Source code for NiaPy.benchmarks.powell

# encoding=utf8

"""Implementations of Levy function."""

from NiaPy.benchmarks.benchmark import Benchmark

__all__ = ['Powell']

class Powell(Benchmark):
	r"""Implementations of Powell functions.

	Date: 2018

	Author: Klemen Berkovič

	License: MIT

	Function:
	**Levy Function**

		:math:`f(\textbf{x}) = \sum_{i = 1}^{D / 4} \left( (x_{4 i - 3} + 10 x_{4 i - 2})^2 + 5 (x_{4 i - 1} - x_{4 i})^2 + (x_{4 i - 2} - 2 x_{4 i - 1})^4 + 10 (x_{4 i - 3} - x_{4 i})^4 \right)`

		**Input domain:**
		The function can be defined on any input domain but it is usually
		evaluated on the hypercube :math:`x_i ∈ [-4, 5]`, for all :math:`i = 1, 2,..., D`.

		**Global minimum:**
		:math:`f(\textbf{x}^*) = 0` at :math:`\textbf{x}^* = (0, \cdots, 0)`

	LaTeX formats:
		Inline:
				$f(\textbf{x}) = \sum_{i = 1}^{D / 4} \left( (x_{4 i - 3} + 10 x_{4 i - 2})^2 + 5 (x_{4 i - 1} - x_{4 i})^2 + (x_{4 i - 2} - 2 x_{4 i - 1})^4 + 10 (x_{4 i - 3} - x_{4 i})^4 \right)$

		Equation:
				\begin{equation} f(\textbf{x}) = \sum_{i = 1}^{D / 4} \left( (x_{4 i - 3} + 10 x_{4 i - 2})^2 + 5 (x_{4 i - 1} - x_{4 i})^2 + (x_{4 i - 2} - 2 x_{4 i - 1})^4 + 10 (x_{4 i - 3} - x_{4 i})^4 \right) \end{equation}

		Domain:
				$-4 \leq x_i \leq 5$

	Reference:
		https://www.sfu.ca/~ssurjano/levy.html
	"""
	Name = ['Powell']

	def __init__(self, Lower=-4.0, Upper=5.0):
		r"""Initialize of Powell 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)

	@staticmethod
	def latex_code():
		r"""Return the latex code of the problem.

		Returns:
			str: Latex code
		"""
		return r'''$f(\textbf{x}) = \sum_{i = 1}^{D / 4} \left( (x_{4 i - 3} + 10 x_{4 i - 2})^2 + 5 (x_{4 i - 1} - x_{4 i})^2 + (x_{4 i - 2} - 2 x_{4 i - 1})^4 + 10 (x_{4 i - 3} - x_{4 i})^4 \right)$'''

	def function(self):
		r"""Return benchmark evaluation function.

		Returns:
			Callable[[int, Union[int, float, List[int, float], numpy.ndarray]], float]: Fitness function
		"""
		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(1, (D // 4) + 1): v += (X[4 * i - 4] + 10 * X[4 * i - 3]) ** 2 + 5 * (X[4 * i - 2] - X[4 * i - 1]) ** 2 + (X[4 * i - 3] - 2 * X[4 * i - 2]) ** 4 + 10 * (X[4 * i - 4] - X[4 * i - 1]) ** 4
			return v
		return f

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