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Examples

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.

GlobalSearch example


Discontinuous functions are another category that Global Optimization easily solves but other available tools simply cannot.

Discontinuous function solution


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.

GlobalPenaltyFn example

It is possible to find multiple solutions, if they exist. For example, in the function below, several solutions exist.

b=GlobalSearch[(y-x^2*5.1/(4.*π^2)+5.*x/π-6.)^2+10.*(1.-1./(8.*π))*Cos[x]+10.,{-40-x,x-40,-40-y,y-40},{},{{x,-40,40},{y,-40,40}},.000001,Starts->80,ParallelOption->True];

This gives:

Multiple solutions graph

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).

Piecewise linear graph