SIMULATED ANNEALING IN THE MICROCANONICAL ENSEMBLE

In earlier work we have extended the microcanonical Monte Carlo method , which had been introduced for systems described by continuous potent ials [Phys. Rev. A 44, 4061 (1991)] to discrete lattice systems [Phys. Rev. E 53, 3402 (1996)], such as the Ising model. This microcanonical ensemble Monte Carlo method is rigorously based on statistical mechan ics and one has available the entire structure of equilibrium statisti cal mechanics, such as the full set of fluctuation formulas, which are useful in numerical estimates of the equilibrium properties of the sy stem. In the present paper we explore the use of the microcanonical en semble Monte Carlo probability distribution to study combinatorial opt imization problems using simulated annealing. In particular, we presen t the results of a detailed study of a particular 20-city traveling sa lesman problem in both the canonical and microcanonical ensembles.