class_docstr: LennardJones objective function.
  
  This class defines the Lennard-Jones global optimization problem. This
  is a multimodal minimization problem defined as follows:
  
  .. math::
  
      f_{\text{LennardJones}}(\mathbf{x}) = \sum_{i=0}^{n-2}\sum_{j>1}^{n-1}
      \frac{1}{r_{ij}^{12}} - \frac{1}{r_{ij}^{6}}
  
  
  Where, in this exercise:
  
  .. math::
  
      r_{ij} = \sqrt{(x_{3i}-x_{3j})^2 + (x_{3i+1}-x_{3j+1})^2)
      + (x_{3i+2}-x_{3j+2})^2}
  
  
  Valid for any dimension, :math:`n = 3*k, k=2 , 3, 4, ..., 20`. :math:`k`
  is the number of atoms in 3-D space constraints: unconstrained type:
  multi-modal with one global minimum; non-separable
  
  Value-to-reach: :math:`minima[k-2] + 0.0001`. See array of minima below;
  additional minima available at the Cambridge cluster database:
  
  http://www-wales.ch.cam.ac.uk/~jon/structures/LJ/tables.150.html
  
  Here, :math:`n` represents the number of dimensions and
  :math:`x_i \in [-4, 4]` for :math:`i = 1 ,..., n`.
  
  *Global optimum*:
  
  .. math::
  
      \text{minima} = [-1.,-3.,-6.,-9.103852,-12.712062,-16.505384,\\
                       -19.821489, -24.113360, -28.422532,-32.765970,\\
                       -37.967600,-44.326801, -47.845157,-52.322627,\\
                       -56.815742,-61.317995, -66.530949, -72.659782,\\
                       -77.1777043]\\
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code: def change_dimensions(self, ndim):
      if ndim not in range(6, 61):
          raise ValueError("LJ dimensions must be in (6, 60)")
  
      Benchmark.change_dimensions(self, ndim)
      self.fglob = self.minima[int(self.N / 3) - 2]
  
imports: from numpy import sum, cos, exp, pi, arange, sin
  from .go_benchmark import Benchmark
label_desc: Use image node_id 2 for calling the LennardJones obj's underlying member method code with example usage: obj.change_dimensions(ndim) without return types