8: Whitley's function

Minimize:

$$f_{8}(\vec x)= \sum_{i=1}^D \sum_{j=1}^D \left( \frac{ \left( 100... ... \right)^2}{4000} - \cos \left( 100(x_i^2 -x_j)^2+(1-x_j)^2 \right) +1 \right)$$

With constraints:

$$Unconstrained$$

Global optimum:

$$f_{8}(\vec x^*)=0$$

$${x_i}^*=1, \quad i=1,\ldots,D$$

Features:

Multimodal, Non-separable

Figure 16: Whitley's function: Large scale

Figure 17: Whitley's function: The area near optimum, values above are 10 cut out