Question

我正在尝试使用CVXPY对图形着色问题的约束进行编码。我对混合整数编程（MIP）还是很陌生，并且在指定约束时遇到了一些困难。我有输入数据，例如下面的“边”列表。列表中的每个元组都是从一个节点开始到另一节点结束的边。例如，第一条边开始于节点“ 0”，结束于节点“ 1”。

我要指定的约束是：

每个节点只能有一种颜色。
共享一条边的顶点应具有不同的颜色。
每个节点必须至少具有一种颜色。

目标函数是所用颜色的数量。

对于选择变量，我想指定每个节点采用的颜色。

我正在使用colors数组乘以选择变量，然后对每个节点求和，以选择节点的颜色并指定每个节点只能具有一种颜色。

我在下面收到错误消息。我可以正确构造选择变量吗？

这似乎是很多工作，有人看到一种更简单的方法吗？还是没有人知道使用CVXPY解决图形着色问题的示例吗？

还有一件事，如果我转置颜色数组，错误就会消失。

输入数据：

边缘

[(0, 1), (1, 2), (1, 3)]

代码：

# 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

错误：

---------------------------------------------------------------------------
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)

使用CVXPY设置约束进行图形着色

0 个答案: