ToySolver.Data.MIP.Base

Mixed-Integer Programming Problems with some commmonly used extensions

Documentation

data Problem

Problem

Constructors

Problem

Fields

• name :: Maybe String
• objectiveFunction :: ObjectiveFunction
• constraints :: [Constraint]
• sosConstraints :: [SOSConstraint]
• userCuts :: [Constraint]
• varType :: Map Var VarType
• varBounds :: Map Var Bounds

Instances

Eq Problem

Methods

(==) :: Problem -> Problem -> Bool

(/=) :: Problem -> Problem -> Bool

Ord Problem

Methods

compare :: Problem -> Problem -> Ordering

(<) :: Problem -> Problem -> Bool

(<=) :: Problem -> Problem -> Bool

(>) :: Problem -> Problem -> Bool

(>=) :: Problem -> Problem -> Bool

max :: Problem -> Problem -> Problem

min :: Problem -> Problem -> Problem

Show Problem

Methods

showsPrec :: Int -> Problem -> ShowS

show :: Problem -> String

showList :: [Problem] -> ShowS

Default Problem

Methods

def :: Problem

Variables Problem

Methods

vars :: Problem -> Set Var

newtype Expr

expressions

Constructors

Expr [Term]

Instances

Eq Expr

Methods

(==) :: Expr -> Expr -> Bool

(/=) :: Expr -> Expr -> Bool

Num Expr

Methods

(+) :: Expr -> Expr -> Expr

(-) :: Expr -> Expr -> Expr

(*) :: Expr -> Expr -> Expr

negate :: Expr -> Expr

abs :: Expr -> Expr

signum :: Expr -> Expr

fromInteger :: Integer -> Expr

Ord Expr

Methods

compare :: Expr -> Expr -> Ordering

(<) :: Expr -> Expr -> Bool

(<=) :: Expr -> Expr -> Bool

(>) :: Expr -> Expr -> Bool

(>=) :: Expr -> Expr -> Bool

max :: Expr -> Expr -> Expr

min :: Expr -> Expr -> Expr

Show Expr

Methods

showsPrec :: Int -> Expr -> ShowS

show :: Expr -> String

showList :: [Expr] -> ShowS

Variables Expr

Methods

vars :: Expr -> Set Var

varExpr :: Var -> Expr

constExpr :: Rational -> Expr

terms :: Expr -> [Term]

data Term

terms

Constructors

Term Rational [Var]

Instances

Eq Term

Methods

(==) :: Term -> Term -> Bool

(/=) :: Term -> Term -> Bool

Ord Term

Methods

compare :: Term -> Term -> Ordering

(<) :: Term -> Term -> Bool

(<=) :: Term -> Term -> Bool

(>) :: Term -> Term -> Bool

(>=) :: Term -> Term -> Bool

max :: Term -> Term -> Term

min :: Term -> Term -> Term

Show Term

Methods

showsPrec :: Int -> Term -> ShowS

show :: Term -> String

showList :: [Term] -> ShowS

Variables Term

Methods

vars :: Term -> Set Var

data OptDir :: *

The OptDir type represents optimization directions.

Constructors

OptMin

minimization

OptMax

maximization

Instances

Bounded OptDir

Methods

minBound :: OptDir

maxBound :: OptDir

Enum OptDir

Methods

succ :: OptDir -> OptDir

pred :: OptDir -> OptDir

toEnum :: Int -> OptDir

fromEnum :: OptDir -> Int

enumFrom :: OptDir -> [OptDir]

enumFromThen :: OptDir -> OptDir -> [OptDir]

enumFromTo :: OptDir -> OptDir -> [OptDir]

enumFromThenTo :: OptDir -> OptDir -> OptDir -> [OptDir]

Eq OptDir

Methods

(==) :: OptDir -> OptDir -> Bool

(/=) :: OptDir -> OptDir -> Bool

Data OptDir

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> OptDir -> c OptDir

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c OptDir

toConstr :: OptDir -> Constr

dataTypeOf :: OptDir -> DataType

dataCast1 :: Typeable (* -> *) t => (forall d. Data d => c (t d)) -> Maybe (c OptDir)

dataCast2 :: Typeable (* -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c OptDir)

gmapT :: (forall b. Data b => b -> b) -> OptDir -> OptDir

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> OptDir -> r

gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> OptDir -> r

gmapQ :: (forall d. Data d => d -> u) -> OptDir -> [u]

gmapQi :: Int -> (forall d. Data d => d -> u) -> OptDir -> u

gmapM :: Monad m => (forall d. Data d => d -> m d) -> OptDir -> m OptDir

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> OptDir -> m OptDir

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> OptDir -> m OptDir

Ord OptDir

Methods

compare :: OptDir -> OptDir -> Ordering

(<) :: OptDir -> OptDir -> Bool

(<=) :: OptDir -> OptDir -> Bool

(>) :: OptDir -> OptDir -> Bool

(>=) :: OptDir -> OptDir -> Bool

max :: OptDir -> OptDir -> OptDir

min :: OptDir -> OptDir -> OptDir

Read OptDir

Methods

readsPrec :: Int -> ReadS OptDir

readList :: ReadS [OptDir]

readPrec :: ReadPrec OptDir

readListPrec :: ReadPrec [OptDir]

Show OptDir

Methods

showsPrec :: Int -> OptDir -> ShowS

show :: OptDir -> String

showList :: [OptDir] -> ShowS

Ix OptDir

Methods

range :: (OptDir, OptDir) -> [OptDir]

index :: (OptDir, OptDir) -> OptDir -> Int

unsafeIndex :: (OptDir, OptDir) -> OptDir -> Int

inRange :: (OptDir, OptDir) -> OptDir -> Bool

rangeSize :: (OptDir, OptDir) -> Int

unsafeRangeSize :: (OptDir, OptDir) -> Int

Hashable OptDir

Methods

hashWithSalt :: Int -> OptDir -> Int

hash :: OptDir -> Int

data ObjectiveFunction

objective function

Constructors

ObjectiveFunction

Fields

• objLabel :: Maybe Label
• objDir :: OptDir
• objExpr :: Expr

Instances

Eq ObjectiveFunction

Methods

(==) :: ObjectiveFunction -> ObjectiveFunction -> Bool

(/=) :: ObjectiveFunction -> ObjectiveFunction -> Bool

Ord ObjectiveFunction

Methods

compare :: ObjectiveFunction -> ObjectiveFunction -> Ordering

(<) :: ObjectiveFunction -> ObjectiveFunction -> Bool

(<=) :: ObjectiveFunction -> ObjectiveFunction -> Bool

(>) :: ObjectiveFunction -> ObjectiveFunction -> Bool

(>=) :: ObjectiveFunction -> ObjectiveFunction -> Bool

max :: ObjectiveFunction -> ObjectiveFunction -> ObjectiveFunction

min :: ObjectiveFunction -> ObjectiveFunction -> ObjectiveFunction

Show ObjectiveFunction

Methods

showsPrec :: Int -> ObjectiveFunction -> ShowS

show :: ObjectiveFunction -> String

showList :: [ObjectiveFunction] -> ShowS

Default ObjectiveFunction

Methods

def :: ObjectiveFunction

Variables ObjectiveFunction

Methods

vars :: ObjectiveFunction -> Set Var

data Constraint

constraint

Constructors

Constraint

Fields

• constrLabel :: Maybe Label
• constrIndicator :: Maybe (Var, Rational)
• constrExpr :: Expr
• constrLB :: BoundExpr
• constrUB :: BoundExpr
• constrIsLazy :: Bool

Instances

Eq Constraint

Methods

(==) :: Constraint -> Constraint -> Bool

(/=) :: Constraint -> Constraint -> Bool

Ord Constraint

Methods

compare :: Constraint -> Constraint -> Ordering

(<) :: Constraint -> Constraint -> Bool

(<=) :: Constraint -> Constraint -> Bool

(>) :: Constraint -> Constraint -> Bool

(>=) :: Constraint -> Constraint -> Bool

max :: Constraint -> Constraint -> Constraint

min :: Constraint -> Constraint -> Constraint

Show Constraint

Methods

showsPrec :: Int -> Constraint -> ShowS

show :: Constraint -> String

showList :: [Constraint] -> ShowS

Default Constraint

Methods

def :: Constraint

Variables Constraint

Methods

vars :: Constraint -> Set Var

(.==.) :: Expr -> Expr -> Constraint infix 4

(.<=.) :: Expr -> Expr -> Constraint infix 4

(.>=.) :: Expr -> Expr -> Constraint infix 4

type Bounds = (BoundExpr, BoundExpr)

type for representing lower/upper bound of variables

type Label = String

label

type Var = InternedString

variable

data VarType

Constructors

ContinuousVariable

IntegerVariable

SemiContinuousVariable

SemiIntegerVariable

Instances

Eq VarType

Methods

(==) :: VarType -> VarType -> Bool

(/=) :: VarType -> VarType -> Bool

Ord VarType

Methods

compare :: VarType -> VarType -> Ordering

(<) :: VarType -> VarType -> Bool

(<=) :: VarType -> VarType -> Bool

(>) :: VarType -> VarType -> Bool

(>=) :: VarType -> VarType -> Bool

max :: VarType -> VarType -> VarType

min :: VarType -> VarType -> VarType

Show VarType

Methods

showsPrec :: Int -> VarType -> ShowS

show :: VarType -> String

showList :: [VarType] -> ShowS

Default VarType

Methods

def :: VarType

type BoundExpr = Extended Rational

type for representing lower/upper bound of variables

data Extended r :: * -> *

Extended r is an extension of r with positive/negative infinity (±∞).

Constructors

NegInf

negative infinity (-∞)

Finite ~r

finite value

PosInf

positive infinity (+∞)

Instances

Functor Extended

Methods

fmap :: (a -> b) -> Extended a -> Extended b

(<$) :: a -> Extended b -> Extended a

Bounded (Extended r)

Methods

minBound :: Extended r

maxBound :: Extended r

Eq r => Eq (Extended r)

Methods

(==) :: Extended r -> Extended r -> Bool

(/=) :: Extended r -> Extended r -> Bool

(Fractional r, Ord r) => Fractional (Extended r)

Note that Extended r is not a field, nor a ring.

Methods

(/) :: Extended r -> Extended r -> Extended r

recip :: Extended r -> Extended r

fromRational :: Rational -> Extended r

Data r => Data (Extended r)

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Extended r -> c (Extended r)

gunfold :: (forall b a. Data b => c (b -> a) -> c a) -> (forall a. a -> c a) -> Constr -> c (Extended r)

toConstr :: Extended r -> Constr

dataTypeOf :: Extended r -> DataType

dataCast1 :: Typeable (* -> *) t => (forall d. Data d => c (t d)) -> Maybe (c (Extended r))

dataCast2 :: Typeable (* -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Extended r))

gmapT :: (forall b. Data b => b -> b) -> Extended r -> Extended r

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Extended r -> r

gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Extended r -> r

gmapQ :: (forall d. Data d => d -> u) -> Extended r -> [u]

gmapQi :: Int -> (forall d. Data d => d -> u) -> Extended r -> u

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Extended r -> m (Extended r)

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Extended r -> m (Extended r)

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Extended r -> m (Extended r)

(Num r, Ord r) => Num (Extended r)

Note that Extended r is not a field, nor a ring.

PosInf + NegInf is left undefined as usual, but we define 0 * PosInf = 0 * NegInf = 0 by following the convention of probability or measure theory.

Methods

(+) :: Extended r -> Extended r -> Extended r

(-) :: Extended r -> Extended r -> Extended r

(*) :: Extended r -> Extended r -> Extended r

negate :: Extended r -> Extended r

abs :: Extended r -> Extended r

signum :: Extended r -> Extended r

fromInteger :: Integer -> Extended r

Ord r => Ord (Extended r)

Methods

compare :: Extended r -> Extended r -> Ordering

(<) :: Extended r -> Extended r -> Bool

(<=) :: Extended r -> Extended r -> Bool

(>) :: Extended r -> Extended r -> Bool

(>=) :: Extended r -> Extended r -> Bool

max :: Extended r -> Extended r -> Extended r

min :: Extended r -> Extended r -> Extended r

Read r => Read (Extended r)

Methods

readsPrec :: Int -> ReadS (Extended r)

readList :: ReadS [Extended r]

readPrec :: ReadPrec (Extended r)

readListPrec :: ReadPrec [Extended r]

Show r => Show (Extended r)

Methods

showsPrec :: Int -> Extended r -> ShowS

show :: Extended r -> String

showList :: [Extended r] -> ShowS

NFData r => NFData (Extended r)

Methods

rnf :: Extended r -> ()

Hashable r => Hashable (Extended r)

Methods

hashWithSalt :: Int -> Extended r -> Int

hash :: Extended r -> Int

data RelOp

relational operators

Constructors

Le

Ge

Eql

Instances

Enum RelOp

Methods

succ :: RelOp -> RelOp

pred :: RelOp -> RelOp

toEnum :: Int -> RelOp

fromEnum :: RelOp -> Int

enumFrom :: RelOp -> [RelOp]

enumFromThen :: RelOp -> RelOp -> [RelOp]

enumFromTo :: RelOp -> RelOp -> [RelOp]

enumFromThenTo :: RelOp -> RelOp -> RelOp -> [RelOp]

Eq RelOp

Methods

(==) :: RelOp -> RelOp -> Bool

(/=) :: RelOp -> RelOp -> Bool

Ord RelOp

Methods

compare :: RelOp -> RelOp -> Ordering

(<) :: RelOp -> RelOp -> Bool

(<=) :: RelOp -> RelOp -> Bool

(>) :: RelOp -> RelOp -> Bool

(>=) :: RelOp -> RelOp -> Bool

max :: RelOp -> RelOp -> RelOp

min :: RelOp -> RelOp -> RelOp

Show RelOp

Methods

showsPrec :: Int -> RelOp -> ShowS

show :: RelOp -> String

showList :: [RelOp] -> ShowS

data SOSType

types of SOS (special ordered sets) constraints

Constructors

S1

Type 1 SOS constraint

S2

Type 2 SOS constraint

Instances

Enum SOSType

Methods

succ :: SOSType -> SOSType

pred :: SOSType -> SOSType

toEnum :: Int -> SOSType

fromEnum :: SOSType -> Int

enumFrom :: SOSType -> [SOSType]

enumFromThen :: SOSType -> SOSType -> [SOSType]

enumFromTo :: SOSType -> SOSType -> [SOSType]

enumFromThenTo :: SOSType -> SOSType -> SOSType -> [SOSType]

Eq SOSType

Methods

(==) :: SOSType -> SOSType -> Bool

(/=) :: SOSType -> SOSType -> Bool

Ord SOSType

Methods

compare :: SOSType -> SOSType -> Ordering

(<) :: SOSType -> SOSType -> Bool

(<=) :: SOSType -> SOSType -> Bool

(>) :: SOSType -> SOSType -> Bool

(>=) :: SOSType -> SOSType -> Bool

max :: SOSType -> SOSType -> SOSType

min :: SOSType -> SOSType -> SOSType

Read SOSType

Methods

readsPrec :: Int -> ReadS SOSType

readList :: ReadS [SOSType]

readPrec :: ReadPrec SOSType

readListPrec :: ReadPrec [SOSType]

Show SOSType

Methods

showsPrec :: Int -> SOSType -> ShowS

show :: SOSType -> String

showList :: [SOSType] -> ShowS

data SOSConstraint

SOS (special ordered sets) constraints

Constructors

SOSConstraint

Fields

• sosLabel :: Maybe Label
• sosType :: SOSType
• sosBody :: [(Var, Rational)]

Instances

Eq SOSConstraint

Methods

(==) :: SOSConstraint -> SOSConstraint -> Bool

(/=) :: SOSConstraint -> SOSConstraint -> Bool

Ord SOSConstraint

Methods

compare :: SOSConstraint -> SOSConstraint -> Ordering

(<) :: SOSConstraint -> SOSConstraint -> Bool

(<=) :: SOSConstraint -> SOSConstraint -> Bool

(>) :: SOSConstraint -> SOSConstraint -> Bool

(>=) :: SOSConstraint -> SOSConstraint -> Bool

max :: SOSConstraint -> SOSConstraint -> SOSConstraint

min :: SOSConstraint -> SOSConstraint -> SOSConstraint

Show SOSConstraint

Methods

showsPrec :: Int -> SOSConstraint -> ShowS

show :: SOSConstraint -> String

showList :: [SOSConstraint] -> ShowS

Variables SOSConstraint

Methods

vars :: SOSConstraint -> Set Var

defaultBounds :: Bounds

default bounds

defaultLB :: BoundExpr

default lower bound (0)

defaultUB :: BoundExpr

default upper bound (+∞)

toVar :: String -> Var

convert a string into a variable

fromVar :: Var -> String

convert a variable into a string

getVarType :: Problem -> Var -> VarType

looking up bounds for a variable

getBounds :: Problem -> Var -> Bounds

looking up bounds for a variable

variables :: Problem -> Set Var

integerVariables :: Problem -> Set Var

semiContinuousVariables :: Problem -> Set Var

semiIntegerVariables :: Problem -> Set Var

Utilities

class Variables a where

Minimal complete definition

vars

Methods

vars :: a -> Set Var

Instances

Variables SOSConstraint

Methods

vars :: SOSConstraint -> Set Var

Variables Constraint

Methods

vars :: Constraint -> Set Var

Variables ObjectiveFunction

Methods

vars :: ObjectiveFunction -> Set Var

Variables Term

Methods

vars :: Term -> Set Var

Variables Expr

Methods

vars :: Expr -> Set Var

Variables Problem

Methods

vars :: Problem -> Set Var

Variables a => Variables [a]

Methods

vars :: [a] -> Set Var

(Variables a, Variables b) => Variables (Either a b)

Methods

vars :: Either a b -> Set Var

intersectBounds :: Bounds -> Bounds -> Bounds