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: $$f(\textbf{x}) = \sum_{i = 1}^D \left( x_i - 1 \right)^2 - \sum_{i = 2}^D x_i x_{i - 1}$$ 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