Stability of simultaneous recurrent neural network dynamics for static optimization

A new trainable and recurrent neural optimization algorithm, which has potentially superior capabilities compared to existing neural search algorithms to compute high quality solutions of static optimization problems in a computationally efficient manner, is studied. Specifically, local stability analysis of the dynamics of a relaxation-based recurrent neural network, the Simultaneous Recurrent Neural network, for static optimization problems is presented. The results of theoretical as well as its correlated simulation study lead to the conjecture that the Simultaneous Recurrent Neural network dynamics appears to demonstrate desirable stability characteristics. Dynamics often converge to fixed points upon conclusion of a relaxation cycle, which facilitates adaptation of weights through one of many fixed-point training algorithms. The trainability of this neural algorithm results relatively high quality solutions to be computed for large-scale problem instances with computational efficiency, particularly when compared to solutions computed by the Hopfield network and its derivative algorithms including those with stochastic search control mechanisms.