Module ImportFrom alias alias alias ImportFrom alias alias alias alias alias alias alias alias ImportFrom alias ClassDef bases NameLoad body Expr Str FunctionDef arguments args NameParam NameParam defaults Num body Expr Call AttributeLoad NameLoad attr NameLoad NameLoad Assign AttributeStore NameLoad attr Call NameLoad BinOpMult ListLoad Num AttributeLoad NameLoad attr BinOpMult ListLoad Num AttributeLoad NameLoad attr Assign AttributeStore NameLoad attr ListLoad ListComp Num comprehension NameStore Call NameLoad AttributeLoad NameLoad attr Assign AttributeStore NameLoad attr Num Assign AttributeStore NameLoad attr NameLoad decorator_list FunctionDef arguments args NameParam NameParam defaults vararg body AugAssignAdd AttributeStore NameLoad attr Num Assign NameStore Call NameLoad BinOpPow NameLoad Num Assign NameStore Call NameLoad Call NameLoad BinOpMult BinOpMult Num NameLoad NameLoad Return BinOpAdd BinOpAdd BinOpSub BinOpMult Num Call NameLoad BinOpMult Num Call NameLoad BinOpDiv NameLoad AttributeLoad NameLoad attr Call NameLoad BinOpDiv NameLoad AttributeLoad NameLoad attr Num Call NameLoad Num decorator_list decorator_list ClassDef bases NameLoad body Expr Str FunctionDef arguments args NameParam NameParam defaults Num body Expr Call AttributeLoad NameLoad attr NameLoad NameLoad Assign AttributeStore NameLoad attr Call NameLoad BinOpMult ListLoad Num AttributeLoad NameLoad attr BinOpMult ListLoad Num AttributeLoad NameLoad attr Assign AttributeStore NameLoad attr ListLoad ListComp Num comprehension NameStore Call NameLoad AttributeLoad NameLoad attr Assign AttributeStore NameLoad attr Num decorator_list FunctionDef arguments args NameParam NameParam defaults vararg body AugAssignAdd AttributeStore NameLoad attr Num Return BinOpMult Num Call NameLoad BinOpMult Num Call NameLoad BinOpAdd BinOpPow SubscriptLoad NameLoad Index Num Num BinOpPow SubscriptLoad NameLoad Index Num Num decorator_list decorator_list ClassDef bases NameLoad body Expr Str FunctionDef arguments args NameParam NameParam defaults Num body Expr Call AttributeLoad NameLoad attr NameLoad NameLoad Assign AttributeStore NameLoad attr Call NameLoad BinOpMult ListLoad Num AttributeLoad NameLoad attr BinOpMult ListLoad Num AttributeLoad NameLoad attr Assign AttributeStore NameLoad attr ListLoad ListLoad Num Num Assign AttributeStore NameLoad attr Num decorator_list FunctionDef arguments args NameParam NameParam defaults vararg body AugAssignAdd AttributeStore NameLoad attr Num Assign NameStore BinOpMult Num Call NameLoad BinOpMult Num Call NameLoad BinOpAdd BinOpPow SubscriptLoad NameLoad Index Num Num BinOpPow SubscriptLoad NameLoad Index Num Num AugAssignAdd NameStore BinOpMult Num Call NameLoad BinOpAdd Call NameLoad BinOpMult Num SubscriptLoad NameLoad Index Num Call NameLoad BinOpMult Num SubscriptLoad NameLoad Index Num Return NameLoad decorator_list decorator_list ClassDef bases NameLoad body Expr Str FunctionDef arguments args NameParam NameParam defaults Num body Expr Call AttributeLoad NameLoad attr NameLoad NameLoad Assign AttributeStore NameLoad attr TupleLoad ListLoad Num Num ListLoad Num Num Assign AttributeStore NameLoad attr ListLoad ListLoad Num Num Assign AttributeStore NameLoad attr Num decorator_list FunctionDef arguments args NameParam NameParam defaults vararg body AugAssignAdd AttributeStore NameLoad attr Num Return BinOpSub BinOpMult Call NameLoad SubscriptLoad NameLoad Index Num Call NameLoad SubscriptLoad NameLoad Index Num BinOpDiv SubscriptLoad NameLoad Index Num BinOpAdd BinOpPow SubscriptLoad NameLoad Index Num Num Num decorator_list decorator_list ClassDef bases NameLoad body Expr Str FunctionDef arguments args NameParam NameParam defaults Num body Expr Call AttributeLoad NameLoad attr NameLoad NameLoad Assign AttributeStore NameLoad attr Call NameLoad BinOpMult ListLoad Num AttributeLoad NameLoad attr BinOpMult ListLoad Num AttributeLoad NameLoad attr Assign AttributeStore NameLoad attr ListLoad ListComp Num comprehension NameStore Call NameLoad AttributeLoad NameLoad attr Assign AttributeStore NameLoad attr Num Assign AttributeStore NameLoad attr NameLoad decorator_list FunctionDef arguments args NameParam NameParam defaults vararg body AugAssignAdd AttributeStore NameLoad attr Num Return Call NameLoad Call NameLoad BinOpAdd BinOpMult NameLoad Call NameLoad NameLoad BinOpMult Num NameLoad decorator_list decorator_list ClassDef bases NameLoad body Expr Str FunctionDef arguments args NameParam NameParam defaults Num body Expr Call AttributeLoad NameLoad attr NameLoad NameLoad Assign AttributeStore NameLoad attr Call NameLoad BinOpMult ListLoad Num AttributeLoad NameLoad attr BinOpMult ListLoad Num AttributeLoad NameLoad attr Assign AttributeStore NameLoad attr ListLoad ListLoad Num Num Assign AttributeStore NameLoad attr Num Assign AttributeStore NameLoad attr NameLoad decorator_list FunctionDef arguments args NameParam NameParam defaults vararg body AugAssignAdd AttributeStore NameLoad attr Num Return Call NameLoad BinOpMult Call NameLoad NameLoad Call NameLoad NameLoad decorator_list decorator_list ClassDef bases NameLoad body Expr Str FunctionDef arguments args NameParam NameParam defaults Num body Expr Call AttributeLoad NameLoad attr NameLoad NameLoad Assign AttributeStore NameLoad attr Call NameLoad BinOpMult ListLoad Num AttributeLoad NameLoad attr BinOpMult ListLoad Num AttributeLoad NameLoad attr Assign AttributeStore NameLoad attr ListLoad ListLoad Num Num Assign AttributeStore NameLoad attr Num Assign AttributeStore NameLoad attr NameLoad decorator_list FunctionDef arguments args NameParam NameParam defaults vararg body AugAssignAdd AttributeStore NameLoad attr Num Assign NameStore Call NameLoad NameLoad Assign NameStore Call NameLoad NameLoad Assign NameStore BinOpDiv NameLoad AttributeLoad NameLoad attr Assign NameStore BinOpPow NameLoad BinOpDiv Num AttributeLoad NameLoad attr Assign NameStore BinOpPow BinOpSub NameLoad NameLoad Num Return NameLoad decorator_list decorator_list
N/A __future__ division print_function absolute_import numpy abs cos exp pi prod sin sqrt sum go_benchmark Benchmark Ackley01 N/A Benchmark N/A N/A 
    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.
     __init__ N/A N/A self dimensions N/A 2 N/A N/A N/A N/A Benchmark __init__ self dimensions N/A N/A self _bounds N/A zip N/A N/A -35.0 N/A self N N/A N/A 35.0 N/A self N N/A N/A self global_optimum N/A N/A 0 N/A _ N/A range N/A self N N/A N/A self fglob 0.0 N/A N/A self change_dimensionality True N/A fun N/A N/A self x N/A args N/A N/A N/A self nfev 1 N/A u N/A sum N/A x 2 N/A v N/A sum N/A cos N/A N/A 2 pi x N/A N/A N/A N/A N/A -20.0 N/A exp N/A -0.2 N/A sqrt N/A u N/A self N N/A exp N/A v N/A self N 20.0 N/A exp 1.0 N/A N/A Ackley02 N/A Benchmark N/A N/A 
    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.

     __init__ N/A N/A self dimensions N/A 2 N/A N/A N/A N/A Benchmark __init__ self dimensions N/A N/A self _bounds N/A zip N/A N/A -32.0 N/A self N N/A N/A 32.0 N/A self N N/A N/A self global_optimum N/A N/A 0 N/A _ N/A range N/A self N N/A N/A self fglob -200.0 N/A fun N/A N/A self x N/A args N/A N/A N/A self nfev 1 N/A N/A -200 N/A exp N/A -0.02 N/A sqrt N/A N/A N/A x N/A 0 2 N/A N/A x N/A 1 2 N/A N/A Ackley03 N/A Benchmark N/A N/A 
    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
     __init__ N/A N/A self dimensions N/A 2 N/A N/A N/A N/A Benchmark __init__ self dimensions N/A N/A self _bounds N/A zip N/A N/A -32.0 N/A self N N/A N/A 32.0 N/A self N N/A N/A self global_optimum N/A N/A -0.68255758 -0.36070859 N/A N/A self fglob -195.629028259 N/A fun N/A N/A self x N/A args N/A N/A N/A self nfev 1 N/A a N/A -200 N/A exp N/A -0.02 N/A sqrt N/A N/A N/A x N/A 0 2 N/A N/A x N/A 1 2 N/A a N/A 5 N/A exp N/A N/A cos N/A 3 N/A x N/A 0 N/A sin N/A 3 N/A x N/A 1 N/A a N/A N/A Adjiman N/A Benchmark N/A N/A 
    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.
     __init__ N/A N/A self dimensions N/A 2 N/A N/A N/A N/A Benchmark __init__ self dimensions N/A N/A self _bounds N/A N/A -1.0 2.0 N/A -1.0 1.0 N/A N/A self global_optimum N/A N/A 2.0 0.10578 N/A N/A self fglob -2.02180678 N/A fun N/A N/A self x N/A args N/A N/A N/A self nfev 1 N/A N/A N/A N/A cos N/A x N/A 0 N/A sin N/A x N/A 1 N/A N/A x N/A 0 N/A N/A N/A x N/A 1 2 1 N/A N/A Alpine01 N/A Benchmark N/A N/A 
    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.
     __init__ N/A N/A self dimensions N/A 2 N/A N/A N/A N/A Benchmark __init__ self dimensions N/A N/A self _bounds N/A zip N/A N/A -10.0 N/A self N N/A N/A 10.0 N/A self N N/A N/A self global_optimum N/A N/A 0 N/A _ N/A range N/A self N N/A N/A self fglob 0.0 N/A N/A self change_dimensionality True N/A fun N/A N/A self x N/A args N/A N/A N/A self nfev 1 N/A N/A sum N/A abs N/A N/A x N/A sin x N/A 0.1 x N/A N/A Alpine02 N/A Benchmark N/A N/A 
    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.
     __init__ N/A N/A self dimensions N/A 2 N/A N/A N/A N/A Benchmark __init__ self dimensions N/A N/A self _bounds N/A zip N/A N/A 0.0 N/A self N N/A N/A 10.0 N/A self N N/A N/A self global_optimum N/A N/A 7.91705268 4.81584232 N/A N/A self fglob -6.1295 N/A N/A self change_dimensionality True N/A fun N/A N/A self x N/A args N/A N/A N/A self nfev 1 N/A N/A prod N/A N/A sqrt x N/A sin x N/A N/A AMGM N/A Benchmark N/A N/A 
    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.
     __init__ N/A N/A self dimensions N/A 2 N/A N/A N/A N/A Benchmark __init__ self dimensions N/A N/A self _bounds N/A zip N/A N/A 0.0 N/A self N N/A N/A 10.0 N/A self N N/A N/A self global_optimum N/A N/A 1 1 N/A N/A self fglob 0.0 N/A N/A self change_dimensionality True N/A fun N/A N/A self x N/A args N/A N/A N/A self nfev 1 N/A f1 N/A sum x N/A f2 N/A prod x N/A f1 N/A f1 N/A self N N/A f2 N/A f2 N/A 1.0 N/A self N N/A f N/A N/A f1 f2 2 N/A f N/A N/A