  A framework is presented for carrying out simulations of equilibrium systems
in the microcanonical ensemble using annealing in an energy ceiling. The
framework encompasses an equilibrium version of simulated annealing, population
annealing and hybrid algorithms that interpolate between these extremes. These
equilibrium, microcanonical annealing algorithms are applied to the thermal
first-order transition in the 20-state, two-dimensional Potts model. All of
these algorithms are observed to perform well at the first-order transition
though for the system sizes studied here, equilibrium simulated annealing is
most efficient.
