class_docstr: A CMA-ES strategy that combines the :math:`(1 + \lambda)` paradigm
  [Igel2007]_, the mixed integer modification [Hansen2011]_, active
  covariance update [Arnold2010]_ and constraint handling [Arnold2012]_.
  This version of CMA-ES requires the random vector and the mutation
  that created each individual. The vector and mutation are stored in each
  individual as :attr:`_z` and :attr:`_y` respectively. Updating with
  individuals not containing these attributes will result in an
  :class:`AttributeError`.
  Notes:
      When using this strategy (especially when using constraints) you should
      monitor the strategy :attr:`condition_number`. If it goes above a given
      threshold (say :math:`10^{12}`), you should think of restarting the
      optimization as the covariance matrix is going degenerate. See the
      constrained active CMA-ES example for a simple example of restart.
  :param parent: An iterable object that indicates where to start the
                 evolution. The parent requires a fitness attribute.
  :param sigma: The initial standard deviation of the distribution.
  :param step: The minimal step size for each dimension. Use 0 for
               continuous dimensions.
  :param lambda_: Number of offspring to produce from the parent.
                  (optional, defaults to 1)
  :param **kwargs: One or more parameter to pass to the strategy as
                   described in the following table. (optional)
  +----------------+---------------------------+------------------------------+
  | Parameter      | Default                   | Details                      |
  +================+===========================+==============================+
  | ``d``          | ``1.0 + N / (2.0 *        | Damping for step-size.       |
  |                | lambda_)``                |                              |
  +----------------+---------------------------+------------------------------+
  | ``ptarg``      | ``1.0 / (5 + sqrt(lambda_)| Target success rate          |
  |                | / 2.0)``                  | (from 1 + lambda algorithm). |
  +----------------+---------------------------+------------------------------+
  | ``cp``         | ``ptarg * lambda_ / (2.0 +| Step size learning rate.     |
  |                | ptarg * lambda_)``        |                              |
  +----------------+---------------------------+------------------------------+
  | ``cc``         | ``2.0 / (N + 2.0)``       | Cumulation time horizon.     |
  +----------------+---------------------------+------------------------------+
  | ``ccov``       | ``2.0 / (N**2 + 6.0)``    | Covariance matrix learning   |
  |                |                           | rate.                        |
  +----------------+---------------------------+------------------------------+
  | ``ccovn``      | ``0.4 / (N**1.6 + 1.0)``  | Covariance matrix negative   |
  |                |                           | learning rate.               |
  +----------------+---------------------------+------------------------------+
  | ``cconst``     | ``1.0 / (N + 2.0)``       | Constraint vectors learning  |
  |                |                           | rate.                        |
  +----------------+---------------------------+------------------------------+
  | ``beta``       | ``0.1 / (lambda_ * (N +   | Covariance matrix learning   |
  |                |   2.0))``                 | rate for constraints.        |
  |                |                           |                              |
  +----------------+---------------------------+------------------------------+
  | ``pthresh``    | ``0.44``                  | Threshold success rate.      |
  +----------------+---------------------------+------------------------------+
  .. [Igel2007] Igel, Hansen and Roth. Covariance matrix adaptation for
     multi-objective optimization. 2007
  .. [Arnold2010] Arnold and Hansen. Active covariance matrix adaptation for
     the (1+1)-CMA-ES. 2010.
  .. [Hansen2011] Hansen. A CMA-ES for Mixed-Integer Nonlinear Optimization.
     Research Report] RR-7751, INRIA. 2011
  .. [Arnold2012] Arnold and Hansen. A (1+1)-CMA-ES for Constrained Optimisation.
     2012
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docstr: Generate a population of :math:`\lambda` individuals of type
  *ind_init* from the current strategy.
  :param ind_init: A function object that is able to initialize an
                   individual from a list.
  :returns: A list of individuals.
docstr_tok: ["Generate","a","population","of",":","math",":","`","\\lambda","`","individuals","of","type","*","ind_init","*","from","the","current","strategy",".",":","param","ind_init",":","A","function","object","that","is","able","to","initialize","an","individual","from","a","list",".",":","returns",":","A","list","of","individuals","."]
code: def generate(self, ind_init):
      r"""Generate a population of :math:`\lambda` individuals of type
      *ind_init* from the current strategy.
      :param ind_init: A function object that is able to initialize an
                       individual from a list.
      :returns: A list of individuals.
      """
      # Generate individuals
      z = numpy.random.standard_normal((self.lambda_, self.dim))
      y = numpy.dot(self.A, z.T).T
      x = (
          self.parent
          + self.sigma * y
          + self.S_int * self._integer_mutation()
      )
  
      if any(self.S_int > 0):
          # Bring values to the integer steps
          round_values = numpy.tile(self.S_int > 0, (self.lambda_, 1))
          steps = numpy.tile(self.S_int, (self.lambda_, 1))
          x[round_values] = steps[round_values] * numpy.around(
              x[round_values] / steps[round_values]
          )
  
      # The update method requires to remember the y of each individual
      population = list(map(ind_init, x))
      for ind, yi, zi in zip(population, y, z):
          ind._y = yi
          ind._z = zi
  
      return population
  
imports: import copy
  from math import sqrt, log, exp
  from itertools import cycle
  import warnings
  import numpy
  from .None import tools
label_desc: Use image node_id 5 for calling the StrategyActiveOnePlusLambda obj's underlying member method code with example usage: obj.generate(ind_init) and returns: population