4: Generalized Rosenbrock's function (The 2nd De Jong's function) [1]

Minimize:

$$f_{4}(\vec x)=\sum_{i=1}^{D-1} \left( 100({x_i}^2-x_{i+1})^2 + (1-x_i)^2 \right)$$

With constraints:

$$Unconstrained$$

Global optimum:

$$f_{4}(\vec x^*)=0$$

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

Features:

Multimomodal with $D>3$ [2] otherwise Unimodal, Non-separable

Figure 4: Rosenbrock's function