We propose a method to reduce the relaxation time towards equilibrium in
stochastic sampling of complex energy landscapes in statistical systems with
discrete degrees of freedom by generalizing the platform previously developed
for continuous systems. The method starts from a master equation, in contrast
to the Fokker-Planck equation for the continuous case. The master equation is
transformed into an imaginary-time Schr\"odinger equation. The Hamiltonian of
the Schr\"odinger equation is modified by adding a projector to its known
ground state. We show how this transformation decreases the relaxation time and
propose a way to use it to accelerate simulated annealing for optimization
problems. We implement our method in a simplified kinetic Monte Carlo scheme
and show an acceleration by an order of magnitude in simulated annealing of the
symmetric traveling salesman problem. Comparisons of simulated annealing are
made with the exchange Monte Carlo algorithm for the three-dimensional Ising
spin glass. Our implementation can be seen as a step toward accelerating the
stochastic sampling of generic systems with complex landscapes and long
equilibration times.Comment: 18 pages, 6 figures, to appear in Phys. Rev.