Cellular neural networks 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 with our optimization algorithm 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 10times10 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.

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