N-D Test Functions O¶

class OddSquare(dimensions=2)¶

Odd Square objective function.

This class defines the Odd Square global optimization problem. This is a multimodal minimization problem defined as follows:

$f_{\text{OddSquare}}(x) = -e^{-\frac{d}{2\pi}} \cos(\pi d) \left( 1 + \frac{0.02h}{d + 0.01} \right )$

Where, in this exercise:

$\begin{cases} d = n \cdot \smash{\displaystyle\max_{1 \leq i \leq n}} \left[ (x_i - b_i)^2 \right ] \\ \\ h = \sum_{i=1}^{n} (x_i - b_i)^2 \\ \end{cases}$

And $b = [1, 1.3, 0.8, -0.4, -1.3, 1.6, -0.2, -0.6, 0.5, 1.4, 1, 1.3, 0.8, -0.4, -1.3, 1.6, -0.2, -0.6, 0.5, 1.4]$

Here, $n$ represents the number of dimensions and $x_i \in [-5 \pi, 5 \pi]$ for $i = 1, ..., n$ and $n \leq 20$ .

Two-dimensional OddSquare function

Global optimum: $f(x_i) = -1.0084$ for $x \approx b$

Gavana, A. Global Optimization Benchmarks and AMPGO

Todo

The best solution changes on dimensionality

class Osborne(dimensions=5)¶: Osborne objective function.

N-D Test Functions O¶

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