6.1: Randomly rotated Normalized Schwefel function

Minimize:

$$f_{6.1}(\vec y)= \frac{\sum_{i=1}^D -y_i \sin(\sqrt{\vert y_i\vert})}{D}$$

Where:

$$\vec y={[\vec o_1,\ldots, \vec o_D]}^T \vec x$$

The matrix ${[\vec o_1,\ldots, \vec o_D]}^T$ implements an angle preserving linear transformation of $\vec x$ [4].

With constraints:

$$-512 \le y_i \le 512, \quad i=1,\ldots,D$$

Global optimum:

$$f_{6.1}(\vec y^*)=-418.982887272433799807913601398$$

$${y_i}^*=420.968746, \quad i=1,\ldots,D$$

Features:

Multimodal, Non-separable, The rotation angle changes each run.

Figure 14: Rotated Schwefel function