Optimization 如何解决CVXPY中的设施位置分配（IP）问题

我正在学习使用CVXPY解决优化问题，因此我从以下简单的设施位置分配问题开始

CVXPY中的代码如下所示：

Fi  =   np.array([1,1,1]) # Fixed cost of each facility
Ci  =   np.array([15, 10, 10]) # Capacity of each facility
Dj  =   np.array([5, 5, 5, 3, 3, 4]) # Demand of each facility
Cij =   np.ones(m,n)


n   = len(Dj)
m   = len(Fi)


# Decision Variables
Xij = cvx.Bool(m,n)   # (m,n) vector
Yi = cvx.Bool(m)     # column vector of length (m,1)

# Objective
fixed_cost   = cvx.sum_entries(Fi*Yi)
var_cost     = cvx.sum_entries(Cij.T * Dj *Xij)
total_cost   = fixed_cost + var_cost
objective    = cvx.Minimize(total_cost)

# Maximum facility locations to be selected?
constraints.append(cvx.sum_entries(Yi)==2)

# Sum of demands allocated to a facility shall be <= facility capacity - 
# Capacity Fixed Cost
constraints.append(cvx.sum_entries(Dj * Xij.T, axis=0) <= Ci*Yi)

# Every demand point shall be supplied by only one facility.
constraints.append(cvx.sum_entries(Xij, axis=1) == 1) 


# Solve the problem
prob = cvx.Problem(objective, constraints)
prob.solve(solver=cvx.GLPK_MI)

# Print the values
#print("status:", prob.status)
print("optimal value", prob.value)
print("Selected Facility Locations", Yi.value)
print("Assigned Nodes", Xij.value, )

Xij.value应该是这样的：

Using CVXPY version: 0.4.10
status: optimal
optimal value 91.0
Selected Facility Locations [[1.]
 [1.]
 [0.]]
Assigned Nodes to Facility 1) [[1. 1. 1. 0. 0. 0.]]
Assigned Nodes to Facility 2) [[0. 0. 0. 1. 1. 1.]]
Assigned Nodes to Facility 3) [[0. 0. 0. 0. 0. 0.]]

也就是说，选择了设施1和设施2。

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前三个点分配给设施1，后三个点分配给设施2。

X==1告诉它所有的值都是1否，即使我删除了约束，X.value仍然是一个矩阵。您的代码不起作用，例如m，n是在第一次使用后定义的。如果您可以提供与cvxpy 1.0兼容的可复制代码，那么我很乐意提供帮助。@MichalAdamaszek&OP:Hi，我将代码更新为cvxpy 1.0并使其可运行

Using CVXPY version: 0.4.10
status: optimal
optimal value 91.0
Selected Facility Locations [[1.]
 [1.]
 [0.]]
Assigned Nodes to Facility 1) [[1. 1. 1. 0. 0. 0.]]
Assigned Nodes to Facility 2) [[0. 0. 0. 1. 1. 1.]]
Assigned Nodes to Facility 3) [[0. 0. 0. 0. 0. 0.]]