Source code for NiaPy.benchmarks.dixonprice

# encoding=utf8

"""Implementations of Dixon Price function."""

from NiaPy.benchmarks.benchmark import Benchmark

__all__ = ['DixonPrice']

class DixonPrice(Benchmark):
	r"""Implementations of Dixon Price function.

	Date: 2018

	Author: Klemen Berkovič

	License: MIT

	Function:
	**Levy Function**

		:math:`f(\textbf{x}) = (x_1 - 1)^2 + \sum_{i = 2}^D i (2x_i^2 - x_{i - 1})^2`

		**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}^* = (2^{-\frac{2^1 - 2}{2^1}}, \cdots , 2^{-\frac{2^i - 2}{2^i}} , \cdots , 2^{-\frac{2^D - 2}{2^D}})`

	LaTeX formats:
		Inline:
				$f(\textbf{x}) = (x_1 - 1)^2 + \sum_{i = 2}^D i (2x_i^2 - x_{i - 1})^2$

		Equation:
				\begin{equation} f(\textbf{x}) = (x_1 - 1)^2 + \sum_{i = 2}^D i (2x_i^2 - x_{i - 1})^2 \end{equation}

		Domain:
				$-10 \leq x_i \leq 10$

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

	def __init__(self, Lower=-10.0, Upper=10):
		r"""Initialize of Dixon Price 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'''$f(\textbf{x}) = (x_1 - 1)^2 + \sum_{i = 2}^D i (2x_i^2 - x_{i - 1})^2$'''

	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(2, D): v += i * (2 * X[i] ** 2 - X[i - 1]) ** 2
			return (X[0] - 1) ** 2 + v
		return f

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