Combinatorial optimization neural network having maximum functions in the energy function

Abstract

AbstractCombinatorial optimization problems are solved here by using a neural network that includes maximum functions in the energy functions. Because the energy function is bilinear in the original Hopfield neural network, the objective optimization problem must be formulated in bilinear form. It is shown that an energy function having maximum functions can be formulated; in addition, the neural network corresponding to the energy function is able to solve optimization problems. The example used here solves the maximum satisfiability problem and the results are compared with two simple algorithms. An oscillatory unit already in use is applied to the proposed neural network and the effect is examined. Neural networks can handle solutions for a logical function having 5—20 literals and 100—100,000 nodes. The neural network with oscillatory units presented here puts out better solutions.