Source code for niapy.problems.pinter

# encoding=utf8

"""Implementation of Pinter function."""

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

__all__ = ['Pinter']

[docs]class Pinter(Problem): r"""Implementation of Pintér function. Date: 2018 Author: Lucija Brezočnik License: MIT Function: **Pintér function** :math:f(\mathbf{x}) = \sum_{i=1}^D ix_i^2 + \sum_{i=1}^D 20i \sin^2 A + \sum_{i=1}^D i \log_{10} (1 + iB^2); :math:A = (x_{i-1}\sin(x_i)+\sin(x_{i+1}))\quad \text{and} \quad :math:B = (x_{i-1}^2 - 2x_i + 3x_{i+1} - \cos(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 ∈ [-10, 10], for all :math:i = 1, 2,..., D. **Global minimum:** :math:f(x^*) = 0, at :math:x^* = (0,...,0) LaTeX formats: Inline: $f(\mathbf{x}) = \sum_{i=1}^D ix_i^2 + \sum_{i=1}^D 20i \sin^2 A + \sum_{i=1}^D i \log_{10} (1 + iB^2); A = (x_{i-1}\sin(x_i)+\sin(x_{i+1}))\quad \text{and} \quad B = (x_{i-1}^2 - 2x_i + 3x_{i+1} - \cos(x_i) + 1)$ Equation: f(\mathbf{x}) = \sum_{i=1}^D ix_i^2 + \sum_{i=1}^D 20i \sin^2 A + \sum_{i=1}^D i \log_{10} (1 + iB^2); A = (x_{i-1}\sin(x_i)+\sin(x_{i+1}))\quad \text{and} \quad B = (x_{i-1}^2 - 2x_i + 3x_{i+1} - \cos(x_i) + 1) Domain: $-10 \leq x_i \leq 10$ Reference paper: Jamil, M., and Yang, X. S. (2013). A literature survey of benchmark functions for global optimisation problems. International Journal of Mathematical Modelling and Numerical Optimisation, 4(2), 150-194. """
[docs] def __init__(self, dimension=4, lower=-10.0, upper=10.0, *args, **kwargs): r"""Initialize Pinter 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. See Also: :func:niapy.problems.Problem.__init__ """ super().__init__(dimension, lower, upper, *args, **kwargs)
[docs] @staticmethod def latex_code(): r"""Return the latex code of the problem. Returns: str: Latex code. """ return r''' $f(\mathbf{x}) = \sum_{i=1}^D ix_i^2 + \sum_{i=1}^D 20i \sin^2 A + \sum_{i=1}^D i \log_{10} (1 + iB^2); A = (x_{i-1}\sin(x_i)+\sin(x_{i+1}))\quad \text{and} \quad B = (x_{i-1}^2 - 2x_i + 3x_{i+1} - \cos(x_i) + 1)$'''
def _evaluate(self, x): sub = np.roll(x, 1) add = np.roll(x, - 1) indices = np.arange(1, self.dimension + 1) a = (sub * np.sin(x) + np.sin(add)) b = ((sub * sub) - 2.0 * x + 3.0 * add - np.cos(x) + 1.0) val1 = np.sum(indices * x * x) val2 = np.sum(20.0 * indices * np.power(np.sin(a), 2.0)) val3 = np.sum(indices * np.log10(1.0 + indices * np.power(b, 2.0))) return val1 + val2 + val3