Asymmetric mean-field neural networks for multiprocessor scheduling

Hopfield and Tank's proposed technique for embedding optimization problems, such as the travelling salesman, in mean-field thermodynamic networks suffers from several restrictions. In particular, each discrete optimization problem must be reduced to the minimization of a 0–1 Hamiltonian. Hopfield and Tank's technique yields fully-connected networks of functionally homogeneous visible units with low-order symmetric connections. We present a program-constructive approach to embedding difficult problems in neural networks. Our derivation method overcomes the Hamiltonian reducibility requirement and promotes networks with functionally heterogeneous hidden units and asymmetric connections of both low and high-order. The underlying mechanism involves the decomposition of arbitrary problem energy gradients into piecewise linear functions which can be modeled as the outputs of small groups of hidden units. To illustrate our method, we derive thermodynamic mean-field neural networks for multiprocessor scheduling. Simulation of tuned networks of up to 2,400 units to yields very good, and often, exact solutions.