Cellular Neural Networks for NP-Hard Optimization

A cellular neural/nonlinear network (CNN) is used for NP-hard optimization. We prove that a CNN in which the parameters of all cells can be separately controlled is the analog correspondent of a two-dimensional Ising-type (Edwards-Anderson) spin-glass system. Using the properties of CNN, we show that one single operation (template) always yields a local minimum of the spin-glass energy function. This way, a very fast optimization method, similar to simulated annealing, can be built. Estimating the simulation time needed on CNN-based computers, and comparing it with the time needed on normal digital computers using the simulated annealing algorithm, the results are astonishing. CNN computers could be faster than digital computers already at 10 x 10 lattice sizes. The local control of the template parameters was already partially realized on some of the hardwares, we think this study could further motivate their development in this direction. Copyright (C) 2009 Maria Ercsey-Ravasz et al.