Solve your integer linear programming problems with CBC. This library uses the constructors in limp to define integer linear programming problems, then passes them to the CBC solver to find solutions.
You can define an integer linear program using the Program type.
This type is parameterised over three type parameters: Program z r c, where z is the type of integer-valued variables; r is the type of real-valued variables, and c is a description of how to represent results.
This solver only supports the IntDouble representation type – that is, integers are represented as machine Ints and reals as double-precision floating point values.
You can define a program with an integer variable "a" and a real variable "b" as follows:
import Numeric.Limp.Rep
import Numeric.Limp.Program
-- Minimise a + b
-- Subject to a + 2b >= 3
-- Where 0 <= a <= 10 :: Z
-- 0 <= b <= 10 :: R
problem1 :: Direction -> Program String String IntDouble
problem1 dir
= program dir
(z1 "a" .+. r1 "b" )
(z1 "a" .+. r "b" 2 :>= con 3)
[ lowerUpperZ 0 "a" 10
, lowerUpperR 0 "b" 10 ]
You can then use Numeric.Limp.Solvers.Cbc.solve to find a solution using CBC. This gives you an Assignment z r IntDouble for the variables, which is a mapping from z to Int and a mapping from r to Double:
import Numeric.Limp.Solvers.Cbc
solve_problem :: (Show z, Show r, Ord z, Ord r) => (Direction -> Program z r IntDouble) -> IO ()
solve_problem problem
= do let a1 = solve $ problem Minimise
putStrLn "*** Minimise *** "
show_result a1
let a2 = solve $ problem Maximise
putStrLn "*** Maximise *** "
show_result a2
show_result :: (Show z, Show r, Ord z, Ord r) => Either Error (Assignment z r IntDouble) -> IO ()
show_result as
= case as of
Left e
-> do putStrLn "Error:"
print e
Right a
-> do putStrLn "Success:"
print a
Further examples are available in the examples directory.