Cellular neural networks for NP-hard optimization problems

TL;DR

Cellular Neural Networks (CNN) can efficiently solve NP-hard optimization problems on lattices, outperforming traditional digital computers in speed, with practical hardware implementations already feasible and promising for future applications.

Contribution

This paper demonstrates that CNNs are suitable for solving NP-hard problems and establishes their equivalence to spin-glass systems, offering a fast optimization method compared to digital algorithms.

Findings

CNNs outperform digital computers at 10x10 lattice sizes.

Current hardware can handle 176x144 size CNNs.

CNN-based optimization is faster than simulated annealing.

Abstract

Nowadays, Cellular Neural Networks (CNN) are practically implemented in parallel, analog computers, showing a fast developing trend. Physicist must be aware that such computers are appropriate for solving in an elegant manner practically important problems, which are extremely slow on the classical digital architecture. Here, CNN is used for solving NP-hard optimization problems on lattices. It is proved, 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 computers a fast optimization method can be built for such problems. Estimating the simulation time needed for solving such NP-hard optimization problems 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 would be faster than digital computers already at 10*10 lattice sizes. Hardwares realized nowadays are of 176*144 size. Also, there seems to be no technical difficulties adapting CNN chips for such problems and the needed local control is expected to be fully developed in the near future.