code: def differential_evolution(
      func,
      bounds,
      args=(),
      strategy="best1bin",
      maxiter=1000,
      popsize=15,
      tol=0.01,
      mutation=(0.5, 1),
      recombination=0.7,
      seed=None,
      callback=None,
      disp=False,
      polish=True,
      init="latinhypercube",
      atol=0,
      updating="immediate",
      workers=1,
  ):
      """Finds the global minimum of a multivariate function.
  
      Differential Evolution is stochastic in nature (does not use gradient
      methods) to find the minimium, and can search large areas of candidate
      space, but often requires larger numbers of function evaluations than
      conventional gradient based techniques.
  
      The algorithm is due to Storn and Price [1]_.
  
      Parameters
      ----------
      func : callable
          The objective function to be minimized.  Must be in the form
          ``f(x, *args)``, where ``x`` is the argument in the form of a 1-D array
          and ``args`` is a  tuple of any additional fixed parameters needed to
          completely specify the function.
      bounds : sequence
          Bounds for variables.  ``(min, max)`` pairs for each element in ``x``,
          defining the lower and upper bounds for the optimizing argument of
          `func`. It is required to have ``len(bounds) == len(x)``.
          ``len(bounds)`` is used to determine the number of parameters in ``x``.
      args : tuple, optional
          Any additional fixed parameters needed to
          completely specify the objective function.
      strategy : str, optional
          The differential evolution strategy to use. Should be one of:
  
              - 'best1bin'
              - 'best1exp'
              - 'rand1exp'
              - 'randtobest1exp'
              - 'currenttobest1exp'
              - 'best2exp'
              - 'rand2exp'
              - 'randtobest1bin'
              - 'currenttobest1bin'
              - 'best2bin'
              - 'rand2bin'
              - 'rand1bin'
  
          The default is 'best1bin'.
      maxiter : int, optional
          The maximum number of generations over which the entire population is
          evolved. The maximum number of function evaluations (with no polishing)
          is: ``(maxiter + 1) * popsize * len(x)``
      popsize : int, optional
          A multiplier for setting the total population size.  The population has
          ``popsize * len(x)`` individuals (unless the initial population is
          supplied via the `init` keyword).
      tol : float, optional
          Relative tolerance for convergence, the solving stops when
          ``np.std(pop) <= atol + tol * np.abs(np.mean(population_energies))``,
          where and `atol` and `tol` are the absolute and relative tolerance
          respectively.
      mutation : float or tuple(float, float), optional
          The mutation constant. In the literature this is also known as
          differential weight, being denoted by F.
          If specified as a float it should be in the range [0, 2].
          If specified as a tuple ``(min, max)`` dithering is employed. Dithering
          randomly changes the mutation constant on a generation by generation
          basis. The mutation constant for that generation is taken from
          ``U[min, max)``. Dithering can help speed convergence significantly.
          Increasing the mutation constant increases the search radius, but will
          slow down convergence.
      recombination : float, optional
          The recombination constant, should be in the range [0, 1]. In the
          literature this is also known as the crossover probability, being
          denoted by CR. Increasing this value allows a larger number of mutants
          to progress into the next generation, but at the risk of population
          stability.
      seed : int or `np.random.RandomState`, optional
          If `seed` is not specified the `np.RandomState` singleton is used.
          If `seed` is an int, a new `np.random.RandomState` instance is used,
          seeded with seed.
          If `seed` is already a `np.random.RandomState instance`, then that
          `np.random.RandomState` instance is used.
          Specify `seed` for repeatable minimizations.
      disp : bool, optional
          Display status messages
      callback : callable, `callback(xk, convergence=val)`, optional
          A function to follow the progress of the minimization. ``xk`` is
          the current value of ``x0``. ``val`` represents the fractional
          value of the population convergence.  When ``val`` is greater than one
          the function halts. If callback returns `True`, then the minimization
          is halted (any polishing is still carried out).
      polish : bool, optional
          If True (default), then `scipy.optimize.minimize` with the `L-BFGS-B`
          method is used to polish the best population member at the end, which
          can improve the minimization slightly.
      init : str or array-like, optional
          Specify which type of population initialization is performed. Should be
          one of:
  
              - 'latinhypercube'
              - 'random'
              - array specifying the initial population. The array should have
                shape ``(M, len(x))``, where len(x) is the number of parameters.
                `init` is clipped to `bounds` before use.
  
          The default is 'latinhypercube'. Latin Hypercube sampling tries to
          maximize coverage of the available parameter space. 'random'
          initializes the population randomly - this has the drawback that
          clustering can occur, preventing the whole of parameter space being
          covered. Use of an array to specify a population subset could be used,
          for example, to create a tight bunch of initial guesses in an location
          where the solution is known to exist, thereby reducing time for
          convergence.
      atol : float, optional
          Absolute tolerance for convergence, the solving stops when
          ``np.std(pop) <= atol + tol * np.abs(np.mean(population_energies))``,
          where and `atol` and `tol` are the absolute and relative tolerance
          respectively.
      updating : {'immediate', 'deferred'}, optional
          If ``'immediate'``, the best solution vector is continuously updated
          within a single generation [4]_. This can lead to faster convergence as
          trial vectors can take advantage of continuous improvements in the best
          solution.
          With ``'deferred'``, the best solution vector is updated once per
          generation. Only ``'deferred'`` is compatible with parallelization, and
          the `workers` keyword can over-ride this option.
  
          .. versionadded:: 1.2.0
  
      workers : int or map-like callable, optional
          If `workers` is an int the population is subdivided into `workers`
          sections and evaluated in parallel (uses `multiprocessing.Pool`).
          Supply -1 to use all available CPU cores.
          Alternatively supply a map-like callable, such as
          `multiprocessing.Pool.map` for evaluating the population in parallel.
          This evaluation is carried out as ``workers(func, iterable)``.
          This option will override the `updating` keyword to
          ``updating='deferred'`` if ``workers != 1``.
          Requires that `func` be pickleable.
  
          .. versionadded:: 1.2.0
  
      Returns
      -------
      res : OptimizeResult
          The optimization result represented as a `OptimizeResult` object.
          Important attributes are: ``x`` the solution array, ``success`` a
          Boolean flag indicating if the optimizer exited successfully and
          ``message`` which describes the cause of the termination. See
          `OptimizeResult` for a description of other attributes.  If `polish`
          was employed, and a lower minimum was obtained by the polishing, then
          OptimizeResult also contains the ``jac`` attribute.
  
      Notes
      -----
      Differential evolution is a stochastic population based method that is
      useful for global optimization problems. At each pass through the population
      the algorithm mutates each candidate solution by mixing with other candidate
      solutions to create a trial candidate. There are several strategies [2]_ for
      creating trial candidates, which suit some problems more than others. The
      'best1bin' strategy is a good starting point for many systems. In this
      strategy two members of the population are randomly chosen. Their difference
      is used to mutate the best member (the `best` in `best1bin`), :math:`b_0`,
      so far:
  
      .. math::
  
          b' = b_0 + mutation * (population[rand0] - population[rand1])
  
      A trial vector is then constructed. Starting with a randomly chosen 'i'th
      parameter the trial is sequentially filled (in modulo) with parameters from
      ``b'`` or the original candidate. The choice of whether to use ``b'`` or the
      original candidate is made with a binomial distribution (the 'bin' in
      'best1bin') - a random number in [0, 1) is generated.  If this number is
      less than the `recombination` constant then the parameter is loaded from
      ``b'``, otherwise it is loaded from the original candidate.  The final
      parameter is always loaded from ``b'``.  Once the trial candidate is built
      its fitness is assessed. If the trial is better than the original candidate
      then it takes its place. If it is also better than the best overall
      candidate it also replaces that.
      To improve your chances of finding a global minimum use higher `popsize`
      values, with higher `mutation` and (dithering), but lower `recombination`
      values. This has the effect of widening the search radius, but slowing
      convergence.
      By default the best solution vector is updated continuously within a single
      iteration (``updating='immediate'``). This is a modification [4]_ of the
      original differential evolution algorithm which can lead to faster
      convergence as trial vectors can immediately benefit from improved
      solutions. To use the original Storn and Price behaviour, updating the best
      solution once per iteration, set ``updating='deferred'``.
  
      .. versionadded:: 0.15.0
  
      Examples
      --------
      Let us consider the problem of minimizing the Rosenbrock function. This
      function is implemented in `rosen` in `scipy.optimize`.
  
      >>> from scipy.optimize import rosen, differential_evolution
      >>> bounds = [(0,2), (0, 2), (0, 2), (0, 2), (0, 2)]
      >>> result = differential_evolution(rosen, bounds)
      >>> result.x, result.fun
      (array([1., 1., 1., 1., 1.]), 1.9216496320061384e-19)
  
      Now repeat, but with parallelization.
  
      >>> bounds = [(0,2), (0, 2), (0, 2), (0, 2), (0, 2)]
      >>> result = differential_evolution(rosen, bounds, updating='deferred',
      ...                                 workers=2)
      >>> result.x, result.fun
      (array([1., 1., 1., 1., 1.]), 1.9216496320061384e-19)
  
      Next find the minimum of the Ackley function
      (https://en.wikipedia.org/wiki/Test_functions_for_optimization).
  
      >>> from scipy.optimize import differential_evolution
      >>> import numpy as np
      >>> def ackley(x):
      ...     arg1 = -0.2 * np.sqrt(0.5 * (x[0] ** 2 + x[1] ** 2))
      ...     arg2 = 0.5 * (np.cos(2. * np.pi * x[0]) + np.cos(2. * np.pi * x[1]))
      ...     return -20. * np.exp(arg1) - np.exp(arg2) + 20. + np.e
      >>> bounds = [(-5, 5), (-5, 5)]
      >>> result = differential_evolution(ackley, bounds)
      >>> result.x, result.fun
      (array([ 0.,  0.]), 4.4408920985006262e-16)
  
      References
      ----------
      .. [1] Storn, R and Price, K, Differential Evolution - a Simple and
             Efficient Heuristic for Global Optimization over Continuous Spaces,
             Journal of Global Optimization, 1997, 11, 341 - 359.
      .. [2] http://www1.icsi.berkeley.edu/~storn/code.html
      .. [3] http://en.wikipedia.org/wiki/Differential_evolution
      .. [4] Wormington, M., Panaccione, C., Matney, K. M., Bowen, D. K., -
             Characterization of structures from X-ray scattering data using
             genetic algorithms, Phil. Trans. R. Soc. Lond. A, 1999, 357,
             2827-2848
      """
  
      # using a context manager means that any created Pool objects are
      # cleared up.
      with DifferentialEvolutionSolver(
          func,
          bounds,
          args=args,
          strategy=strategy,
          maxiter=maxiter,
          popsize=popsize,
          tol=tol,
          mutation=mutation,
          recombination=recombination,
          seed=seed,
          polish=polish,
          callback=callback,
          disp=disp,
          init=init,
          atol=atol,
          updating=updating,
          workers=workers,
      ) as solver:
          ret = solver.solve()
  
      return ret
  
imports: from __future__ import division, print_function, absolute_import
  import warnings
  import numpy
  from scipy.optimize import OptimizeResult, minimize
  from scipy.optimize.optimize import _status_message
  from scipy._lib._util import check_random_state, MapWrapper
  from scipy._lib.six import xrange, string_types
label_desc: Use image node_id 1 for calling a global function with example usage: differential_evolution(func, bounds, args, strategy, maxiter, popsize, tol, mutation, recombination, seed, callback, disp, polish, init, atol, updating, workers) and returns: ret