RGLPK 约束问题

Question

我有一个优化问题，它提供了一些问题。

当我运行以下代码时，我得到了一个最佳解决方案。

objective <- DK$DK.proj

objective.variable.types <- rep("B", length(DK$player))
constraint.matrix <- rbind(as.numeric(DK$pos == "SP"),
                       as.numeric(DK$pos == "C"),
                       as.numeric(DK$pos == "1B"),
                       as.numeric(DK$pos == "2B"),
                       as.numeric(DK$pos == "SS"),
                       as.numeric(DK$pos == "3B"),
                       as.numeric(DK$pos == "OF"),
                       DK$salary)
constraint.directions <- c(
"==", # SP
"==", # C
"==", # 1B
"==", # 2B
"==", # SS
"==", # 3B
"==", # OF,
"<=") # max salary

rhs <- c(
2, # SP
1, # C
1, # 1B
1, # 2B
1, # SS
1, # 3B
3, # OF
50000) # max salary

Rglpk_solve_LP(obj = objective, mat = constraint.matrix, dir = constraint.directions, rhs = rhs,
                  types = objective.variable.types, max = TRUE)

但问题是数据框中的一些球员是重复的，因为他们有多个位置。同一个玩家有2行，只是位置列不同，但我每个玩家只能使用一次。所以我在里面添加了以下约束。

objective <- DK$DK.proj

objective.variable.types <- rep("B", length(DK$player))
constraint.matrix <- rbind(as.numeric(DK$pos == "SP"),
                         as.numeric(DK$pos == "C"),
                         as.numeric(DK$pos == "1B"),
                         as.numeric(DK$pos == "2B"),
                         as.numeric(DK$pos == "SS"),
                         as.numeric(DK$pos == "3B"),
                         as.numeric(DK$pos == "OF"),
                         DK$salary,
                         n_distinct(DK$player))
constraint.directions <- c(
"==", # SP
"==", # C
"==", # 1B
"==", # 2B
"==", # SS
"==", # 3B
"==", # OF,
"<=", # max salary
"==") # max players

rhs <- c(
2, # SP
1, # C
1, # 1B
1, # 2B
1, # SS
1, # 3B
3, # OF
50000, # max salary
10) # max players



Rglpk_solve_LP(obj = objective, mat = constraint.matrix, dir = constraint.directions, rhs = rhs,
             types = objective.variable.types, max = TRUE)

现在我无法找到可行的解决方案。关于我应该将约束更改为什么以便我可以始终拥有 10 个唯一的、非重复的玩家，同时遵循其他约束的任何建议？

Answer 1

问题是你的约束矩阵没有按照你的想法做。如果查看您编码的约束矩阵，您会看到底行包含的所有条目等于 DK 数据帧中唯一玩家的数量。当约束矩阵乘以解向量时，必须达到线性规划约束。解向量中的单个 1 和矩阵乘法后的结果条目将是唯一玩家总数。所以约束不能实现，也不收敛。

这是一个可行的技巧。它不漂亮，但它完成了工作。

objective <- DK$DK.proj
playerMatrix <- lapply(unique(DK$player), function(name) as.numeric(DK$player==name))
playerMatrix <- t(matrix(unlist(playerMatrix), ncol=n_distinct(DK$player)))

objective.variable.types <- rep("B", length(DK$player))
constraint.matrix <- rbind(as.numeric(DK$pos == "SP"),
                           as.numeric(DK$pos == "C"),
                           as.numeric(DK$pos == "1B"),
                           as.numeric(DK$pos == "2B"),
                           as.numeric(DK$pos == "SS"),
                           as.numeric(DK$pos == "3B"),
                           as.numeric(DK$pos == "OF"),
                           DK$salary,
                           playerMatrix)
constraint.directions <- c(
  "==", # SP
  "==", # C
  "==", # 1B
  "==", # 2B
  "==", # SS
  "==", # 3B
  "==", # OF,
  "<=", # max salary
  rep("<=", nrow(playerMatrix))) # unique players

rhs <- c(
  2, # SP
  1, # C
  1, # 1B
  1, # 2B
  1, # SS
  1, # 3B
  3, # OF
  50000, # max salary
  rep(1, nrow(playerMatrix))) # unique players

  sol <- Rglpk_solve_LP(obj = objective, mat = constraint.matrix, 
           dir = constraint.directions, rhs = rhs,
           types = objective.variable.types, max = TRUE)

玩家矩阵具有与唯一玩家相同的行数，并跟踪确保不会多次选择唯一玩家。