Robust optimization with transiently chaotic dynamical systems

Hungarian Physics Institute, Faculty of Physics, Babeş-Bolyai University - Mihail Kogălniceanu 1, 400084 Cluj-Napoca, Romania

^(a) robert.sumi@phys.ubbcluj.ro
^(b) ercsey.ravasz@phys.ubbcluj.ro

Received: 29 January 2014
Accepted: 24 April 2014

Abstract

Efficiently solving hard optimization problems has been a strong motivation for progress in analog computing. In a recent study we presented a continuous-time dynamical system for solving the NP-complete Boolean satisfiability (SAT) problem, with a one-to-one correspondence between its stable attractors and the SAT solutions. While physical implementations could offer great efficiency, the transiently chaotic dynamics raises the question of operability in the presence of noise, unavoidable on analog devices. Here we show that the probability of finding solutions is robust to noise intensities well above those present on real hardware. We also developed a cellular neural network model realizable with analog circuits, which tolerates even larger noise intensities. These methods represent an opportunity for robust and efficient physical implementations.