Source code for niapy.problems.trid
# encoding=utf8
"""Implementations of Trid function."""
import numpy as np
from niapy.problems.problem import Problem
__all__ = ['Trid']
[docs]class Trid(Problem):
r"""Implementations of Trid functions.
Date: 2018
Author: Klemen Berkovič
License: MIT
Function:
**Trid Function**
:math:`f(\textbf{x}) = \sum_{i = 1}^D \left( x_i - 1 \right)^2 - \sum_{i = 2}^D x_i x_{i - 1}`
**Input domain:**
The function can be defined on any input domain but it is usually
evaluated on the hypercube :math:`x_i ∈ [-D^2, D^2]`, for all :math:`i = 1, 2,..., D`.
**Global minimum:**
:math:`f(\textbf{x}^*) = \frac{-D(D + 4)(D - 1)}{6}` at :math:`\textbf{x}^* = (1 (D + 1 - 1), \cdots , i (D + 1 - i) , \cdots , D (D + 1 - D))`
LaTeX formats:
Inline:
$f(\textbf{x}) = \sum_{i = 1}^D \left( x_i - 1 \right)^2 - \sum_{i = 2}^D x_i x_{i - 1}$
Equation:
\begin{equation} f(\textbf{x}) = \sum_{i = 1}^D \left( x_i - 1 \right)^2 - \sum_{i = 2}^D x_i x_{i - 1} \end{equation}
Domain:
$-D^2 \leq x_i \leq D^2$
Reference:
https://www.sfu.ca/~ssurjano/trid.html
"""
[docs] def __init__(self, dimension=4, *args, **kwargs):
r"""Initialize Trid problem..
Args:
dimension (Optional[int]): Dimension of the problem.
See Also:
:func:`niapy.problems.Problem.__init__`
"""
kwargs.pop('lower', None)
kwargs.pop('upper', None)
super().__init__(dimension, -(dimension ** 2), dimension ** 2, *args, **kwargs)
[docs] @staticmethod
def latex_code():
r"""Return the latex code of the problem.
Returns:
str: Latex code.
"""
return r'''$f(\textbf{x}) = \sum_{i = 1}^D \left( x_i - 1 \right)^2 - \sum_{i = 2}^D x_i x_{i - 1}$'''
def _evaluate(self, x):
sum1 = np.sum((x - 1) ** 2)
sum2 = np.sum(x[1:] * x[:-1])
return sum1 - sum2