Graph coloring with CVXPY set up constraints - python-3.x

Question

I am trying to code the constraints for the graph coloring problem using CVXPY. I am pretty new to mixed-integer programming (MIP), and I am having some difficulty specifying the constraints. I have input data like the “edges” list below. Where each tuple in the list is an edge that starts on one node and ends on the other. For example the first edge starts on node “0” and ends on node “1”.
The constraints I would like to specify are:
each node can have only one color.
vertices sharing one edge should have different colors.
each node must have at least one color.
The objective function would be the number of colors used.
For a selection variable I want to specify the color each node takes.
I’m using the colors array to multiply with the selection variable and then sum for each node, to select the color for the node and specify that each node can only have one color.
I’m getting the error below. Am I constructing the selection variable correctly?
Also this seems like a lot of work, does anyone see a simpler way to do this? Or does anyone know of an example of solving the graph coloring problem with CVXPY?
One more thing, if I transpose the colors array the error goes away.
Input data:
edges
[(0, 1), (1, 2), (1, 3)]
code:
# selection variable
# 4 is the number of nodes
selection = cvxpy.Variable(4, boolean=True)
# array for colors
colors = np.array([[1,0,0,0],
[0,1,0,0],
[0,0,1,0],
[0,0,0,1],
[1,1,0,0],
[1,1,1,0],
[1,1,1,1],
[0,1,1,1],
[0,0,1,1],
[1,0,1,0],
[0,1,0,1],
[0,1,1,0],
[1,1,0,0],
[0,0,0,0]])
# each node can only have one color constraint
one_color = cvxpy.sum(selection * colors, axis=0) == 1
error:
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
<ipython-input-18-b22226c89a2f> in <module>()
1 # each node can only have one color constraint
2
----> 3 one_color = cvxpy.sum(selection * colors, axis=0) == 1
~/anaconda2/envs/py36/lib/python3.6/site-packages/cvxpy/expressions/expression.py in cast_op(self, other)
47 """
48 other = self.cast_to_const(other)
---> 49 return binary_op(self, other)
50 return cast_op
51
~/anaconda2/envs/py36/lib/python3.6/site-packages/cvxpy/expressions/expression.py in __mul__(self, other)
385 return cvxtypes.multiply_expr()(self, other)
386 elif self.is_constant() or other.is_constant():
--> 387 return cvxtypes.mul_expr()(self, other)
388 else:
389 warnings.warn("Forming a nonconvex expression.")
~/anaconda2/envs/py36/lib/python3.6/site-packages/cvxpy/atoms/affine/binary_operators.py in __init__(self, lh_exp, rh_exp)
41
42 def __init__(self, lh_exp, rh_exp):
---> 43 super(BinaryOperator, self).__init__(lh_exp, rh_exp)
44
45 def name(self):
~/anaconda2/envs/py36/lib/python3.6/site-packages/cvxpy/atoms/atom.py in __init__(self, *args)
42 self.args = [Atom.cast_to_const(arg) for arg in args]
43 self.validate_arguments()
---> 44 self._shape = self.shape_from_args()
45 if len(self._shape) > 2:
46 raise ValueError("Atoms must be at most 2D.")
~/anaconda2/envs/py36/lib/python3.6/site-packages/cvxpy/atoms/affine/binary_operators.py in shape_from_args(self)
107 """Returns the (row, col) shape of the expression.
108 """
--> 109 return u.shape.mul_shapes(self.args[0].shape, self.args[1].shape)
110
111 def is_atom_convex(self):
~/anaconda2/envs/py36/lib/python3.6/site-packages/cvxpy/utilities/shape.py in mul_shapes(lh_shape, rh_shape)
140 lh_old = lh_shape
141 rh_old = rh_shape
--> 142 lh_shape, rh_shape, shape = mul_shapes_promote(lh_shape, rh_shape)
143 if lh_shape != lh_old:
144 shape = shape[1:]
~/anaconda2/envs/py36/lib/python3.6/site-packages/cvxpy/utilities/shape.py in mul_shapes_promote(lh_shape, rh_shape)
107 if lh_mat_shape[1] != rh_mat_shape[0]:
108 raise ValueError("Incompatible dimensions %s %s" % (
--> 109 lh_shape, rh_shape))
110 if lh_shape[:-2] != rh_shape[:-2]:
111 raise ValueError("Incompatible dimensions %s %s" % (
ValueError: Incompatible dimensions (1, 4) (14, 4)