Combinatorial optimization with Gaussian machines

Abstract

An artificial neuron model, called the Gaussian machine, is introduced. Gaussian machines have graded output responses, as well as stochastic behavior caused by random noise added to the input of each neuron. The Gaussian machine model includes the McCulloch-Pitts model, the Hopfield machine, and the Boltzmann machine as special cases. To demonstrate the efficiency of Gaussian machines, a solution of the traveling salesperson problem (TSP) is presented. Gaussian machines show an ability to solve combinatorial optimization problems better than either Hopfield or Boltzmann machines. The excellent performance of this model is also confirmed for the n-Queen's problem and the polyamino puzzle.