This package provides extensions to MathOptInterface in order to support constraint programming. This allows to use the same user model with several solvers.
On top of providing a uniform interface, this package also implements a quantity of bridges, i.e. reformulations of constraints, to bridge the gap when a solver does not support a specific constraint. In particular, the set of bridges should make it possible to transform any CP model into a MIP model.
Currently, the following solvers are using this interface:
- Chuffed.jl, wrapper for the open-source Chuffed solver
- ConstraintSolver.jl, a native Julia open-source solver
- CPLEXCP.jl, wrapper for the commercial CPLEX CP Optimizer solver
For instance, you can use this package to formulate a colouring problem on a map:
using MathOptInterface
using ConstraintProgrammingExtensions
using … # Import your solver.
const MOI = MathOptInterface
const CP = ConstraintProgrammingExtensions
model = … # Depending on the solver you want to use.
# Create the variables: six countriers; the value is the colour number for each country
belgium, _ = MOI.add_constrained_variable(model, MOI.Integer())
denmark, _ = MOI.add_constrained_variable(model, MOI.Integer())
france, _ = MOI.add_constrained_variable(model, MOI.Integer())
germany, _ = MOI.add_constrained_variable(model, MOI.Integer())
luxembourg, _ = MOI.add_constrained_variable(model, MOI.Integer())
netherlands, _ = MOI.add_constrained_variable(model, MOI.Integer())
# Constrain the colours to be in {0, 1, 2, 3}
MOI.add_constraint(model, belgium, MOI.Interval(0, 3))
MOI.add_constraint(model, denmark, MOI.Interval(0, 3))
MOI.add_constraint(model, france, MOI.Interval(0, 3))
MOI.add_constraint(model, germany, MOI.Interval(0, 3))
MOI.add_constraint(model, luxembourg, MOI.Interval(0, 3))
MOI.add_constraint(model, netherlands, MOI.Interval(0, 3))
# Two adjacent countries must have different colours.
countries(c1, c2) = MOI.ScalarAffineFunction(MOI.ScalarAffineTerm.([1, -1], [c1, c2]), 0)
MOI.add_constraint(model, countries(belgium, france), CP.DifferentFrom(0))
MOI.add_constraint(model, countries(belgium, germany), CP.DifferentFrom(0))
MOI.add_constraint(model, countries(belgium, netherlands), CP.DifferentFrom(0))
MOI.add_constraint(model, countries(belgium, luxembourg), CP.DifferentFrom(0))
MOI.add_constraint(model, countries(denmark, germany), CP.DifferentFrom(0))
MOI.add_constraint(model, countries(france, germany), CP.DifferentFrom(0))
MOI.add_constraint(model, countries(france, luxembourg), CP.DifferentFrom(0))
MOI.add_constraint(model, countries(germany, luxembourg), CP.DifferentFrom(0))
MOI.add_constraint(model, countries(germany, netherlands), CP.DifferentFrom(0))
# Solve the model.
MOI.optimize!(model)
# Check if the solution is optimum.
@assert MOI.get(model, MOI.TerminationStatus()) == MOI.OPTIMAL
# Get the solution
@show MOI.get(model, MOI.VariablePrimal(), belgium)
@show MOI.get(model, MOI.VariablePrimal(), denmark)
@show MOI.get(model, MOI.VariablePrimal(), france)
@show MOI.get(model, MOI.VariablePrimal(), germany)
@show MOI.get(model, MOI.VariablePrimal(), luxembourg)
@show MOI.get(model, MOI.VariablePrimal(), netherlands)
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