Optimization problems are important in the physical sciences[1,2], biological sciences[3], mathematics[4], and operations research[5]. Current methods for approaching optimization problems include Monte Carlo simulation, analytic methods, symmetry considerations, and the method of simulated annealing (SA)[5]. Here we present a new method for optimization--- the method of constrained global optimization (CGO). CGO, like SA, makes iterative use of the Metropolis algorithm[6]. CGO uses a Glauber spin flip probability to insure in general that only those variables making excessively large contributions to the function to be minimized are assigned new values at a given iteration, while the values of the other variables remain the same. SA changes the values of one or more randomly--selected variables at each iteration.
We first describe CGO, then illustrate its use on two problems--- Thomson's Problem of finding the configuration of unit charges on a the surface of a sphere with minimum potential energy, and the office assignment problem (OAP)---for which CGO obtained better results than other methods.