[Haskell-cafe] Linear programming in Haskell

[Henning Thielemann]

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
   ...