Quantized Hopfield networks for integer programming
Satoshi Matsuda · Systems and Computers in Japan · 1999
A new model of Hopfield network, the quantized Hopfield network (QHN), is presented, where each neuron takes a quantized value, e.g., an integer, rather than just a binary or continuous value. First, the energy minimization theorem is given for QHNs. Applying QHNs to integer optimization problems, which are combinatorial optimization problems whose variables take integer values, we can greatly decrease the number of neurons and connections between neurons compared to the traditional Hopfield networks with binary or continuous neurons. Therefore, we can expect QHNs to obtain optimal or nearly optimal solutions more quickly than traditional networks. Simulations of the Hitchcock problem illustrate these advantages. It is also illustrated, through simulations, that the fluctuation associated with this quantization may enable the network to escape from local minima, to converge to global minima, and consequently to obtain optimal solutions very frequently and much more quickly than pure QHNs. Thus, we can expect QHNs, with or without fluctuations, to obtain optimal or nearly optimal solutions very quickly. © 1999 Scripta Technica, Syst Comp Jpn, 30(6): 1–12, 1999