Computational Promise of Simultaneous Recurrent Neural Network for Combinatorial Optimization : A Dynamic Systems Perspective

This paper studies the Simultaneous Recurrent Neural Network (SRN), a trainable recurrent neural network, as a nonlinear dynamic system operating in relaxation mode for combinatorial optimization. Stability and convergence properties of the SRN dynamics in order to facilitate application of a fixed-point training algorithm are explored. Stability of hypercube corners of the SRN dynamics, which are equilibrium points for high-gain node dynamics and useful entities to represent solutions of combinatorial optimization problems, is examined. A theorem that suggests feasibility of instantiating network weights to establish a given hypercube corner as a stable equilibrium point is proposed. Simulation studies validating the theoretical findings are performed. Theoretical findings and correlating simulation study performed suggests the SRN dynamics operating in relaxation mode possess desirable stability characteristics as a trainable recurrent neural network for addressing combinatorial optimization problems