1.8 Sum of different power function 9	Contents	1.10 Langermann's function 11

1 Parametric Optimization

1.9 Ackley's Path function 10

Ackley's Path [Ack87] is a widely used multimodal test function.

function definition

f10(x)=-a·exp(-b·sqrt(1/n·sum(x(i)^2)))-exp(1/n·sum(cos(c·x(i))))+a+exp(1);
a=20; b=0.2; c=2·pi; i=1:n;
-32.768<=x(i)<=32.768.

global minimum

f(x)=0; x(i)=0, i=1:n.

This function is implemented in objfun10.

The figures below show the function at two different zoom ratios. The graphic on the left side employs the whole definition area of the function - from -30 to 30. The graphic on the right side zooms into the area of the global minimum giving a better impression of the properties of the function.