Module ImportFrom alias alias alias ImportFrom 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 ListLoad Num Num Num Num Num Num Assign AttributeStore NameLoad attr Num decorator_list FunctionDef arguments args NameParam NameParam defaults vararg body AugAssignAdd AttributeStore NameLoad attr Num Assign NameStore AttributeLoad Call NameLoad Call NameLoad Num attr Assign NameStore BinOpDiv NameLoad Num Assign NameStore Call NameLoad Num Assign NameStore Call NameLoad Num Assign NameStore Call NameLoad BinOpMult BinOpMult BinOpAdd NameLoad Num BinOpPow NameLoad NameLoad SubscriptLoad NameLoad Slice Num keyword Num Assign NameStore Call NameLoad BinOpMult BinOpPow NameLoad NameLoad NameLoad keyword Num Assign NameStore BinOpPow BinOpSub BinOpSub NameLoad BinOpPow NameLoad Num Num Num Return BinOpAdd Call NameLoad NameLoad 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 UnaryOpUSub NameLoad AttributeLoad NameLoad attr BinOpMult ListLoad NameLoad 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 BinOpSub Num BinOpMult BinOpDiv Num AttributeLoad NameLoad attr Call NameLoad BinOpMult Call NameLoad BinOpMult Num NameLoad Call NameLoad BinOpDiv UnaryOpUSub BinOpPow NameLoad 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 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 BinOpAdd BinOpPow BinOpSub BinOpAdd BinOpPow SubscriptLoad NameLoad Index Num Num BinOpPow SubscriptLoad NameLoad Index Num Num Num Num BinOpPow BinOpSub BinOpAdd BinOpMult Num SubscriptLoad NameLoad Index Num 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 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 Assign NameStore BinOpPow BinOpSub BinOpSub Num BinOpMult Num BinOpPow BinOpSub SubscriptLoad NameLoad Index Num Num Num BinOpMult Num BinOpPow BinOpSub SubscriptLoad NameLoad Index Num Num Num Num Assign NameStore BinOpPow BinOpSub SubscriptLoad NameLoad Index Num Num Num Return BinOpAdd 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 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 Num Assign TupleStore NameStore NameStore TupleLoad Num Num Assign NameStore AttributeLoad Call NameLoad Call NameLoad BinOpAdd NameLoad Num attr Assign NameStore BinOpMult BinOpPow NameLoad NameLoad Call NameLoad BinOpMult BinOpMult BinOpMult Num NameLoad BinOpPow NameLoad NameLoad BinOpAdd NameLoad Num Assign NameStore BinOpMult AttributeLoad NameLoad attr Call NameLoad BinOpMult BinOpPow NameLoad AttributeLoad NameLoad attr Call NameLoad BinOpMult NameLoad BinOpPow NameLoad AttributeLoad NameLoad attr Return BinOpSub Call NameLoad Call NameLoad NameLoad keyword 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 TupleLoad ListLoad Num Num ListLoad Num Num 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 NameLoad Assign NameStore AttributeLoad Call NameLoad NameLoad attr Assign NameStore BinOpAdd BinOpMult Num BinOpSub BinOpPow NameLoad Num NameLoad BinOpPow BinOpSub Num NameLoad Num Assign NameStore BinOpAdd BinOpSub BinOpDiv BinOpPow NameLoad Num Num Call NameLoad NameLoad Num Return Call NameLoad Call NameLoad NameLoad keyword 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 BinOpAdd BinOpMult BinOpDiv Num Num BinOpPow BinOpSub BinOpAdd BinOpPow SubscriptLoad NameLoad Index Num Num BinOpPow SubscriptLoad NameLoad Index Num Num BinOpMult SubscriptLoad NameLoad Index Num SubscriptLoad NameLoad Index Num Num SubscriptLoad NameLoad Index Num decorator_list decorator_list
N/A __future__ division print_function absolute_import numpy atleast_2d arange sum cos exp pi go_benchmark Benchmark Watson N/A Benchmark N/A N/A 
    Watson objective function.

    This class defines the Watson [1]_ global optimization problem. This is a
    unimodal minimization problem defined as follows:

    .. math::

        f_{\text{Watson}}(x) = \sum_{i=0}^{29} \left\{
                               \sum_{j=0}^4 ((j + 1)a_i^j x_{j+1})
                               - \left[ \sum_{j=0}^5 a_i^j
                               x_{j+1} \right ]^2 - 1 \right\}^2
                               + x_1^2


    Where, in this exercise, :math:`a_i = i/29`.

    with :math:`x_i \in [-5, 5]` for :math:`i = 1, ..., 6`.

    *Global optimum*: :math:`f(x) = 0.002288` for
    :math:`x = [-0.0158, 1.012, -0.2329, 1.260, -1.513, 0.9928]`

    .. [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 Jamil #161 writes equation using (j - 1).  According to code in Adorio
    and Gavana it should be (j+1). However the equations in those papers
    contain (j - 1) as well.  However, I've got the right global minimum!!!
     __init__ N/A N/A self dimensions N/A 6 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 -5.0 N/A self N N/A N/A 5.0 N/A self N N/A N/A self global_optimum N/A N/A -0.0158 1.012 -0.2329 1.26 -1.513 0.9928 N/A N/A self fglob 0.002288 N/A fun N/A N/A self x N/A args N/A N/A N/A self nfev 1 N/A i N/A N/A atleast_2d N/A arange 30.0 T N/A a N/A i 29.0 N/A j N/A arange 5.0 N/A k N/A arange 6.0 N/A t1 N/A sum N/A N/A N/A j 1 N/A a j N/A x N/A 1 axis 1 N/A t2 N/A sum N/A N/A a k x axis 1 N/A inner N/A N/A N/A t1 N/A t2 2 1 2 N/A N/A N/A sum inner N/A N/A x N/A 0 2 N/A N/A Wavy N/A Benchmark N/A N/A 
    Wavy objective function.

    This class defines the W / Wavy [1]_ global optimization problem. This is a
    multimodal minimization problem defined as follows:

    .. math::

        f_{\text{Wavy}}(x) = 1 - \frac{1}{n} \sum_{i=1}^{n}
                             \cos(kx_i)e^{-\frac{x_i^2}{2}}


    Where, in this exercise, :math:`k = 10`. The number of local minima is
    :math:`kn` and :math:`(k + 1)n` for odd and even :math:`k` respectively.

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

    *Global optimum*: :math:`f(x) = 0` 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 N/A pi N/A self N N/A N/A pi N/A self N N/A N/A self global_optimum N/A N/A 0.0 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 1.0 N/A N/A 1.0 N/A self N N/A sum N/A N/A cos N/A 10 x N/A exp N/A N/A N/A x 2.0 2.0 N/A N/A WayburnSeader01 N/A Benchmark N/A N/A 
    Wayburn and Seader 1 objective function.

    This class defines the Wayburn and Seader 1 [1]_ global optimization
    problem. This is a unimodal minimization problem defined as follows:

    .. math::

        f_{\text{WayburnSeader01}}(x) = (x_1^6 + x_2^4 - 17)^2
                                        + (2x_1 + x_2 - 4)^2


    with :math:`x_i \in [-5, 5]` for :math:`i = 1, 2`.

    *Global optimum*: :math:`f(x) = 0` for :math:`x = [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.
     __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 -5.0 N/A self N N/A N/A 5.0 N/A self N N/A N/A self custom_bounds N/A N/A -2 2 N/A -2 2 N/A N/A self global_optimum N/A N/A 1.0 2.0 N/A N/A self fglob 0.0 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 N/A N/A N/A N/A N/A x N/A 0 6 N/A N/A x N/A 1 4 17 2 N/A N/A N/A N/A 2 N/A x N/A 0 N/A x N/A 1 4 2 N/A N/A WayburnSeader02 N/A Benchmark N/A N/A 
    Wayburn and Seader 2 objective function.

    This class defines the Wayburn and Seader 2 [1]_ global optimization
    problem. This is a unimodal minimization problem defined as follows:

    .. math::

        f_{\text{WayburnSeader02}}(x) = \left[ 1.613 - 4(x_1 - 0.3125)^2
                                        - 4(x_2 - 1.625)^2 \right]^2
                                        + (x_2 - 1)^2


    with :math:`x_i \in [-500, 500]` for :math:`i = 1, 2`.

    *Global optimum*: :math:`f(x) = 0` for :math:`x = [0.2, 1]`

    .. [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 -500.0 N/A self N N/A N/A 500.0 N/A self N N/A N/A self custom_bounds N/A N/A -1 2 N/A -1 2 N/A N/A self global_optimum N/A N/A 0.2 1.0 N/A N/A self fglob 0.0 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 N/A N/A 1.613 N/A 4 N/A N/A N/A x N/A 0 0.3125 2 N/A 4 N/A N/A N/A x N/A 1 1.625 2 2 N/A v N/A N/A N/A x N/A 1 1 2 N/A N/A u v N/A N/A Weierstrass N/A Benchmark N/A N/A 
    Weierstrass objective function.

    This class defines the Weierstrass [1]_ global optimization problem.
    This is a multimodal minimization problem defined as follows:

    .. math::

       f_{\text{Weierstrass}}(x) = \sum_{i=1}^{n} \left [
                                   \sum_{k=0}^{kmax} a^k \cos 
                                   \left( 2 \pi b^k (x_i + 0.5) \right) - n
                                   \sum_{k=0}^{kmax} a^k \cos(\pi b^k) \right ]


    Where, in this exercise, :math:`kmax = 20`, :math:`a = 0.5` and
    :math:`b = 3`.

    Here, :math:`n` represents the number of dimensions and
    :math:`x_i \in [-0.5, 0.5]` for :math:`i = 1, ..., n`.

    *Global optimum*: :math:`f(x) = 4` for :math:`x_i = 0` for
    :math:`i = 1, ..., n`

    .. [1] Mishra, S. Global Optimization by Differential Evolution and
    Particle Swarm Methods: Evaluation on Some Benchmark Functions.
    Munich Personal RePEc Archive, 2006, 1005

    TODO line 1591.
    TODO Jamil, Gavana have got it wrong.  The second term is not supposed to
    be included in the outer sum. Mishra code has it right as does the
    reference referred to in Jamil#166.
     __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 -0.5 N/A self N N/A N/A 0.5 N/A self N N/A N/A self global_optimum N/A N/A 0.0 N/A _ N/A range N/A self N N/A N/A self fglob 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 kmax 20 N/A N/A a b N/A 0.5 3.0 N/A k N/A N/A atleast_2d N/A arange N/A kmax 1.0 T N/A t1 N/A N/A a k N/A cos N/A N/A N/A 2 pi N/A b k N/A x 0.5 N/A t2 N/A N/A self N N/A sum N/A N/A a N/A k T N/A cos N/A pi N/A b N/A k T N/A N/A N/A sum N/A sum t1 axis 0 t2 N/A N/A Whitley N/A Benchmark N/A N/A 
    Whitley objective function.

    This class defines the Whitley [1]_ global optimization problem. This
    is a multimodal minimization problem defined as follows:

    .. math::

        f_{\text{Whitley}}(x) = \sum_{i=1}^n \sum_{j=1}^n
                                \left[\frac{(100(x_i^2-x_j)^2
                                + (1-x_j)^2)^2}{4000} - \cos(100(x_i^2-x_j)^2
                                + (1-x_j)^2)+1 \right]


    Here, :math:`n` represents the number of dimensions and
    :math:`x_i \in [-10.24, 10.24]` for :math:`i = 1, ..., n`.

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

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

    TODO Jamil#167 has '+ 1' inside the cos term, when it should be outside it.
     __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 -10.24 N/A self N N/A N/A 10.24 N/A self N N/A N/A self custom_bounds N/A N/A -1 2 N/A -1 2 N/A N/A self global_optimum N/A N/A 1.0 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 XI x N/A XJ N/A N/A atleast_2d x T N/A temp N/A N/A 100.0 N/A N/A XI 2.0 XJ N/A N/A 1.0 XJ 2.0 N/A inner N/A N/A N/A N/A temp 2.0 4000.0 N/A cos temp 1.0 N/A N/A sum N/A sum inner axis 0 N/A N/A Wolfe N/A Benchmark N/A N/A 
    Wolfe objective function.

    This class defines the Wolfe [1]_ global optimization problem. This
    is a multimodal minimization problem defined as follows:

    .. math::

       f_{\text{Wolfe}}(x) = \frac{4}{3}(x_1^2 + x_2^2 - x_1x_2)^{0.75} + x_3


    with :math:`x_i \in [0, 2]` for :math:`i = 1, 2, 3`.

    *Global optimum*: :math:`f(x) = 0` for :math:`x = [0, 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 3 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 2.0 N/A self N N/A N/A self global_optimum N/A N/A 0.0 N/A _ N/A range N/A self N N/A N/A self fglob 0.0 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 N/A N/A 4 3 N/A N/A N/A N/A N/A x N/A 0 2 N/A N/A x N/A 1 2 N/A N/A x N/A 0 N/A x N/A 1 0.75 N/A x N/A 2 N/A N/A