1.9 Ackley's Path function 10	Contents	1.11 Michalewicz's function 12

1 Parametric Optimization

1.10 Langermann's function 11

The Langermann function is a multimodal test function. The local minima are unevenly distributed.

function definition

f11(x)=-sum(c(i)·(exp(-1/pi·sum((x-A(i))^2))·cos(pi·sum((x-A(i))^2)))), i=1:m, m=5;
0<=x(i)<=10.
For the value of A and c look at the mfile objfun11.

global minimum

f(x)=-1.4 (for m=5); x(i)=???, i=1:n.

This function is implemented in objfun11.

The figures below display Langermann's function with different variables. The graphic on the left side shows a mesh plot of the first and second variable. The graphic on the right side uses the second and third variable while the first variable is set to 0.