ToySolver.Data.MIP.Base

Mixed-Integer Programming Problems with some commmonly used extensions

The MIP Problem type

data Problem c

Problem

Constructors

Problem

Fields

• name :: Maybe Text
• objectiveFunction :: ObjectiveFunction c
• constraints :: [Constraint c]
• sosConstraints :: [SOSConstraint c]
• userCuts :: [Constraint c]
• varType :: Map Var VarType
• varBounds :: Map Var (Bounds c)

Instances

Functor Problem

Methods

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

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

Eq c => Eq (Problem c)

Methods

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

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

Ord c => Ord (Problem c)

Methods

compare :: Problem c -> Problem c -> Ordering

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

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

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

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

max :: Problem c -> Problem c -> Problem c

min :: Problem c -> Problem c -> Problem c

Show c => Show (Problem c)

Methods

showsPrec :: Int -> Problem c -> ShowS

show :: Problem c -> String

showList :: [Problem c] -> ShowS

Default (Problem c)

Methods

def :: Problem c

Variables (Problem c)

Methods

vars :: Problem c -> Set Var

type Label = Text

label

Variables

type Var = InternedText

variable

toVar :: String -> Var

convert a string into a variable

fromVar :: Var -> String

convert a variable into a string

Variable types

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

getVarType :: Problem c -> Var -> VarType

looking up bounds for a variable

Variable bounds

type BoundExpr c = Extended c

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

type Bounds c = (BoundExpr c, BoundExpr c)

type for representing lower/upper bound of variables

defaultBounds :: Num c => Bounds c

default bounds

defaultLB :: Num c => BoundExpr c

default lower bound (0)

defaultUB :: BoundExpr c

default upper bound (+∞)

getBounds :: Num c => Problem c -> Var -> Bounds c

looking up bounds for a variable

Variable getters

variables :: Problem c -> Set Var

integerVariables :: Problem c -> Set Var

semiContinuousVariables :: Problem c -> Set Var

semiIntegerVariables :: Problem c -> Set Var

Expressions

newtype Expr c

expressions

Constructors

Expr [Term c]

Instances

Functor Expr

Methods

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

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

Eq c => Eq (Expr c)

Methods

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

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

Num c => Num (Expr c)

Methods

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

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

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

negate :: Expr c -> Expr c

abs :: Expr c -> Expr c

signum :: Expr c -> Expr c

fromInteger :: Integer -> Expr c

Ord c => Ord (Expr c)

Methods

compare :: Expr c -> Expr c -> Ordering

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

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

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

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

max :: Expr c -> Expr c -> Expr c

min :: Expr c -> Expr c -> Expr c

Show c => Show (Expr c)

Methods

showsPrec :: Int -> Expr c -> ShowS

show :: Expr c -> String

showList :: [Expr c] -> ShowS

Variables (Expr c)

Methods

vars :: Expr c -> Set Var

varExpr :: Num c => Var -> Expr c

constExpr :: (Eq c, Num c) => c -> Expr c

terms :: Expr c -> [Term c]

data Term c

terms

Constructors

Term c [Var]

Instances

Functor Term

Methods

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

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

Eq c => Eq (Term c)

Methods

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

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

Ord c => Ord (Term c)

Methods

compare :: Term c -> Term c -> Ordering

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

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

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

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

max :: Term c -> Term c -> Term c

min :: Term c -> Term c -> Term c

Show c => Show (Term c)

Methods

showsPrec :: Int -> Term c -> ShowS

show :: Term c -> String

showList :: [Term c] -> ShowS

Variables (Term c)

Methods

vars :: Term c -> Set Var

Objective function

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 c

objective function

Constructors

ObjectiveFunction

Fields

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

Instances

Functor ObjectiveFunction

Methods

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

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

Eq c => Eq (ObjectiveFunction c)

Methods

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

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

Ord c => Ord (ObjectiveFunction c)

Methods

compare :: ObjectiveFunction c -> ObjectiveFunction c -> Ordering

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

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

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

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

max :: ObjectiveFunction c -> ObjectiveFunction c -> ObjectiveFunction c

min :: ObjectiveFunction c -> ObjectiveFunction c -> ObjectiveFunction c

Show c => Show (ObjectiveFunction c)

Methods

showsPrec :: Int -> ObjectiveFunction c -> ShowS

show :: ObjectiveFunction c -> String

showList :: [ObjectiveFunction c] -> ShowS

Default (ObjectiveFunction c)

Methods

def :: ObjectiveFunction c

Variables (ObjectiveFunction c)

Methods

vars :: ObjectiveFunction c -> Set Var

Constraints

Linear (or Quadratic or Polynomial) constraints

data Constraint c

constraint

Constructors

Constraint

Fields

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

Instances

Functor Constraint

Methods

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

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

Eq c => Eq (Constraint c)

Methods

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

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

Ord c => Ord (Constraint c)

Methods

compare :: Constraint c -> Constraint c -> Ordering

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

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

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

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

max :: Constraint c -> Constraint c -> Constraint c

min :: Constraint c -> Constraint c -> Constraint c

Show c => Show (Constraint c)

Methods

showsPrec :: Int -> Constraint c -> ShowS

show :: Constraint c -> String

showList :: [Constraint c] -> ShowS

Default (Constraint c)

Methods

def :: Constraint c

Variables (Constraint c)

Methods

vars :: Constraint c -> Set Var

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

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

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

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

SOS constraints

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 c

SOS (special ordered sets) constraints

Constructors

SOSConstraint

Fields

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

Instances

Functor SOSConstraint

Methods

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

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

Eq c => Eq (SOSConstraint c)

Methods

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

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

Ord c => Ord (SOSConstraint c)

Methods

compare :: SOSConstraint c -> SOSConstraint c -> Ordering

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

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

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

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

max :: SOSConstraint c -> SOSConstraint c -> SOSConstraint c

min :: SOSConstraint c -> SOSConstraint c -> SOSConstraint c

Show c => Show (SOSConstraint c)

Methods

showsPrec :: Int -> SOSConstraint c -> ShowS

show :: SOSConstraint c -> String

showList :: [SOSConstraint c] -> ShowS

Variables (SOSConstraint c)

Methods

vars :: SOSConstraint c -> Set Var

Solutions

data Solution r

Constructors

Solution

Fields

• solStatus :: Status
• solObjectiveValue :: Maybe r
• solVariables :: Map Var r

Instances

Functor Solution

Methods

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

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

Eq r => Eq (Solution r)

Methods

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

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

Ord r => Ord (Solution r)

Methods

compare :: Solution r -> Solution r -> Ordering

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

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

(>) :: Solution r -> Solution r -> Bool

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

max :: Solution r -> Solution r -> Solution r

min :: Solution r -> Solution r -> Solution r

Show r => Show (Solution r)

Methods

showsPrec :: Int -> Solution r -> ShowS

show :: Solution r -> String

showList :: [Solution r] -> ShowS

Default (Solution r)

Methods

def :: Solution r

data Status

MIP status with the following partial order:

Constructors

StatusUnknown

StatusFeasible

StatusOptimal

StatusInfeasibleOrUnbounded

StatusInfeasible

StatusUnbounded

Instances

Bounded Status

Methods

minBound :: Status

maxBound :: Status

Enum Status

Methods

succ :: Status -> Status

pred :: Status -> Status

toEnum :: Int -> Status

fromEnum :: Status -> Int

enumFrom :: Status -> [Status]

enumFromThen :: Status -> Status -> [Status]

enumFromTo :: Status -> Status -> [Status]

enumFromThenTo :: Status -> Status -> Status -> [Status]

Eq Status

Methods

(==) :: Status -> Status -> Bool

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

Ord Status

Methods

compare :: Status -> Status -> Ordering

(<) :: Status -> Status -> Bool

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

(>) :: Status -> Status -> Bool

(>=) :: Status -> Status -> Bool

max :: Status -> Status -> Status

min :: Status -> Status -> Status

Show Status

Methods

showsPrec :: Int -> Status -> ShowS

show :: Status -> String

showList :: [Status] -> ShowS

MeetSemiLattice Status

Methods

(/\) :: Status -> Status -> Status

meet :: Status -> Status -> Status

PartialOrd Status

Methods

leq :: Status -> Status -> Bool

comparable :: Status -> Status -> Bool

File I/O options

data FileOptions

Constructors

FileOptions

Fields

• optFileEncoding :: Maybe TextEncoding

Instances

Show FileOptions

Methods

showsPrec :: Int -> FileOptions -> ShowS

show :: FileOptions -> String

showList :: [FileOptions] -> ShowS

Default FileOptions

Methods

def :: FileOptions

Utilities

class Variables a where

Minimal complete definition

vars

Methods

vars :: a -> Set Var

Instances

Variables a => Variables [a]

Methods

vars :: [a] -> Set Var

Variables (SOSConstraint c)

Methods

vars :: SOSConstraint c -> Set Var

Variables (Constraint c)

Methods

vars :: Constraint c -> Set Var

Variables (ObjectiveFunction c)

Methods

vars :: ObjectiveFunction c -> Set Var

Variables (Term c)

Methods

vars :: Term c -> Set Var

Variables (Expr c)

Methods

vars :: Expr c -> Set Var

Variables (Problem c)

Methods

vars :: Problem c -> Set Var

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

Methods

vars :: Either a b -> Set Var

intersectBounds :: Ord c => Bounds c -> Bounds c -> Bounds c