Source code for NiaPy.benchmarks.levy

# encoding=utf8

"""Implementations of Levy function."""

from numpy import sin, pi
from NiaPy.benchmarks.benchmark import Benchmark

__all__ = ['Levy']

[docs]class Levy(Benchmark): r"""Implementations of Levy functions. Date: 2018 Author: Klemen Berkovič License: MIT Function: **Levy Function** :math:`f(\textbf{x}) = \sin^2 (\pi w_1) + \sum_{i = 1}^{D - 1} (w_i - 1)^2 \left( 1 + 10 \sin^2 (\pi w_i + 1) \right) + (w_d - 1)^2 (1 + \sin^2 (2 \pi w_d)) \\ w_i = 1 + \frac{x_i - 1}{4}` **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(\textbf{x}^*) = 0` at :math:`\textbf{x}^* = (1, \cdots, 1)` LaTeX formats: Inline: $f(\textbf{x}) = \sin^2 (\pi w_1) + \sum_{i = 1}^{D - 1} (w_i - 1)^2 \left( 1 + 10 \sin^2 (\pi w_i + 1) \right) + (w_d - 1)^2 (1 + \sin^2 (2 \pi w_d)) \\ w_i = 1 + \frac{x_i - 1}{4}$ Equation: \begin{equation} f(\textbf{x}) = \sin^2 (\pi w_1) + \sum_{i = 1}^{D - 1} (w_i - 1)^2 \left( 1 + 10 \sin^2 (\pi w_i + 1) \right) + (w_d - 1)^2 (1 + \sin^2 (2 \pi w_d)) \\ w_i = 1 + \frac{x_i - 1}{4} \end{equation} Domain: $-10 \leq x_i \leq 10$ Reference: https://www.sfu.ca/~ssurjano/levy.html """ Name = ['Levy']
[docs] def __init__(self, Lower=0.0, Upper=pi): r"""Initialize of Levy benchmark. Args: Lower (Optional[float]): Lower bound of problem. Upper (Optional[float]): Upper bound of problem. See Also: :func:`NiaPy.benchmarks.Benchmark.__init__` """ Benchmark.__init__(self, Lower, Upper)
[docs] @staticmethod def latex_code(): r"""Return the latex code of the problem. Returns: str: Latex code """ return r'''$f(\textbf{x}) = \sin^2 (\pi w_1) + \sum_{i = 1}^{D - 1} (w_i - 1)^2 \left( 1 + 10 \sin^2 (\pi w_i + 1) \right) + (w_d - 1)^2 (1 + \sin^2 (2 \pi w_d)) \\ w_i = 1 + \frac{x_i - 1}{4}$'''
[docs] def function(self): r"""Return benchmark evaluation function. Returns: Callable[[int, Union[int, float, List[int, float], numpy.ndarray]], float]: Fitness function """ def w(x): return 1 + (x - 1) / 4 def f(D, X): r"""Fitness function. Args: D (int): Dimensionality of the problem sol (Union[int, float, List[int, float], numpy.ndarray]): Solution to check. Returns: float: Fitness value for the solution. """ v = 0.0 for i in range(D - 1): v += (w(X[i]) - 1) ** 2 * (1 + 10 * sin(pi * w(X[i]) + 1) ** 2) + (w(X[-1]) - 1) ** 2 * (1 + sin(2 * pi * w(X[-1]) ** 2)) return sin(pi * w(X[0])) ** 2 + v return f
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