DOI: 10.1051/jp1:1991146
J. Phys. I France 1 (1991) 455-470

Ensemble approach to simulated annealing

George Ruppeiner¹, Jacob Mørch Pedersen² and Peter Salamon<sup>3

1</sup>  Division of Natural Sciences, New College of the University of South Florida, Sarasota, Florida 34243, U.S.A.
²  Physics Laboratory, H. C. Ørsted Institute, University of Copenhagen, Universitetsparken 5, DK-2100 Copenhagen, Denmark
³  Department of Mathematical Sciences, San Diego State University, San Diego, California 92182, U.S.A.

(Received 16 November 1990, accepted 9 January 1991)

Abstract
We present three reasons for implementing simulated annealing with an ensemble of random walkers which search the configuration space in parrallel. First, an ensemble allows the implementation of an adaptive cooling schedule because it provides good statistics for collecting thermodynamic information. This new adaptive implementation is general, simple, and, in some sense, optimal. Second, the ensemble can tell us how to optimally allocate our effort in the search for a good solution, i.e., given the total computer time available, how many members to use in the ensemble. Third, an ensemble can reveal otherwise hidden properties of the configuration space, e.g., by examining Hamming distance distributions among the ensemble members. We present numerical results on the bipartitioning of random graphs and on a graph bipartitioning problem whose static thermodynamic properties may be solved for exactly.

© Les Editions de Physique 1991