continually oscillates but relaxes into a solution in polynomial time. In addition, it appears that the net solves the queens problem regardless of the dimension n or the initialized values. The net uses only few parameters to fix the weights; all globally determined as a function of n.