  Natural dynamics is often dominated by sudden nonlinear processes such as
neuroavalanches, gamma-ray bursts, solar flares \emph{etc}. that exhibit
scale-free statistics much in the spirit of the logarithmic Ritcher scale for
earthquake magnitudes. On phase diagrams, stochastic dynamical systems (DSs)
exhibiting this type of dynamics belong to the finite-width phase (N-phase for
brevity) that precedes ordinary chaotic behavior and that is known under such
names as noise-induced chaos, self-organized criticality, dynamical complexity
\emph{etc.} Within the recently formulated approximation-free supersymemtric
theory of stochastics, the N-phase can be roughly interpreted as the
noise-induced "overlap" between integrable and chaotic deterministic dynamics.
As a result, the N-phase dynamics inherits the properties of the both. Here, we
analyze this unique set of properties and conclude that the N-phase DSs must
naturally be the most efficient optimizers: on one hand, N-phase DSs have
integrable flows with well-defined attractors that can be associated with
candidate solutions and, on the other hand, the noise-induced
attractor-to-attractor dynamics in the N-phase is effectively chaotic or
a-periodic so that a DS must avoid revisiting solutions/attractors thus
accelerating the search for the best solution. Based on this understanding, we
propose a method for stochastic dynamical optimization using the N-phase DSs.
This method can be viewed as a hybrid of the simulated and chaotic annealing
methods. Our proposition can result in a new generation of hardware devices for
efficient solution of various search and/or combinatorial optimization
problems.
