Solver’s multistart methods for global optimization can overcome some of the limitations of the GRG Solving method alone, but they are not a panacea. The multistart methods will automatically run the GRG method from a number of starting points and will display the best of several locally optimal solutions found, as the probable globally optimal solution. Because the starting points are selected at random and then “clustered” together, they will provide a reasonable degree of “coverage” of the space enclosed by the bounds on the variables. The tighter the variable bounds you specify and the longer Solver runs, the better the coverage.
However, the performance of the multistart methods is generally limited by the performance of the GRG method on the subproblems. If the GRG method stops prematurely due to slow convergence, or fails to find a feasible point on a given run, the multistart method can improve upon this only by finding another starting point from which the GRG method can find a feasible solution, or a better locally optimal solution, by following a different path into the same region.
If the GRG method reaches the same locally optimal solution on many different runs initiated by the multistart method, this will tend to decrease a Bayesian estimate of the number of locally optimal solutions in the problem, causing the multistart method to stop relatively quickly. In many cases this indicates that the globally optimal solution has been found – but you should always inspect and think about the solution, and consider whether you should run the GRG method manually from starting points selected based on your knowledge of the problem.