thursday/go_benchmark_functions/go_funcs_A.py

# -*- coding: utf-8 -*-
from numpy import abs, cos, exp, pi, prod, sin, sqrt, sum
from .go_benchmark import Benchmark


class Ackley01(Benchmark):

    r"""
    Ackley01 objective function.

    The Ackley01 [1]_ global optimization problem is a multimodal minimization
    problem defined as follows:

    .. math::

        f_{\text{Ackley01}}(x) = -20 e^{-0.2 \sqrt{\frac{1}{n} \sum_{i=1}^n
         x_i^2}} - e^{\frac{1}{n} \sum_{i=1}^n \cos(2 \pi x_i)} + 20 + e


    Here, :math:`n` represents the number of dimensions and :math:`x_i \in
    [-35, 35]` for :math:`i = 1, ..., n`.

    *Global optimum*: :math:`f(x) = 0` for :math:`x_i = 0` for
    :math:`i = 1, ..., n`

    .. [1] Adorio, E. MVF - "Multivariate Test Functions Library in C for
    Unconstrained Global Optimization", 2005

    TODO: the -0.2 factor in the exponent of the first term is given as
    -0.02 in Jamil et al.
    """

    def __init__(self, dimensions=2):
        Benchmark.__init__(self, dimensions)

        self._bounds = list(zip([-35.0] * self.N, [35.0] * self.N))
        self.global_optimum = [[0 for _ in range(self.N)]]
        self.fglob = 0.0
        self.change_dimensionality = True

    def fun(self, x, *args):
        self.nfev += 1
        u = sum(x ** 2)
        v = sum(cos(2 * pi * x))
        return (-20. * exp(-0.2 * sqrt(u / self.N))
                - exp(v / self.N) + 20. + exp(1.))


class Ackley02(Benchmark):

    r"""
    Ackley02 objective function.

    The Ackley02 [1]_ global optimization problem is a multimodal minimization
    problem defined as follows:

    .. math::

        f_{\text{Ackley02}(x) = -200 e^{-0.02 \sqrt{x_1^2 + x_2^2}}


    with :math:`x_i \in [-32, 32]` for :math:`i=1, 2`.

    *Global optimum*: :math:`f(x) = -200` for :math:`x = [0, 0]`

    .. [1] Jamil, M. & Yang, X.-S. A Literature Survey of Benchmark Functions
    For Global Optimization Problems Int. Journal of Mathematical Modelling
    and Numerical Optimisation, 2013, 4, 150-194.

    """
    def __init__(self, dimensions=2):
        Benchmark.__init__(self, dimensions)

        self._bounds = list(zip([-32.0] * self.N, [32.0] * self.N))
        self.global_optimum = [[0 for _ in range(self.N)]]
        self.fglob = -200.

    def fun(self, x, *args):
        self.nfev += 1
        return -200 * exp(-0.02 * sqrt(x[0] ** 2 + x[1] ** 2))


class Ackley03(Benchmark):

    r"""
    Ackley03 [1]_ objective function.

    The Ackley03 global optimization problem is a multimodal minimization
    problem defined as follows:

    .. math::

        f_{\text{Ackley03}}(x) = -200 e^{-0.02 \sqrt{x_1^2 + x_2^2}} +
            5e^{\cos(3x_1) + \sin(3x_2)}


    with :math:`x_i \in [-32, 32]` for :math:`i=1, 2`.

    *Global optimum*: :math:`f(x) = -195.62902825923879` for :math:`x
    = [-0.68255758, -0.36070859]`

    .. [1] Jamil, M. & Yang, X.-S. A Literature Survey of Benchmark Functions
    For Global Optimization Problems Int. Journal of Mathematical Modelling
    and Numerical Optimisation, 2013, 4, 150-194.

     TODO: I think the minus sign is missing in front of the first term in eqn3
      in [1]_.  This changes the global minimum
    """

    def __init__(self, dimensions=2):
        Benchmark.__init__(self, dimensions)

        self._bounds = list(zip([-32.0] * self.N, [32.0] * self.N))
        self.global_optimum = [[-0.68255758, -0.36070859]]
        self.fglob = -195.62902825923879

    def fun(self, x, *args):
        self.nfev += 1
        a = -200 * exp(-0.02 * sqrt(x[0] ** 2 + x[1] ** 2))
        a += 5 * exp(cos(3 * x[0]) + sin(3 * x[1]))
        return a


class Adjiman(Benchmark):

    r"""
    Adjiman objective function.

    The Adjiman [1]_ global optimization problem is a multimodal minimization
    problem defined as follows:

    .. math::

        f_{\text{Adjiman}}(x) = \cos(x_1)\sin(x_2) - \frac{x_1}{(x_2^2 + 1)}


    with, :math:`x_1 \in [-1, 2]` and :math:`x_2 \in [-1, 1]`.

    *Global optimum*: :math:`f(x) = -2.02181` for :math:`x = [2.0, 0.10578]`

    .. [1] Jamil, M. & Yang, X.-S. A Literature Survey of Benchmark Functions
    For Global Optimization Problems Int. Journal of Mathematical Modelling
    and Numerical Optimisation, 2013, 4, 150-194.
    """

    def __init__(self, dimensions=2):
        Benchmark.__init__(self, dimensions)

        self._bounds = ([-1.0, 2.0], [-1.0, 1.0])
        self.global_optimum = [[2.0, 0.10578]]
        self.fglob = -2.02180678

    def fun(self, x, *args):
        self.nfev += 1
        return cos(x[0]) * sin(x[1]) - x[0] / (x[1] ** 2 + 1)


class Alpine01(Benchmark):

    r"""
    Alpine01 objective function.

    The Alpine01 [1]_ global optimization problem is a multimodal minimization
    problem defined as follows:

    .. math::

        f_{\text{Alpine01}}(x) = \sum_{i=1}^{n} \lvert {x_i \sin \left( x_i
        \right) + 0.1 x_i} \rvert


    Here, :math:`n` represents the number of dimensions and :math:`x_i \in
    [-10, 10]` for :math:`i = 1, ..., n`.

    *Global optimum*: :math:`f(x) = 0` for :math:`x_i = 0` for
    :math:`i = 1, ..., n`

    .. [1] Jamil, M. & Yang, X.-S. A Literature Survey of Benchmark Functions
    For Global Optimization Problems Int. Journal of Mathematical Modelling
    and Numerical Optimisation, 2013, 4, 150-194.
    """

    def __init__(self, dimensions=2):
        Benchmark.__init__(self, dimensions)

        self._bounds = list(zip([-10.0] * self.N, [10.0] * self.N))
        self.global_optimum = [[0 for _ in range(self.N)]]
        self.fglob = 0.0
        self.change_dimensionality = True

    def fun(self, x, *args):
        self.nfev += 1

        return sum(abs(x * sin(x) + 0.1 * x))


class Alpine02(Benchmark):

    r"""
    Alpine02 objective function.

    The Alpine02 [1]_ global optimization problem is a multimodal minimization
    problem defined as follows:

    .. math::

        f_{\text{Alpine02}(x) = \prod_{i=1}^{n} \sqrt{x_i} \sin(x_i)


    Here, :math:`n` represents the number of dimensions and :math:`x_i \in [0,
    10]` for :math:`i = 1, ..., n`.

    *Global optimum*: :math:`f(x) = -6.1295` for :math:`x =
    [7.91705268, 4.81584232]` for :math:`i = 1, 2`

    .. [1] Jamil, M. & Yang, X.-S. A Literature Survey of Benchmark Functions
    For Global Optimization Problems Int. Journal of Mathematical Modelling
    and Numerical Optimisation, 2013, 4, 150-194.

    TODO: eqn 7 in [1]_ has the wrong global minimum value.
    """

    def __init__(self, dimensions=2):
        Benchmark.__init__(self, dimensions)

        self._bounds = list(zip([0.0] * self.N, [10.0] * self.N))
        self.global_optimum = [[7.91705268, 4.81584232]]
        self.fglob = -6.12950
        self.change_dimensionality = True

    def fun(self, x, *args):
        self.nfev += 1

        return prod(sqrt(x) * sin(x))


class AMGM(Benchmark):

    r"""
    AMGM objective function.

    The AMGM (Arithmetic Mean - Geometric Mean Equality) global optimization
    problem is a multimodal minimization problem defined as follows

    .. math::

        f_{\text{AMGM}}(x) = \left ( \frac{1}{n} \sum_{i=1}^{n} x_i -
         \sqrt[n]{ \prod_{i=1}^{n} x_i} \right )^2


    Here, :math:`n` represents the number of dimensions and :math:`x_i \in
    [0, 10]` for :math:`i = 1, ..., n`.

    *Global optimum*: :math:`f(x) = 0` for :math:`x_1 = x_2 = ... = x_n` for
    :math:`i = 1, ..., n`

    .. [1] Gavana, A. Global Optimization Benchmarks and AMPGO, retrieved 2015

    TODO: eqn 7 in [1]_ has the wrong global minimum value.
    """

    def __init__(self, dimensions=2):
        Benchmark.__init__(self, dimensions)

        self._bounds = list(zip([0.0] * self.N, [10.0] * self.N))
        self.global_optimum = [[1, 1]]
        self.fglob = 0.0
        self.change_dimensionality = True

    def fun(self, x, *args):
        self.nfev += 1

        f1 = sum(x)
        f2 = prod(x)
        f1 = f1 / self.N
        f2 = f2 ** (1.0 / self.N)
        f = (f1 - f2) ** 2

        return f