Optimal schedules for annealing algorithms
arxiv(2024)
摘要
Annealing algorithms such as simulated annealing and population annealing are
widely used both for sampling the Gibbs distribution and solving optimization
problems (i.e. finding ground states). For both statistical mechanics and
optimization, additional parameters beyond temperature are often needed such as
chemical potentials, external fields or Lagrange multipliers enforcing
constraints. In this paper we derive a formalism for optimal annealing
schedules in multidimensional parameter spaces using methods from
non-equilibrium statistical mechanics. The results are closely related to work
on optimal control of thermodynamic systems [Sivak and Crooks, PRL 108, 190602
(2012)]. Within the formalism, we compare the efficiency of population
annealing and multiple weighted runs of simulated annealing ("annealed
importance sampling") and discuss the effects of non-ergodicity on both
algorithms. Theoretical results are supported by numerical simulations of spin
glasses.
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