[Haskell-cafe] Linear programming in Haskell
Henning Thielemann
schlepptop at henning-thielemann.de
Sun Feb 28 18:24:26 EST 2010
Louis Wasserman schrieb:
> Yo,
>
> Man, I'd never used FFI before, but it's really not as scary as I'd
> feared.
>
> I've implemented a more comprehensive interface to GLPK's simplex
> solver and -- rather importantly, for my own needs -- its MIP solver.
> This doesn't depend on hmatrix, and in fact, it doesn't require any
> matrix or vector manipulation at all -- linear functions are specified
> as a straight-up Data.Map from an arbitrary variable type to their
> coefficients.
>
> The library is now available as glpk-hs on hackage.
>
> Example:
>
> import Data.LinearProgram.LPMonad
> import Data.LinearProgram
> import Data.LinearProgram.GLPK
>
> objFun :: LinFunc String Int
> objFun = linCombination [(10, "x1"), (6, "x2"), (4, "x3")]
>
> lp :: LP String Int
> lp = execLPM $ do setDirection Max
> setObjective objFun
> leqTo (varSum ["x1", "x2", "x3"]) 100
> leqTo (10 *^ var "x1" ^+^ 4 *& "x2" ^+^ 5 *^ var "x3") 600
> -- c *^ var v, c *& v, and linCombination [(c, v)] are all equivalent.
> -- ^+^ is the addition operation on linear functions.
> leqTo (linCombination [(2, "x1"), (2, "x2"), (6, "x3")]) 300
> varGeq "x1" 0
> varBds "x2" 0 50
> varGeq "x3" 0
> setVarKind "x1" IntVar
> setVarKind "x2" ContVar
Using strings for variable names you cannot check for undefined
variables. How about adding a function for generating new variables to
your LP monad?
The example may then look like
do
setDirection Max
setObjective objFun
x1 <- newVariable
x2 <- newVariable
x3 <- newVariable
leqTo (varSum [x1,x2,x3]) 100
...
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