Stability | provisional |
---|---|
Maintainer | Alberto Ruiz (aruiz at um dot es) |
This module provides an interface to the standard simplex algorithm.
For example, the following LP problem
maximize 4 x_1 - 3 x_2 + 2 x_3 subject to 2 x_1 + x_2 <= 10 x_3 + 5 x_4 <= 20 and x_i >= 0
can be solved as follows:
import Numeric.LinearProgramming prob = Maximize [4, -3, 2] constr1 = Sparse [ [2#1, 1#2] :<=: 10 , [1#2, 5#3] :<=: 20 ] > simplex prob constr1 [] Optimal (28.0,[5.0,0.0,4.0])
The coefficients of the constraint matrix can also be given in dense format:
constr2 = Dense [ [2,1,0] :<=: 10 , [0,1,5] :<=: 20 ]
By default all variables are bounded as x_i >= 0
, but this can be
changed:
> simplex prob constr2 [ 2 :=>: 1, 3 :&: (2,7)] Optimal (22.6,[4.5,1.0,3.8]) > simplex prob constr2 [Free 2] Unbounded
The given bound for a variable completely replaces the default,
so 0 <= x_i <= b
must be explicitly given as i :&: (0,b)
.
Multiple bounds for a variable are not allowed, instead of
[i :=>: a, i:<=: b]
use i :&: (a,b)
.
- simplex :: Optimization -> Constraints -> Bounds -> Solution
- data Optimization
- data Constraints
- type Bounds = [Bound Int]
- data Bound x
- (#) :: Double -> Int -> (Double, Int)
- data Solution