M4: Shubert function

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Minimize:

$\displaystyle f_{m4}(\vec x)=\sum_{i=1}^{5}i\cos((i+1)x_1+i)\cdot\sum_{i=1}^{5}i\cos((i+1)x_2+i)$

With constraints:

$\displaystyle -10 \le x_1,x_2 \le 10$

18 global optima (and 742 local optima):

$\displaystyle f_{m4}(\vec x^*)=-186.7309088$

Features:

Multimodal, Separable, Equally spaced optima.

**Figure 34:** Shubert: large scale
$\includegraphics{graphics/shubert.eps}$

**Figure 35:** Shubert: Area near one optimum peak
$\includegraphics{graphics/shuberts.eps}$

2007-05-09