Global Optimization can solve many problems that other packages
cannot. For example, calculating the minimum value of the following
function is difficult, if not impossible, to do with other tools
unless the initial range or point is close to the
solution. GlobalSearch, on the other hand, can find the
solution even from an unfavorable starting point.
Discontinuous functions are another category that Global
Optimization easily solves but other available tools simply
As another example, the following nonlinear constrained engineering
problem of flow in a pipe network was solved in less than a minute
using GlobalPenaltyFn, whereas other tools took ten times as
long and still did not find the correct solution.
It is possible to find multiple solutions, if they exist. For example, in the function below, several solutions exist.
The following function is piecewise linear (or Integer). Global Optimization can solve it whereas other tools cannot (answer is 0 for x from -1 to 1).