Source code for niapy.benchmarks.trid

# encoding=utf8

"""Implementations of Trid function."""

from niapy.benchmarks.benchmark import Benchmark

__all__ = ['Trid']


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

    Date: 2018

    Author: Klemen Berkovič

    License: MIT

    Function:
    **Trid Function**

        :math:`f(\textbf{x}) = \sum_{i = 1}^D \left( x_i - 1 \right)^2 - \sum_{i = 2}^D x_i 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 ∈ [-D^2, D^2]`, for all :math:`i = 1, 2,..., D`.

        **Global minimum:**
        :math:`f(\textbf{x}^*) = \frac{-D(D + 4)(D - 1)}{6}` at :math:`\textbf{x}^* = (1 (D + 1 - 1), \cdots , i (D + 1 - i) , \cdots , D (D + 1 - D))`

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

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

        Domain:
                $-D^2 \leq x_i \leq D^2$

    Reference:
        https://www.sfu.ca/~ssurjano/trid.html

    """

    Name = ['Trid']

    def __init__(self, dimension=2):
        r"""Initialize of Trid benchmark.

        Args:
            dimension (int): Dimension of the problem used to determine lower and upper bounds.

        See Also:
            :func:`niapy.benchmarks.Benchmark.__init__`

        """
        super().__init__(-(dimension ** 2), dimension ** 2)

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

        Returns:
            str: Latex code.

        """
        return r'''$f(\textbf{x}) = \sum_{i = 1}^D \left( x_i - 1 \right)^2 - \sum_{i = 2}^D x_i x_{i - 1}$'''

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

        Returns:
            Callable[[int, Union[int, float, List[int, float], numpy.ndarray]], float]: Fitness function.

        """
        def f(dimension, x):
            r"""Fitness function.

            Args:
                dimension (int): Dimensionality of the problem
                x (Union[int, float, List[int, float], numpy.ndarray]): Solution to check.

            Returns:
                float: Fitness value for the solution.

            """
            v1, v2 = 0.0, 0.0
            for i in range(dimension):
                v1 += (x[i] - 1) ** 2
            for i in range(1, dimension):
                v2 += x[i] * x[i - 1]
            return v1 - v2

        return f

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