12: Normalized Rana's function with diagonal wrap, EF102 function in [7]

Minimize:

$$f_{12}(\vec x)= \frac{\sum_{i=1}^{D} x_i \sin \left( \sqrt{\vert ... ... x_j+1 -x_i\vert} \right) \sin \left( \sqrt{\vert x_j+1 +x_i\vert} \right)}{D}$$

Where:

$$j=(i+1) mod D$$

With constraints:

$$-520 \le x_i \le 520, \quad i=1,\ldots,D$$

Global optimum:

$$f_{12}(\vec x^*)=-512.753162426239100568636786193$$

$${x_i}^*=-514.041683, \quad i=1,\ldots,D\\$$

Features:

Multimodal, Non-separable

Figure 23: Rana's function: Large scale

Figure 24: Rana's function: The area near optimum