Solver converged in probability to a global solution

If you are using the multistart methods for global optimization, with either the nonlinear GRG Solver, or a field-installable nonlinear Solver engine, this message appears when the multistart method’s Bayesian test has determined that all of the locally optimal solutions have probably been found; the solution displayed on the worksheet is the best of these locally optimal solutions, and is probably the globally optimal solution to the problem.

The Bayesian test initially assumes that the number of locally optimal solutions to be found is equally likely to be 1, 2, 3, … etc. up to infinity, and that the relative sizes of the regions containing each locally optimal solution follow a uniform distribution. After each run of the nonlinear GRG Solver, or field-installable Solver engine, an updated estimate of the most probable total number of locally optimal solutions is computed, based on the number of subproblems solved and the number of locally optimal solutions found so far. When the number of locally optimal solutions actually found so far is within one unit of the most probable total number of locally optimal solutions, the multistart method stops and displays this message.