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"""Implementations of Perm function."""
from NiaPy.benchmarks.benchmark import Benchmark
__all__ = ['Perm']
[docs]class Perm(Benchmark):
r"""Implementations of Perm functions.
Date:
2018
Author:
Klemen Berkovič
License:
MIT
Function:
**Perm Function**
:math:`f(\textbf{x}) = \sum_{i = 1}^D \left( \sum_{j = 1}^D (j - \beta) \left( x_j^i - \frac{1}{j^i} \right) \right)^2`
**Input domain:**
The function can be defined on any input domain but it is usually
evaluated on the hypercube :math:`x_i ∈ [-D, D]`, for all :math:`i = 1, 2,..., D`.
**Global minimum:**
:math:`f(\textbf{x}^*) = 0` at :math:`\textbf{x}^* = (1, \frac{1}{2}, \cdots , \frac{1}{i} , \cdots , \frac{1}{D})`
LaTeX formats:
Inline:
$f(\textbf{x}) = \sum_{i = 1}^D \left( \sum_{j = 1}^D (j - \beta) \left( x_j^i - \frac{1}{j^i} \right) \right)^2$
Equation:
\begin{equation} f(\textbf{x}) = \sum_{i = 1}^D \left( \sum_{j = 1}^D (j - \beta) \left( x_j^i - \frac{1}{j^i} \right) \right)^2 \end{equation}
Domain:
$-D \leq x_i \leq D$
Attributes:
Name (List[str]): Names of the benchmark.
D (float): Function argument.
beta (float): Function argument.
See Also:
* :class:`NiaPy.benchmarks.Benchmark`
Reference:
https://www.sfu.ca/~ssurjano/perm0db.html
"""
Name = ['Perm', 'perm']
D = 10.0
beta = 0.5
[docs] def __init__(self, D=10.0, beta=.5, **kwargs):
r"""Initialize of Bent Cigar benchmark.
Args:
D (Optional[float]): Function argument.
beta (Optional[float]): Function argument.
kwargs (Dict[str, Any]): Additional arguments.
See Also:
:func:`NiaPy.benchmarks.Benchmark.__init__`
"""
Benchmark.__init__(self, -D, D)
self.beta = beta
[docs] @staticmethod
def latex_code():
r"""Return the latex code of the problem.
Returns:
str: Latex code
"""
return r'''$f(\textbf{x}) = \sum_{i = 1}^D \left( \sum_{j = 1}^D (j - \beta) \left( x_j^i - \frac{1}{j^i} \right) \right)^2$'''
[docs] def function(self):
r"""Return benchmark evaluation function.
Returns:
Callable[[int, Union[int, float, list, numpy.ndarray], Dict[str, Any]], float]: Fitness function
"""
beta = self.beta
def f(D, X, **kwargs):
r"""Fitness function.
Args:
D (int): Dimensionality of the problem
X (Union[int, float, list, numpy.ndarray]): Solution to check.
kwargs (Dict[str, Any]): Additional arguments.
Returns:
float: Fitness value for the solution.
"""
v = .0
for i in range(1, D + 1):
vv = .0
for j in range(1, D + 1): vv += (j + beta) * (X[j - 1] ** i - 1 / j ** i)
v += vv ** 2
return v
return f
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