# encoding=utf8
# pylint: disable=anomalous-backslash-in-string
import math
__all__ = ['Ridge']
[docs]class Ridge:
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
"""
def __init__(self, Lower=-64.0, Upper=64.0):
self.Lower = Lower
self.Upper = Upper
[docs] @classmethod
def function(cls):
def evaluate(D, sol):
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