R中的线性目标规划无法找到解
我有一个线性目标规划问题,我正试图用R中的线性目标规划无法找到解,r,loops,mathematical-optimization,linear-programming,R,Loops,Mathematical Optimization,Linear Programming,我有一个线性目标规划问题,我正试图用R解决这个问题: 我尝试使用R以以下矩阵格式进行公式化: 以下是可复制的示例: library("lpSolve") a <- matrix(c(1,2,5, 1/2,1,3, 1/5,1/3,1),nrow=3,byrow=T) f.obj <- c(rep(1,6),rep(0,3)) f.cons <- matrix(c(c(1,-1,0,0,0,0,1,-1,0,
R
解决这个问题:
我尝试使用R
以以下矩阵格式进行公式化:
以下是可复制的示例:
library("lpSolve")
a <- matrix(c(1,2,5,
1/2,1,3,
1/5,1/3,1),nrow=3,byrow=T)
f.obj <- c(rep(1,6),rep(0,3))
f.cons <- matrix(c(c(1,-1,0,0,0,0,1,-1,0,
0,0,1,-1,0,0,1,0,-1,
0,0,0,0,1,-1,0,1,-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)
),nrow=12,byrow=T)
f.dir <- c(rep("=",3),rep(">",9))
f.rhs <- c(c(log(a[1,2]),log(a[1,3]),log(a[2,3])),rep(0,9))
g <- lp ("min", f.obj, f.cons, f.dir, f.rhs)
g$solution
> g$solution
[1] 0.1823216 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 1.6094379 1.0986123 0.0000000
库(“lpSolve”)
a这里有一个使用lpSolveAPI
包的解决方案。对于n=3,它给出了相同的结果。代码也适用于较大的n(和矩阵A):
库(lpSolveAPI)
n是否有wi
的定义?
library(lpSolveAPI)
n <- 3
a <- matrix(c(1,2,5,1/2,1,3,1/5,1/3,1),nrow=n,byrow=T)
num_entries <- n*(n-1)/2
# set up lp
lprec <- make.lp(0, ncol=2*num_entries+n)
set.objfn(lprec, obj=c(rep(1,2*num_entries), rep(0,n)))
# add constraints
dim2idx <- function(xy, i, j, n=3) ifelse(xy=="x", 0, n*(n-1)/2) + n*(n-1)/2 - (n-i)*(n+1-i)/2 + (j-i)
for (i in seq(1,n-1))
for (j in seq(i+1,n))
add.constraint(lprec, xt=c(1,-1,1,-1), indices=c(dim2idx("x", i,j), dim2idx("y", i,j), 2*num_entries+c(i,j)), type="=", rhs=log(a[i,j]))
# solve
solve(lprec)
exp(get.variables(lprec)) # solved for log x, so exp here