A global optimization algorithm using stochastic differential equations

SIGMA is a set of FORTRAN subprograms for solving the global optimization problem, which implements a method founded on the numerical solution of a Cauchy problem for a stochastic differential equation inspired by statistical mechanics. This paper gives a detailed description of the method as implemented in SIGMA and reports the results obtained by SIGMA attacking, on two different computers, a set of 37 test problems which were proposed elsewhere by the present authors to test global optimization software. The main conclusion is that SIGMA performs very well, solving 35 of the problems, including some very hard ones. Unfortunately, the limited results available to us at present do not appear sufficient to enable a conclusive comparison with other global optimization methods.