R中的加权顶点覆盖（作为线性编程）与ROI包

Question

我正在尝试使用R作为家庭作业来解决加权顶点覆盖问题的一个实例，我似乎无法将其弄好。我正在使用ROI包（也可以使用linprog）。

实例看起来像这样：

Edges:
A-B,    A-C,    A-G,
B-C,    B-D,    B-E,    B-G,
C-E,    C-F,
D-F,
E-G,
F-H,    F-I,
G-H

Weights:
A - 10,
B - 7,
C - 4,
D - 7,
E - 12,
F - 25,
G - 27,
H - 3,
I - 9

我的代码是：

    #                                    a  b  c  d  e  f  g  h  i
    constraints <- L_constraint(matrix(c(1, 1, 0, 0, 0, 0, 0, 0, 0, # a b
                                         1, 0, 1, 0, 0, 0, 0, 0, 0, # a c
                                         1, 0, 0, 0, 0, 0, 1, 0, 0, # a g
                                         0, 1, 1, 0, 0, 0, 0, 0, 0, # b c
                                         0, 1, 0, 1, 0, 0, 0, 0, 0, # b d
                                         0, 1, 0, 0, 1, 0, 0, 0, 0, # b e
                                         0, 1, 0, 0, 0, 0, 1, 0, 0, # b g
                                         0, 0, 1, 0, 1, 0, 0, 0, 0, # c e
                                         0, 0, 1, 0, 0, 1, 0, 0, 0, # c f
                                         0, 0, 0, 1, 0, 1, 0, 0, 0, # d f
                                         0, 0, 0, 0, 1, 0, 1, 0, 0, # e g
                                         0, 0, 0, 0, 0, 1, 0, 1, 0, # f h
                                         0, 0, 0, 0, 0, 1, 0, 0, 1, # f i
                                         0, 0, 0, 0, 0, 0, 1, 1, 0, # g h
                                         # end of u + v >= 1
                                         1, 0, 0, 0, 0, 0, 0, 0, 0,
                                         0, 1, 0, 0, 0, 0, 0, 0, 0,
                                         0, 0, 1, 0, 0, 0, 0, 0, 0,
                                         0, 0, 0, 1, 0, 0, 0, 0, 0,
                                         0, 0, 0, 0, 1, 0, 0, 0, 0,
                                         0, 0, 0, 0, 0, 1, 0, 0, 0,
                                         0, 0, 0, 0, 0, 0, 1, 0, 0,
                                         0, 0, 0, 0, 0, 0, 0, 1, 0,
                                         0, 0, 0, 0, 0, 0, 0, 0, 1,
                                         # end of u >= 0
                                         1, 0, 0, 0, 0, 0, 0, 0, 0,
                                         0, 1, 0, 0, 0, 0, 0, 0, 0,
                                         0, 0, 1, 0, 0, 0, 0, 0, 0,
                                         0, 0, 0, 1, 0, 0, 0, 0, 0,
                                         0, 0, 0, 0, 1, 0, 0, 0, 0,
                                         0, 0, 0, 0, 0, 1, 0, 0, 0,
                                         0, 0, 0, 0, 0, 0, 1, 0, 0,
                                         0, 0, 0, 0, 0, 0, 0, 1, 0,
                                         0, 0, 0, 0, 0, 0, 0, 0, 1),
                                         # end of u <= 1
                                       ncol = 9), # matrix
                                dir = c(rep(">=", 14+9), rep("<=", 9)),
                                rhs = c(rep(1, 14), rep(0, 9), rep(1, 9))) # L_constraint

    objective <- L_objective(c(10, 7, 4, 7, 12, 25, 27, 3, 9))

    problem <- OP(objective, constraints, rep("C", 9),
                  maximum = FALSE)

    solution <- ROI_solve(problem, solver = "glpk")

结果是No solution found.我不知道我做错了什么，但它也可能是明显的东西。无法理解它 - 解决方案应始终存在，即使它需要所有顶点（即所有变量都> = 0.5）。

如果重要的话，我在Arch Linux上运行R从存储库（版本2.14）并通过install.packages("...")安装包。

谢谢！

Answer 1

好的，解决了。问题是我没有将byrows = TRUE添加到矩阵定义中。此外，我将ncol = 9改为nrow = ...。显然matrix()功能没有像我预期的那样工作。