Copyright	(c) Masahiro Sakai 2011-2019
License	BSD-style
Maintainer	masahiro.sakai@gmail.com
Stability	provisional
Portability	non-portable
Safe Haskell	None
Language	Haskell2010
Extensions	Cpp

Numeric.Optimization.MIP.Base

Contents

The MIP Problem type
Variables
Expressions
Objective function
Constraints
- Linear (or Quadratic or Polynomial) constraints
- SOS constraints
Solutions
File I/O options
Utilities

Description

Mixed-Integer Programming Problems with some commmonly used extensions

Synopsis

data Problem c = Problem {
- name :: Maybe Text
- objectiveFunction :: ObjectiveFunction c
- constraints :: [Constraint c]
- sosConstraints :: [SOSConstraint c]
- userCuts :: [Constraint c]
- varType :: Map Var VarType
- varBounds :: Map Var (Bounds c)
}
type Label = Text
type Var = InternedText
toVar :: String -> Var
fromVar :: Var -> String
data VarType
- = ContinuousVariable
- | IntegerVariable
- | SemiContinuousVariable
- | SemiIntegerVariable
getVarType :: Problem c -> Var -> VarType
type BoundExpr c = Extended c
data Extended r
- = NegInf
- | Finite !r
- | PosInf
type Bounds c = (BoundExpr c, BoundExpr c)
defaultBounds :: Num c => Bounds c
defaultLB :: Num c => BoundExpr c
defaultUB :: BoundExpr c
getBounds :: Num c => Problem c -> Var -> Bounds c
variables :: Problem c -> Set Var
integerVariables :: Problem c -> Set Var
semiContinuousVariables :: Problem c -> Set Var
semiIntegerVariables :: Problem c -> Set Var
newtype Expr c = Expr [Term c]
varExpr :: Num c => Var -> Expr c
constExpr :: (Eq c, Num c) => c -> Expr c
terms :: Expr c -> [Term c]
data Term c = Term c [Var]
data OptDir
- = OptMin
- | OptMax
data ObjectiveFunction c = ObjectiveFunction {
- objLabel :: Maybe Label
- objDir :: OptDir
- objExpr :: Expr c
}
data Constraint c = Constraint {
- constrLabel :: Maybe Label
- constrIndicator :: Maybe (Var, c)
- constrExpr :: Expr c
- constrLB :: BoundExpr c
- constrUB :: BoundExpr c
- constrIsLazy :: Bool
}
(.==.) :: Num c => Expr c -> Expr c -> Constraint c
(.<=.) :: Num c => Expr c -> Expr c -> Constraint c
(.>=.) :: Num c => Expr c -> Expr c -> Constraint c
data RelOp
- = Le
- | Ge
- | Eql
data SOSType
- = S1
- | S2
data SOSConstraint c = SOSConstraint {
- sosLabel :: Maybe Label
- sosType :: SOSType
- sosBody :: [(Var, c)]
}
data Solution r = Solution {
- solStatus :: Status
- solObjectiveValue :: Maybe r
- solVariables :: Map Var r
}
data Status
- = StatusUnknown
- | StatusFeasible
- | StatusOptimal
- | StatusInfeasibleOrUnbounded
- | StatusInfeasible
- | StatusUnbounded
meetStatus :: Status -> Status -> Status
data FileOptions = FileOptions {
- optFileEncoding :: Maybe TextEncoding
}
class Default a where
- def :: a
class Variables a where
- vars :: a -> Set Var
intersectBounds :: Ord c => Bounds c -> Bounds c -> Bounds c

The MIP Problem type

data Problem c Source #

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

Instances details

Functor Problem Source #
Instance details Defined in Numeric.Optimization.MIP.Base Methods fmap :: (a -> b) -> Problem a -> Problem b # (<$) :: a -> Problem b -> Problem a #
Eq c => Eq (Problem c) Source #
Instance details Defined in Numeric.Optimization.MIP.Base Methods (==) :: Problem c -> Problem c -> Bool # (/=) :: Problem c -> Problem c -> Bool #
Ord c => Ord (Problem c) Source #
Instance details Defined in Numeric.Optimization.MIP.Base 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) Source #
Instance details Defined in Numeric.Optimization.MIP.Base Methods showsPrec :: Int -> Problem c -> ShowS # show :: Problem c -> String # showList :: [Problem c] -> ShowS #
Default (Problem c) Source #
Instance details Defined in Numeric.Optimization.MIP.Base Methods def :: Problem c #
Variables (Problem c) Source #
Instance details Defined in Numeric.Optimization.MIP.Base Methods vars :: Problem c -> Set Var Source #

type Label = Text Source #

label

Variables

type Var = InternedText Source #

variable

toVar :: String -> Var Source #

convert a string into a variable

fromVar :: Var -> String Source #

convert a variable into a string

Variable types

data VarType Source #

Constructors

ContinuousVariable
IntegerVariable
SemiContinuousVariable
SemiIntegerVariable

Instances

Instances details

Eq VarType Source #
Instance details Defined in Numeric.Optimization.MIP.Base Methods (==) :: VarType -> VarType -> Bool # (/=) :: VarType -> VarType -> Bool #
Ord VarType Source #
Instance details Defined in Numeric.Optimization.MIP.Base 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 Source #
Instance details Defined in Numeric.Optimization.MIP.Base Methods showsPrec :: Int -> VarType -> ShowS # show :: VarType -> String # showList :: [VarType] -> ShowS #
Default VarType Source #
Instance details Defined in Numeric.Optimization.MIP.Base Methods def :: VarType #

getVarType :: Problem c -> Var -> VarType Source #

looking up bounds for a variable

Variable bounds

type BoundExpr c = Extended c Source #

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

Instances details

Functor Extended
Instance details Defined in Data.ExtendedReal Methods fmap :: (a -> b) -> Extended a -> Extended b # (<$) :: a -> Extended b -> Extended a #
Bounded (Extended r)
Instance details Defined in Data.ExtendedReal Methods minBound :: Extended r # maxBound :: Extended r #
Eq r => Eq (Extended r)
Instance details Defined in Data.ExtendedReal 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.
Instance details Defined in Data.ExtendedReal Methods (/) :: Extended r -> Extended r -> Extended r # recip :: Extended r -> Extended r # fromRational :: Rational -> Extended r #
Data r => Data (Extended r)
Instance details Defined in Data.ExtendedReal 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 r0. Data b => c (b -> r0) -> c r0) -> (forall r1. r1 -> c r1) -> 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 :: (r0 -> r' -> r0) -> r0 -> (forall d. Data d => d -> r') -> Extended r -> r0 # gmapQr :: forall r0 r'. (r' -> r0 -> r0) -> r0 -> (forall d. Data d => d -> r') -> Extended r -> r0 # 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.
Instance details Defined in Data.ExtendedReal 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)
Instance details Defined in Data.ExtendedReal 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)
Instance details Defined in Data.ExtendedReal Methods readsPrec :: Int -> ReadS (Extended r) # readList :: ReadS [Extended r] # readPrec :: ReadPrec (Extended r) # readListPrec :: ReadPrec [Extended r] #
Show r => Show (Extended r)
Instance details Defined in Data.ExtendedReal Methods showsPrec :: Int -> Extended r -> ShowS # show :: Extended r -> String # showList :: [Extended r] -> ShowS #
NFData r => NFData (Extended r)
Instance details Defined in Data.ExtendedReal Methods rnf :: Extended r -> () #
Hashable r => Hashable (Extended r)
Instance details Defined in Data.ExtendedReal Methods hashWithSalt :: Int -> Extended r -> Int # hash :: Extended r -> Int #

type Bounds c = (BoundExpr c, BoundExpr c) Source #

type for representing lower/upper bound of variables

defaultBounds :: Num c => Bounds c Source #

default bounds

defaultLB :: Num c => BoundExpr c Source #

default lower bound (0)

defaultUB :: BoundExpr c Source #

default upper bound (+∞)

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

looking up bounds for a variable

Variable getters

variables :: Problem c -> Set Var Source #

integerVariables :: Problem c -> Set Var Source #

semiContinuousVariables :: Problem c -> Set Var Source #

semiIntegerVariables :: Problem c -> Set Var Source #

Expressions

newtype Expr c Source #

expressions

Constructors

Expr [Term c]

Instances

Instances details

Functor Expr Source #
Instance details Defined in Numeric.Optimization.MIP.Base Methods fmap :: (a -> b) -> Expr a -> Expr b # (<$) :: a -> Expr b -> Expr a #
Eq c => Eq (Expr c) Source #
Instance details Defined in Numeric.Optimization.MIP.Base Methods (==) :: Expr c -> Expr c -> Bool # (/=) :: Expr c -> Expr c -> Bool #
Num c => Num (Expr c) Source #
Instance details Defined in Numeric.Optimization.MIP.Base 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) Source #
Instance details Defined in Numeric.Optimization.MIP.Base 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) Source #
Instance details Defined in Numeric.Optimization.MIP.Base Methods showsPrec :: Int -> Expr c -> ShowS # show :: Expr c -> String # showList :: [Expr c] -> ShowS #
Variables (Expr c) Source #
Instance details Defined in Numeric.Optimization.MIP.Base Methods vars :: Expr c -> Set Var Source #

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

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

terms :: Expr c -> [Term c] Source #

data Term c Source #

terms

Constructors

Term c [Var]

Instances

Instances details

Functor Term Source #
Instance details Defined in Numeric.Optimization.MIP.Base Methods fmap :: (a -> b) -> Term a -> Term b # (<$) :: a -> Term b -> Term a #
Eq c => Eq (Term c) Source #
Instance details Defined in Numeric.Optimization.MIP.Base Methods (==) :: Term c -> Term c -> Bool # (/=) :: Term c -> Term c -> Bool #
Ord c => Ord (Term c) Source #
Instance details Defined in Numeric.Optimization.MIP.Base 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) Source #
Instance details Defined in Numeric.Optimization.MIP.Base Methods showsPrec :: Int -> Term c -> ShowS # show :: Term c -> String # showList :: [Term c] -> ShowS #
Variables (Term c) Source #
Instance details Defined in Numeric.Optimization.MIP.Base Methods vars :: Term c -> Set Var Source #

Objective function

data OptDir #

The OptDir type represents optimization directions.

Constructors

OptMin	minimization
OptMax	maximization

Instances

Instances details

Bounded OptDir
Instance details Defined in Data.OptDir Methods minBound :: OptDir # maxBound :: OptDir #
Enum OptDir
Instance details Defined in Data.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
Instance details Defined in Data.OptDir Methods (==) :: OptDir -> OptDir -> Bool # (/=) :: OptDir -> OptDir -> Bool #
Data OptDir
Instance details Defined in 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 :: forall r r'. (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
Instance details Defined in Data.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
Instance details Defined in Data.OptDir Methods readsPrec :: Int -> ReadS OptDir # readList :: ReadS [OptDir] # readPrec :: ReadPrec OptDir # readListPrec :: ReadPrec [OptDir] #
Show OptDir
Instance details Defined in Data.OptDir Methods showsPrec :: Int -> OptDir -> ShowS # show :: OptDir -> String # showList :: [OptDir] -> ShowS #
Ix OptDir
Instance details Defined in Data.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 #
Generic OptDir
Instance details Defined in Data.OptDir Associated Types type Rep OptDir :: Type -> Type # Methods from :: OptDir -> Rep OptDir x # to :: Rep OptDir x -> OptDir #
Hashable OptDir
Instance details Defined in Data.OptDir Methods hashWithSalt :: Int -> OptDir -> Int # hash :: OptDir -> Int #
type Rep OptDir
Instance details Defined in Data.OptDir type Rep OptDir = D1 ('MetaData "OptDir" "Data.OptDir" "OptDir-0.0.4-FBOnrIkW0cS4YfvluPHB8j" 'False) (C1 ('MetaCons "OptMin" 'PrefixI 'False) (U1 :: Type -> Type) :+: C1 ('MetaCons "OptMax" 'PrefixI 'False) (U1 :: Type -> Type))

data ObjectiveFunction c Source #

objective function

Constructors

ObjectiveFunction
Fields objLabel :: Maybe Label objDir :: OptDir objExpr :: Expr c

Instances

Instances details

Functor ObjectiveFunction Source #
Instance details Defined in Numeric.Optimization.MIP.Base Methods fmap :: (a -> b) -> ObjectiveFunction a -> ObjectiveFunction b # (<$) :: a -> ObjectiveFunction b -> ObjectiveFunction a #
Eq c => Eq (ObjectiveFunction c) Source #
Instance details Defined in Numeric.Optimization.MIP.Base Methods (==) :: ObjectiveFunction c -> ObjectiveFunction c -> Bool # (/=) :: ObjectiveFunction c -> ObjectiveFunction c -> Bool #
Ord c => Ord (ObjectiveFunction c) Source #
Instance details Defined in Numeric.Optimization.MIP.Base 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) Source #
Instance details Defined in Numeric.Optimization.MIP.Base Methods showsPrec :: Int -> ObjectiveFunction c -> ShowS # show :: ObjectiveFunction c -> String # showList :: [ObjectiveFunction c] -> ShowS #
Default (ObjectiveFunction c) Source #
Instance details Defined in Numeric.Optimization.MIP.Base Methods def :: ObjectiveFunction c #
Variables (ObjectiveFunction c) Source #
Instance details Defined in Numeric.Optimization.MIP.Base Methods vars :: ObjectiveFunction c -> Set Var Source #

Constraints

Linear (or Quadratic or Polynomial) constraints

data Constraint c Source #

constraint

Constructors

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

Instances

Instances details

Functor Constraint Source #
Instance details Defined in Numeric.Optimization.MIP.Base Methods fmap :: (a -> b) -> Constraint a -> Constraint b # (<$) :: a -> Constraint b -> Constraint a #
Eq c => Eq (Constraint c) Source #
Instance details Defined in Numeric.Optimization.MIP.Base Methods (==) :: Constraint c -> Constraint c -> Bool # (/=) :: Constraint c -> Constraint c -> Bool #
Ord c => Ord (Constraint c) Source #
Instance details Defined in Numeric.Optimization.MIP.Base 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) Source #
Instance details Defined in Numeric.Optimization.MIP.Base Methods showsPrec :: Int -> Constraint c -> ShowS # show :: Constraint c -> String # showList :: [Constraint c] -> ShowS #
Default (Constraint c) Source #
Instance details Defined in Numeric.Optimization.MIP.Base Methods def :: Constraint c #
Variables (Constraint c) Source #
Instance details Defined in Numeric.Optimization.MIP.Base Methods vars :: Constraint c -> Set Var Source #

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

Equality constraint.

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

Inequality constraint (≤).

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

Inequality constraint (≥).

data RelOp Source #

relational operators

Constructors

Le
Ge
Eql

Instances

Instances details

Enum RelOp Source #
Instance details Defined in Numeric.Optimization.MIP.Base 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 Source #
Instance details Defined in Numeric.Optimization.MIP.Base Methods (==) :: RelOp -> RelOp -> Bool # (/=) :: RelOp -> RelOp -> Bool #
Ord RelOp Source #
Instance details Defined in Numeric.Optimization.MIP.Base 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 Source #
Instance details Defined in Numeric.Optimization.MIP.Base Methods showsPrec :: Int -> RelOp -> ShowS # show :: RelOp -> String # showList :: [RelOp] -> ShowS #

SOS constraints

data SOSType Source #

types of SOS (special ordered sets) constraints

Constructors

S1	Type 1 SOS constraint
S2	Type 2 SOS constraint

Instances

Instances details

Enum SOSType Source #
Instance details Defined in Numeric.Optimization.MIP.Base 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 Source #
Instance details Defined in Numeric.Optimization.MIP.Base Methods (==) :: SOSType -> SOSType -> Bool # (/=) :: SOSType -> SOSType -> Bool #
Ord SOSType Source #
Instance details Defined in Numeric.Optimization.MIP.Base 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 Source #
Instance details Defined in Numeric.Optimization.MIP.Base Methods readsPrec :: Int -> ReadS SOSType # readList :: ReadS [SOSType] # readPrec :: ReadPrec SOSType # readListPrec :: ReadPrec [SOSType] #
Show SOSType Source #
Instance details Defined in Numeric.Optimization.MIP.Base Methods showsPrec :: Int -> SOSType -> ShowS # show :: SOSType -> String # showList :: [SOSType] -> ShowS #

data SOSConstraint c Source #

SOS (special ordered sets) constraints

Constructors

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

Instances

Instances details

Functor SOSConstraint Source #
Instance details Defined in Numeric.Optimization.MIP.Base Methods fmap :: (a -> b) -> SOSConstraint a -> SOSConstraint b # (<$) :: a -> SOSConstraint b -> SOSConstraint a #
Eq c => Eq (SOSConstraint c) Source #
Instance details Defined in Numeric.Optimization.MIP.Base Methods (==) :: SOSConstraint c -> SOSConstraint c -> Bool # (/=) :: SOSConstraint c -> SOSConstraint c -> Bool #
Ord c => Ord (SOSConstraint c) Source #
Instance details Defined in Numeric.Optimization.MIP.Base 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) Source #
Instance details Defined in Numeric.Optimization.MIP.Base Methods showsPrec :: Int -> SOSConstraint c -> ShowS # show :: SOSConstraint c -> String # showList :: [SOSConstraint c] -> ShowS #
Variables (SOSConstraint c) Source #
Instance details Defined in Numeric.Optimization.MIP.Base Methods vars :: SOSConstraint c -> Set Var Source #

Solutions

data Solution r Source #

Type for representing a solution of MIP problem.

Constructors

Solution
Fields solStatus :: Status solObjectiveValue :: Maybe r solVariables :: Map Var r

Instances

Instances details

Functor Solution Source #
Instance details Defined in Numeric.Optimization.MIP.Base Methods fmap :: (a -> b) -> Solution a -> Solution b # (<$) :: a -> Solution b -> Solution a #
Eq r => Eq (Solution r) Source #
Instance details Defined in Numeric.Optimization.MIP.Base Methods (==) :: Solution r -> Solution r -> Bool # (/=) :: Solution r -> Solution r -> Bool #
Ord r => Ord (Solution r) Source #
Instance details Defined in Numeric.Optimization.MIP.Base 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) Source #
Instance details Defined in Numeric.Optimization.MIP.Base Methods showsPrec :: Int -> Solution r -> ShowS # show :: Solution r -> String # showList :: [Solution r] -> ShowS #
Default (Solution r) Source #
Instance details Defined in Numeric.Optimization.MIP.Base Methods def :: Solution r #

data Status Source #

MIP status with the following partial order:

Constructors

StatusUnknown
StatusFeasible
StatusOptimal
StatusInfeasibleOrUnbounded
StatusInfeasible
StatusUnbounded

Instances

Instances details

Bounded Status Source #
Instance details Defined in Numeric.Optimization.MIP.Base Methods minBound :: Status # maxBound :: Status #
Enum Status Source #
Instance details Defined in Numeric.Optimization.MIP.Base 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 Source #
Instance details Defined in Numeric.Optimization.MIP.Base Methods (==) :: Status -> Status -> Bool # (/=) :: Status -> Status -> Bool #
Ord Status Source #
Instance details Defined in Numeric.Optimization.MIP.Base 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 Source #
Instance details Defined in Numeric.Optimization.MIP.Base Methods showsPrec :: Int -> Status -> ShowS # show :: Status -> String # showList :: [Status] -> ShowS #
PartialOrd Status Source #
Instance details Defined in Numeric.Optimization.MIP.Base Methods leq :: Status -> Status -> Bool # comparable :: Status -> Status -> Bool #

meetStatus :: Status -> Status -> Status Source #

meet (greatest lower bound) operator of the partial order of Status type.

If the version of lattices is <2, then MeetSemiLattice instance can also be used.

File I/O options

data FileOptions Source #

Constructors

FileOptions
Fields optFileEncoding :: Maybe TextEncoding

Instances

Instances details

Show FileOptions Source #
Instance details Defined in Numeric.Optimization.MIP.Base Methods showsPrec :: Int -> FileOptions -> ShowS # show :: FileOptions -> String # showList :: [FileOptions] -> ShowS #
Default FileOptions Source #
Instance details Defined in Numeric.Optimization.MIP.Base Methods def :: FileOptions #

Utilities

class Default a where #

A class for types with a default value.

Minimal complete definition

Nothing

Methods

def :: a #

The default value for this type.

Instances

Instances details

Default Double
Instance details Defined in Data.Default.Class Methods def :: Double #
Default Float
Instance details Defined in Data.Default.Class Methods def :: Float #
Default Int
Instance details Defined in Data.Default.Class Methods def :: Int #
Default Int8
Instance details Defined in Data.Default.Class Methods def :: Int8 #
Default Int16
Instance details Defined in Data.Default.Class Methods def :: Int16 #
Default Int32
Instance details Defined in Data.Default.Class Methods def :: Int32 #
Default Int64
Instance details Defined in Data.Default.Class Methods def :: Int64 #
Default Integer
Instance details Defined in Data.Default.Class Methods def :: Integer #
Default Ordering
Instance details Defined in Data.Default.Class Methods def :: Ordering #
Default Word
Instance details Defined in Data.Default.Class Methods def :: Word #
Default Word8
Instance details Defined in Data.Default.Class Methods def :: Word8 #
Default Word16
Instance details Defined in Data.Default.Class Methods def :: Word16 #
Default Word32
Instance details Defined in Data.Default.Class Methods def :: Word32 #
Default Word64
Instance details Defined in Data.Default.Class Methods def :: Word64 #
Default ()
Instance details Defined in Data.Default.Class Methods def :: () #
Default All
Instance details Defined in Data.Default.Class Methods def :: All #
Default Any
Instance details Defined in Data.Default.Class Methods def :: Any #
Default CShort
Instance details Defined in Data.Default.Class Methods def :: CShort #
Default CUShort
Instance details Defined in Data.Default.Class Methods def :: CUShort #
Default CInt
Instance details Defined in Data.Default.Class Methods def :: CInt #
Default CUInt
Instance details Defined in Data.Default.Class Methods def :: CUInt #
Default CLong
Instance details Defined in Data.Default.Class Methods def :: CLong #
Default CULong
Instance details Defined in Data.Default.Class Methods def :: CULong #
Default CLLong
Instance details Defined in Data.Default.Class Methods def :: CLLong #
Default CULLong
Instance details Defined in Data.Default.Class Methods def :: CULLong #
Default CFloat
Instance details Defined in Data.Default.Class Methods def :: CFloat #
Default CDouble
Instance details Defined in Data.Default.Class Methods def :: CDouble #
Default CPtrdiff
Instance details Defined in Data.Default.Class Methods def :: CPtrdiff #
Default CSize
Instance details Defined in Data.Default.Class Methods def :: CSize #
Default CSigAtomic
Instance details Defined in Data.Default.Class Methods def :: CSigAtomic #
Default CClock
Instance details Defined in Data.Default.Class Methods def :: CClock #
Default CTime
Instance details Defined in Data.Default.Class Methods def :: CTime #
Default CUSeconds
Instance details Defined in Data.Default.Class Methods def :: CUSeconds #
Default CSUSeconds
Instance details Defined in Data.Default.Class Methods def :: CSUSeconds #
Default CIntPtr
Instance details Defined in Data.Default.Class Methods def :: CIntPtr #
Default CUIntPtr
Instance details Defined in Data.Default.Class Methods def :: CUIntPtr #
Default CIntMax
Instance details Defined in Data.Default.Class Methods def :: CIntMax #
Default CUIntMax
Instance details Defined in Data.Default.Class Methods def :: CUIntMax #
Default ParseSettings
Instance details Defined in Text.XML.Stream.Parse Methods def :: ParseSettings #
Default FileOptions Source #
Instance details Defined in Numeric.Optimization.MIP.Base Methods def :: FileOptions #
Default VarType Source #
Instance details Defined in Numeric.Optimization.MIP.Base Methods def :: VarType #
Default SolveOptions Source #
Instance details Defined in Numeric.Optimization.MIP.Solver.Base Methods def :: SolveOptions #
Default CBC Source #
Instance details Defined in Numeric.Optimization.MIP.Solver.CBC Methods def :: CBC #
Default CPLEX Source #
Instance details Defined in Numeric.Optimization.MIP.Solver.CPLEX Methods def :: CPLEX #
Default Glpsol Source #
Instance details Defined in Numeric.Optimization.MIP.Solver.Glpsol Methods def :: Glpsol #
Default GurobiCl Source #
Instance details Defined in Numeric.Optimization.MIP.Solver.GurobiCl Methods def :: GurobiCl #
Default LPSolve Source #
Instance details Defined in Numeric.Optimization.MIP.Solver.LPSolve Methods def :: LPSolve #
Default SCIP Source #
Instance details Defined in Numeric.Optimization.MIP.Solver.SCIP Methods def :: SCIP #
Default [a]
Instance details Defined in Data.Default.Class Methods def :: [a] #
Default (Maybe a)
Instance details Defined in Data.Default.Class Methods def :: Maybe a #
Integral a => Default (Ratio a)
Instance details Defined in Data.Default.Class Methods def :: Ratio a #
Default a => Default (IO a)
Instance details Defined in Data.Default.Class Methods def :: IO a #
(Default a, RealFloat a) => Default (Complex a)
Instance details Defined in Data.Default.Class Methods def :: Complex a #
Default (First a)
Instance details Defined in Data.Default.Class Methods def :: First a #
Default (Last a)
Instance details Defined in Data.Default.Class Methods def :: Last a #
Default a => Default (Dual a)
Instance details Defined in Data.Default.Class Methods def :: Dual a #
Default (Endo a)
Instance details Defined in Data.Default.Class Methods def :: Endo a #
Num a => Default (Sum a)
Instance details Defined in Data.Default.Class Methods def :: Sum a #
Num a => Default (Product a)
Instance details Defined in Data.Default.Class Methods def :: Product a #
Default (Solution r) Source #
Instance details Defined in Numeric.Optimization.MIP.Base Methods def :: Solution r #
Default (Constraint c) Source #
Instance details Defined in Numeric.Optimization.MIP.Base Methods def :: Constraint c #
Default (ObjectiveFunction c) Source #
Instance details Defined in Numeric.Optimization.MIP.Base Methods def :: ObjectiveFunction c #
Default (Problem c) Source #
Instance details Defined in Numeric.Optimization.MIP.Base Methods def :: Problem c #
Default r => Default (e -> r)
Instance details Defined in Data.Default.Class Methods def :: e -> r #
(Default a, Default b) => Default (a, b)
Instance details Defined in Data.Default.Class Methods def :: (a, b) #
(Default a, Default b, Default c) => Default (a, b, c)
Instance details Defined in Data.Default.Class Methods def :: (a, b, c) #
(Default a, Default b, Default c, Default d) => Default (a, b, c, d)
Instance details Defined in Data.Default.Class Methods def :: (a, b, c, d) #
(Default a, Default b, Default c, Default d, Default e) => Default (a, b, c, d, e)
Instance details Defined in Data.Default.Class Methods def :: (a, b, c, d, e) #
(Default a, Default b, Default c, Default d, Default e, Default f) => Default (a, b, c, d, e, f)
Instance details Defined in Data.Default.Class Methods def :: (a, b, c, d, e, f) #
(Default a, Default b, Default c, Default d, Default e, Default f, Default g) => Default (a, b, c, d, e, f, g)
Instance details Defined in Data.Default.Class Methods def :: (a, b, c, d, e, f, g) #

class Variables a where Source #

Methods

vars :: a -> Set Var Source #

Instances

Instances details

Variables a => Variables [a] Source #
Instance details Defined in Numeric.Optimization.MIP.Base Methods vars :: [a] -> Set Var Source #
Variables (SOSConstraint c) Source #
Instance details Defined in Numeric.Optimization.MIP.Base Methods vars :: SOSConstraint c -> Set Var Source #
Variables (Constraint c) Source #
Instance details Defined in Numeric.Optimization.MIP.Base Methods vars :: Constraint c -> Set Var Source #
Variables (ObjectiveFunction c) Source #
Instance details Defined in Numeric.Optimization.MIP.Base Methods vars :: ObjectiveFunction c -> Set Var Source #
Variables (Term c) Source #
Instance details Defined in Numeric.Optimization.MIP.Base Methods vars :: Term c -> Set Var Source #
Variables (Expr c) Source #
Instance details Defined in Numeric.Optimization.MIP.Base Methods vars :: Expr c -> Set Var Source #
Variables (Problem c) Source #
Instance details Defined in Numeric.Optimization.MIP.Base Methods vars :: Problem c -> Set Var Source #
(Variables a, Variables b) => Variables (Either a b) Source #
Instance details Defined in Numeric.Optimization.MIP.Base Methods vars :: Either a b -> Set Var Source #

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