Source code for niapy.problems.weierstrass

# encoding=utf8
"""Implementations of Weierstrass functions."""

import numpy as np
from niapy.problems.problem import Problem

__all__ = ['Weierstrass']


[docs]class Weierstrass(Problem): r"""Implementations of Weierstrass functions. Date: 2018 Author: Klemen Berkovič License: MIT Function: **Weierstrass Function** :math:`f(\textbf{x}) = \sum_{i=1}^D \left( \sum_{k=0}^{k_{max}} a^k \cos\left( 2 \pi b^k ( x_i + 0.5) \right) \right) - D \sum_{k=0}^{k_{max}} a^k \cos \left( 2 \pi b^k \cdot 0.5 \right)` **Input domain:** The function can be defined on any input domain but it is usually evaluated on the hypercube :math:`x_i ∈ [-100, 100]`, for all :math:`i = 1, 2,..., D`. Default value of a = 0.5, b = 3 and k_max = 20. **Global minimum:** :math:`f(x^*) = 0`, at :math:`x^* = (420.968746,...,420.968746)` LaTeX formats: Inline: $$f(\textbf{x}) = \sum_{i=1}^D \left( \sum_{k=0}^{k_{max}} a^k \cos\left( 2 \pi b^k ( x_i + 0.5) \right) \right) - D \sum_{k=0}^{k_{max}} a^k \cos \left( 2 \pi b^k \cdot 0.5 \right) Equation: \begin{equation} f(\textbf{x}) = \sum_{i=1}^D \left( \sum_{k=0}^{k_{max}} a^k \cos\left( 2 \pi b^k ( x_i + 0.5) \right) \right) - D \sum_{k=0}^{k_{max}} a^k \cos \left( 2 \pi b^k \cdot 0.5 \right) \end{equation} Domain: $-100 \leq x_i \leq 100$ Reference: http://www5.zzu.edu.cn/__local/A/69/BC/D3B5DFE94CD2574B38AD7CD1D12_C802DAFE_BC0C0.pdf """
[docs] def __init__(self, dimension=4, lower=-100.0, upper=100.0, a=0.5, b=3, k_max=20, *args, **kwargs): r"""Initialize Bent Cigar problem.. Args: dimension (Optional[int]): Dimension of the problem. lower (Optional[Union[float, Iterable[float]]]): Lower bounds of the problem. upper (Optional[Union[float, Iterable[float]]]): Upper bounds of the problem. a (Optional[float]): The a parameter. b (Optional[float]): The b parameter. k_max (Optional[int]): Number of elements of the series to compute. See Also: :func:`niapy.problems.Problem.__init__` """ super().__init__(dimension, lower, upper, *args, **kwargs) self.a = a self.b = b self.k_max = k_max
[docs] @staticmethod def latex_code(): r"""Return the latex code of the problem. Returns: str: Latex code. """ return r'''$f(\textbf{x}) = \sum_{i=1}^D \left( \sum_{k=0}^{k_{max}} a^k \cos\left( 2 \pi b^k ( x_i + 0.5) \right) \right) - D \sum_{k=0}^{k_{max}} a^k \cos \left( 2 \pi b^k \cdot 0.5 \right)$'''
def _evaluate(self, x): val1 = 0.0 for i in range(self.dimension): val = 0.0 for k in range(self.k_max): val += self.a ** k * np.cos(2.0 * np.pi * self.b ** k * (x[i] + 0.5)) val1 += val val2 = 0.0 for k in range(self.k_max): val2 += self.a ** k * np.cos(2 * np.pi * self.b ** k * 0.5) return val1 - self.dimension * val2