1.6 Schwefel's function 7	Contents	1.8 Sum of different power function 9

1 Parametric Optimization

1.7 Griewangk's function 8

Griewangk's function is similar to Rastrigin's function. It has many widespread local minima. However, the location of the minima are regularly distributed.

function definition

f8(x)=sum(x(i)^2/4000)-prod(cos(x(i)/sqrt(i)))+1, i=1:n;
-600<=x(i)<= 600.

global minimum

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

This function is implemented in objfun8.

The three graphics below depict Griewangk's function using three different resolutions. Each of the graphics represents different properties of the function. The graphic on the left side shows the full definition range of the function. Here, the function looks very similar to De'Jong's function 1. When approaching the inner area, the function looks different. Many small peaks and valleys are visible in the middle graphic. When zooming in on the area of the optimum, grahic on the right side, the peaks and valleys look smooth.