# encoding=utf8
"""Implementation of Ridge function."""
import math
from NiaPy.benchmarks.benchmark import Benchmark
__all__ = ['Ridge']
[docs]class Ridge(Benchmark):
r"""Implementation of Ridge function.
Date: 2018
Author: Lucija Brezočnik
License: MIT
Function: **Ridge function**
:math:`f(\mathbf{x}) = \sum_{i=1}^D (\sum_{j=1}^i x_j)^2`
**Input domain:**
The function can be defined on any input domain but it is usually
evaluated on the hypercube :math:`x_i ∈ [-64, 64]`, for all :math:`i = 1, 2,..., D`.
**Global minimum:** :math:`f(x^*) = 0`, at :math:`x^* = (0,...,0)`
LaTeX formats:
Inline:
$f(\mathbf{x}) = \sum_{i=1}^D (\sum_{j=1}^i x_j)^2 $
Equation:
\begin{equation} f(\mathbf{x}) =
\sum_{i=1}^D (\sum_{j=1}^i x_j)^2 \end{equation}
Domain:
$-64 \leq x_i \leq 64$
Reference:
http://www.cs.unm.edu/~neal.holts/dga/benchmarkFunction/ridge.html
Attributes:
Name (List[str]): Names of the benchmark.
See Also:
* :class:`NiaPy.benchmarks.Benchmark`
"""
Name = ['Ridge', 'ridge']
[docs] def __init__(self, Lower=-64.0, Upper=64.0, **kwargs):
r"""Initialize of Ridge benchmark.
Args:
Lower (Optional[float]): Lower bound of problem.
Upper (Optional[float]): Upper bound of problem.
kwargs (Dict[str, Any]): Additional arguments.
See Also:
* :func:`NiaPy.benchmarks.Benchmark.__init__`
"""
Benchmark.__init__(self, Lower, Upper)
[docs] @staticmethod
def latex_code():
r"""Return the latex code of the problem.
Returns:
str: Latex code
"""
return r'''$f(\mathbf{x}) = \sum_{i=1}^D (\sum_{j=1}^i x_j)^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
"""
def evaluate(D, sol, **kwargs):
r"""Fitness function.
Args:
D (int): Dimensionality of the problem
sol (Union[int, float, list, numpy.ndarray]): Solution to check.
kwargs (Dict[str, Any]): Additional arguments.
Returns:
float: Fitness value for the solution.
"""
val = 0.0
for i in range(D):
val1 = 0.0
for j in range(i + 1):
val1 += sol[j]
val += math.pow(val1, 2)
return val
return evaluate