Benchmark test functions

The following benchmark functions are implemented, each function is defined in the survey[1]:

• Sphere

  The Sphere function is defined as:

  \[f(\mathbf{x}) = \sum_{i=1}^{d} x_i^2\]

  with $d$ the dimension of the design vector $\mathbf{x}$, subject to $0 \leq x_i \leq 10$.

  • The minimum is
    \[f(\mathbf{x^*}) = 0, \quad \mathbf{x^*} = (0, \cdots, 0)\]

• Easom

  The Easom function is defined as:

  \[f(\mathbf{x}) = -\cos{(x_1)} \cos{(x_2)} \exp{[-(x_1 - \pi)^2 - (x_2 - \pi)^2]}\]

  where the design vector is a 2-D vector only, subject to $-100 \leq x_i \leq 100$.

  • The function has the following minimum:
    \[f(\mathbf{x^*}) = -1, \quad \mathbf{x^*} = (\pi, \pi)\]

References