Data.LinearProgram.LPMonad

A collection of operations that can be used to specify linear programming in a simple, monadic way. It is not too difficult to construct LP values explicitly, but this module may help simplify and modularize the construction of the linear program, for example separating different families of constraints in the problem specification.

Many of these functions should be executed in either the LPM v c or the LPT v c IO monad.

Monad definitions

type LPM v c = LPT v c Identity

A simple monad for constructing linear programs. This library is intended to be able to link to a variety of different linear programming implementations.

type LPT v c = StateT (LP v c)

A simple monad transformer for constructing linear programs in an arbitrary monad.

runLPM :: (Ord v, Module r c) => LPM v c a -> (a, LP v c)

runLPT :: (Ord v, Module r c) => LPT v c m a -> m (a, LP v c)

execLPM :: (Ord v, Module r c) => LPM v c a -> LP v c

Constructs a linear programming problem.

execLPT :: (Ord v, Module r c, Monad m) => LPT v c m a -> m (LP v c)

Constructs a linear programming problem in the specified monad.

evalLPM :: (Ord v, Module r c) => LPM v c a -> a

Runs the specified operation in the linear programming monad.

evalLPT :: (Monad m, Ord v, Module r c) => LPT v c m a -> m a

Runs the specified operation in the linear programming monad transformer.

Objective configuration

setDirection :: MonadState (LP v c) m => Direction -> m ()

Sets the optimization direction of the linear program: maximization or minimization.

setObjective :: MonadState (LP v c) m => LinFunc v c -> m ()

Sets the objective function, overwriting the previous objective function.

addObjective :: (Ord v, Module r c, MonadState (LP v c) m) => LinFunc v c -> m ()

Adds this function to the objective function.

addWeightedObjective :: (Ord v, Module r c, MonadState (LP v c) m) => r -> LinFunc v c -> m ()

Adds this function to the objective function, with the specified weight. Equivalent to addObjective (wt *^ obj).

Two-function constraints

leq :: (Ord v, Module r c, MonadState (LP v c) m) => LinFunc v c -> LinFunc v c -> m ()

Specifies the relationship between two functions in the variables.

equal :: (Ord v, Module r c, MonadState (LP v c) m) => LinFunc v c -> LinFunc v c -> m ()

geq :: (Ord v, Module r c, MonadState (LP v c) m) => LinFunc v c -> LinFunc v c -> m ()

leq' :: (Ord v, Module r c, MonadState (LP v c) m) => String -> LinFunc v c -> LinFunc v c -> m ()

Specifies the relationship between two functions in the variables, with a label on the constraint.

equal' :: (Ord v, Module r c, MonadState (LP v c) m) => String -> LinFunc v c -> LinFunc v c -> m ()

geq' :: (Ord v, Module r c, MonadState (LP v c) m) => String -> LinFunc v c -> LinFunc v c -> m ()

One-function constraints

leqTo :: MonadState (LP v c) m => LinFunc v c -> c -> m ()

Sets a constraint on a linear function in the variables.

equalTo :: MonadState (LP v c) m => LinFunc v c -> c -> m ()

geqTo :: MonadState (LP v c) m => LinFunc v c -> c -> m ()

constrain :: MonadState (LP v c) m => LinFunc v c -> Bounds c -> m ()

The most general form of an unlabeled constraint.

leqTo' :: MonadState (LP v c) m => String -> LinFunc v c -> c -> m ()

Sets a labelled constraint on a linear function in the variables.

equalTo' :: MonadState (LP v c) m => String -> LinFunc v c -> c -> m ()

geqTo' :: MonadState (LP v c) m => String -> LinFunc v c -> c -> m ()

constrain' :: MonadState (LP v c) m => String -> LinFunc v c -> Bounds c -> m ()

The most general form of a labeled constraint.

Variable constraints

varLeq :: (Ord v, Ord c, MonadState (LP v c) m) => v -> c -> m ()

Sets a constraint on the value of a variable. If you constrain a variable more than once, the constraints will be combined.

varEq :: (Ord v, Ord c, MonadState (LP v c) m) => v -> c -> m ()

varGeq :: (Ord v, Ord c, MonadState (LP v c) m) => v -> c -> m ()

varBds :: (Ord v, Ord c, MonadState (LP v c) m) => v -> c -> c -> m ()

Bounds the value of a variable on both sides. If you constrain a variable more than once, the constraints will be combined.

setVarBounds :: (Ord v, Ord c, MonadState (LP v c) m) => v -> Bounds c -> m ()

The most general way to set constraints on a variable. If you constrain a variable more than once, the constraints will be combined.

setVarKind :: (Ord v, MonadState (LP v c) m) => v -> VarKind -> m ()

Sets the kind ('type') of a variable. See VarKind.

Solvers

quickSolveMIP :: (Ord v, Real c, MonadState (LP v c) m, MonadIO m) => m (ReturnCode, Maybe (Double, Map v Double))

Solves the linear program with the default settings in GLPK. Returns the return code, and if the solver was successful, the objective function value and the settings of each variable.

quickSolveLP :: (Ord v, Real c, MonadState (LP v c) m, MonadIO m) => m (ReturnCode, Maybe (Double, Map v Double))

glpSolve :: (Ord v, Real c, MonadState (LP v c) m, MonadIO m) => GLPOpts -> m (ReturnCode, Maybe (Double, Map v Double))

Solves the linear program with the specified options in GLPK. Returns the return code, and if the solver was successful, the objective function value and the settings of each variable.

quickSolveMIP' :: (Ord v, Real c, MonadState (LP v c) m, MonadIO m) => m (ReturnCode, Maybe (Double, Map v Double, [RowValue v c]))

Solves the linear program with the default settings in GLPK. Returns the return code, and if the solver was successful, the objective function value, the settings of each variable, and the value of each constraint/row.

quickSolveLP' :: (Ord v, Real c, MonadState (LP v c) m, MonadIO m) => m (ReturnCode, Maybe (Double, Map v Double, [RowValue v c]))

glpSolve' :: (Ord v, Real c, MonadState (LP v c) m, MonadIO m) => GLPOpts -> m (ReturnCode, Maybe (Double, Map v Double, [RowValue v c]))

Solves the linear program with the specified options in GLPK. Returns the return code, and if the solver was successful, the objective function value, the settings of each variable, and the value of each constraint/row.

File I/O

writeLPToFile :: (Ord v, Show v, Real c, MonadState (LP v c) m, MonadIO m) => FilePath -> m ()

readLPFromFile :: (MonadState (LP String Double) m, MonadIO m) => FilePath -> m ()