NiaPy.benchmarks.alpine

Complexity

Total Complexity

8

Size/Duplication

Total Lines	178
Duplicated Lines	0 %

Importance

Changes

0

6 Methods

Rating	Name	Duplication	Size	Complexity
A	Alpine2.latex_code()	0	8	1
A	Alpine1.__init__()	0	11	1
A	Alpine1.latex_code()	0	8	1
A	Alpine2.__init__()	0	11	1
A	Alpine1.function()	0	24	2
A	Alpine2.function()	0	24	2

# encoding=utf8

"""Implementations of Alpine functions."""

import math
from NiaPy.benchmarks.benchmark import Benchmark

__all__ = ['Alpine1', 'Alpine2']


class Alpine1(Benchmark):
    r"""Implementation of Alpine1 function.

    Date: 2018

    Author: Lucija Brezočnik

    License: MIT

    Function: **Alpine1 function**

        :math:`f(\mathbf{x}) = \sum_{i=1}^{D} \lvert x_i \sin(x_i)+0.1x_i \rvert`

        **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:
                $f(\mathbf{x}) = \sum_{i=1}^{D} \lvert x_i \sin(x_i)+0.1x_i \rvert$

        Equation:
                \begin{equation} f(\mathbf{x}) = \sum_{i=1}^{D} \lvert x_i \sin(x_i)+0.1x_i \rvert \end{equation}

        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.
    """
    Name = ['Alpine1']

    def __init__(self, Lower=-10.0, Upper=10.0):
        r"""Initialize of Alpine1 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'''$f(\mathbf{x}) = \sum_{i=1}^{D} \lvert x_i \sin(x_i)+0.1x_i \rvert$'''

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

        Returns:
            Callable[[int, Union[int, float, List[int, float], numpy.ndarray]], float]: Fitness function
        """
        def evaluate(D, sol):
            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.
            """
            val = 0.0

            for i in range(D):
                val += abs(math.sin(sol[i]) + 0.1 * sol[i])

            return val

        return evaluate


class Alpine2(Benchmark):
    r"""Implementation of Alpine2 function.

    Date: 2018

    Author: Lucija Brezočnik

    License: MIT

    Function: **Alpine2 function**

        :math:`f(\mathbf{x}) = \prod_{i=1}^{D} \sqrt{x_i} \sin(x_i)`

        **Input domain:**
        The function can be defined on any input domain but it is usually
        evaluated on the hypercube :math:`x_i ∈ [0, 10]`, for all :math:`i = 1, 2,..., D`.

        **Global minimum:** :math:`f(x^*) = 2.808^D`, at :math:`x^* = (7.917,...,7.917)`

    LaTeX formats:
        Inline:
                $f(\mathbf{x}) = \prod_{i=1}^{D} \sqrt{x_i} \sin(x_i)$

        Equation:
                \begin{equation} f(\mathbf{x}) =
                \prod_{i=1}^{D} \sqrt{x_i} \sin(x_i) \end{equation}

        Domain:
                $0 \leq x_i \leq 10$

    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.
    """
    Name = ['Alpine2']

    def __init__(self, Lower=0.0, Upper=10.0):
        r"""Initialize of Alpine2 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=Lower, Upper=Upper)

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

        Returns:
            str: Latex code
        """
        return r'''$f(\mathbf{x}) = \prod_{i=1}^{D} \sqrt{x_i} \sin(x_i)$'''

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

        Returns:
            Callable[[int, Union[int, float, List[int, float], numpy.ndarray]], float]: Fitness function
        """
        def evaluate(D, sol):
            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.
            """
            val = 1.0

            for i in range(D):
                val *= math.sqrt(sol[i]) * math.sin(sol[i])

            return val

        return evaluate