MiniZinc.jl

MiniZinc.jl is a wrapper for the MiniZinc constraint modeling language.

It provides a way to write MathOptInterface models to .mzn files, and a way to interact with libminizinc.

Affiliation

This wrapper is maintained by the JuMP community and is not part of the MiniZinc project.

License

MiniZinc.jl is licensed under the MIT License.

The underlying project, MiniZinc/libminizinc, is licensed under the MPL 2.0 license.

Install

Install MiniZinc.jl using the Julia package manager:

import Pkg
Pkg.add("MiniZinc")

Windows

On Linux and macOS, this package automatically installs libminizinc. However, we're still working out problems with the install on Windows. To use MiniZinc.jl, you'll need to manually install a copy of libminizinc from minizinc.org or compile one yourself from MiniZinc/libminizinc.

To teach MiniZinc.jl where to look for libminizinc, set the JULIA_LIBMINIZINC_DIR environment variable. For example:

ENV["JULIA_LIBMINIZINC_DIR"] = "C:\\Program Files\\MiniZinc"

Use with MathOptInterface

MiniZinc.jl supports the constraint programming sets defined in MathOptInterface, as well as (in)equality constraints.

The following example solves the following constraint program:

xᵢ ∈ {1, 2, 3} ∀i=1,2,3
zⱼ ∈ {0, 1}    ∀j=1,2
z₁ <-> x₁ != x₂
z₂ <-> x₂ != x₃
z₁ + z₂ = 1

julia> import MiniZinc

julia> import MathOptInterface as MOI

julia> function main()
           model = MOI.Utilities.CachingOptimizer(
               MiniZinc.Model{Int}(),
               MiniZinc.Optimizer{Int}("chuffed"),
           )
           # xᵢ ∈ {1, 2, 3} ∀i=1,2,3
           x = MOI.add_variables(model, 3)
           MOI.add_constraint.(model, x, MOI.Interval(1, 3))
           MOI.add_constraint.(model, x, MOI.Integer())
           # zⱼ ∈ {0, 1}    ∀j=1,2
           z = MOI.add_variables(model, 2)
           MOI.add_constraint.(model, z, MOI.ZeroOne())
           # z₁ <-> x₁ != x₂
           MOI.add_constraint(
               model,
               MOI.VectorOfVariables([z[1], x[1], x[2]]),
               MOI.Reified(MOI.AllDifferent(2)),
           )
           # z₂ <-> x₂ != x₃
           MOI.add_constraint(
               model,
               MOI.VectorOfVariables([z[2], x[2], x[3]]),
               MOI.Reified(MOI.AllDifferent(2)),
           )
           # z₁ + z₂ = 1
           MOI.add_constraint(model, 1 * z[1] + x[2], MOI.EqualTo(1))
           MOI.optimize!(model)
           x_star = MOI.get(model, MOI.VariablePrimal(), x)
           z_star = MOI.get(model, MOI.VariablePrimal(), z)
           return x_star, z_star
       end
main (generic function with 1 method)

julia> main()
([1, 1, 3], [0, 1])

Use with JuMP

You can also call MiniZinc from JuMP, using any solver that libminizinc supports. By default, MiniZinc.jl is compiled with the HiGHS MILP solver, which can be selected by passing the "highs" parameter to MiniZinc.Optimizer:

using JuMP
import MiniZinc
model = Model(() -> MiniZinc.Optimizer{Float64}("highs"))
@variable(model, 1 <= x[1:3] <= 3, Int)
@constraint(model, x in MOI.AllDifferent(3))
@objective(model, Max, sum(i * x[i] for i in 1:3))
optimize!(model)
@show value.(x)

MathOptInterface API

The MiniZinc Optimizer{T} supports the following constraints and attributes.

List of supported objective functions:

• MOI.ObjectiveFunction{MOI.ScalarAffineFunction{T}}
• MOI.ObjectiveFunction{MOI.ScalarQuadraticFunction{T}}
• MOI.ObjectiveFunction{MOI.VariableIndex}

List of supported variable types:

• MOI.Reals

List of supported constraint types:

• MOI.ScalarAffineFunction{T} in MOI.EqualTo{T}
• MOI.ScalarAffineFunction{T} in MOI.GreaterThan{T}
• MOI.ScalarAffineFunction{T} in MOI.Integer
• MOI.ScalarAffineFunction{T} in MOI.Interval{T}
• MOI.ScalarAffineFunction{T} in MOI.LessThan{T}
• MOI.ScalarAffineFunction{T} in MOI.ZeroOne
• MOI.VariableIndex in MOI.EqualTo{T}
• MOI.VariableIndex in MOI.GreaterThan{T}
• MOI.VariableIndex in MOI.Integer
• MOI.VariableIndex in MOI.Interval{T}
• MOI.VariableIndex in MOI.LessThan{T}
• MOI.VariableIndex in MOI.Parameter{T}
• MOI.VariableIndex in MOI.Semicontinuous{T}
• MOI.VariableIndex in MOI.Semiinteger{T}
• MOI.VariableIndex in MOI.ZeroOne
• MOI.VectorOfVariables in MOI.AllDifferent
• MOI.VectorOfVariables in MOI.BinPacking{T}
• MOI.VectorOfVariables in MOI.Circuit
• MOI.VectorOfVariables in MOI.CountAtLeast
• MOI.VectorOfVariables in MOI.CountBelongs
• MOI.VectorOfVariables in MOI.CountDistinct
• MOI.VectorOfVariables in MOI.CountGreaterThan
• MOI.VectorOfVariables in MOI.Cumulative
• MOI.VectorOfVariables in MOI.Path
• MOI.VectorOfVariables in MOI.Table{T}

List of supported model attributes:

• MOI.NLPBlock()
• MOI.Name()
• MOI.ObjectiveSense()

Options

Set options using MOI.RawOptimizerAttribute in MOI or set_attribute in JuMP.

MiniZinc.jl supports the following options:

• model_filename::String = "": the location at which to write out the .mzn file during optimization. This option can be helpful during debugging. If left empty, a temporary file will be used instead.