GLPK.jl

GLPK.jl is a wrapper for the GNU Linear Programming Kit library.

The wrapper has two components:

• a thin wrapper around the complete C API
• an interface to MathOptInterface

Affiliation

This wrapper is maintained by the JuMP community and is not an GNU project.

License

GLPK.jl is licensed under the GPL v3 license.

Installation

Install GLPK using Pkg.add:

import Pkg
Pkg.add("GLPK")

In addition to installing the GLPK.jl package, this will also download and install the GLPK binaries. You do not need to install GLPK separately.

To use a custom binary, read the Custom solver binaries section of the JuMP documentation.

Use with JuMP

To use GLPK with JuMP, use GLPK.Optimizer:

using JuMP, GLPK
model = Model(GLPK.Optimizer)
set_attribute(model, "tm_lim", 60 * 1_000)
set_attribute(model, "msg_lev", GLPK.GLP_MSG_OFF)

If the model is primal or dual infeasible, GLPK will attempt to find a certificate of infeasibility. This can be expensive, particularly if you do not intend to use the certificate. If this is the case, use:

model = Model(() -> GLPK.Optimizer(; want_infeasibility_certificates = false))

MathOptInterface API

The GLPK optimizer supports the following constraints and attributes.

List of supported objective functions:

• MOI.ObjectiveFunction{MOI.ScalarAffineFunction{Float64}}

List of supported variable types:

• MOI.Reals

List of supported constraint types:

• MOI.ScalarAffineFunction{Float64} in MOI.EqualTo{Float64}
• MOI.ScalarAffineFunction{Float64} in MOI.GreaterThan{Float64}
• MOI.ScalarAffineFunction{Float64} in MOI.LessThan{Float64}
• MOI.VariableIndex in MOI.EqualTo{Float64}
• MOI.VariableIndex in MOI.GreaterThan{Float64}
• MOI.VariableIndex in MOI.Integer
• MOI.VariableIndex in MOI.Interval{Float64}
• MOI.VariableIndex in MOI.LessThan{Float64}
• MOI.VariableIndex in MOI.ZeroOne

List of supported model attributes:

• MOI.HeuristicCallback()
• MOI.LazyConstraintCallback()
• MOI.Name()
• MOI.ObjectiveSense()
• MOI.UserCutCallback()

Options

Options for GLPK are comprehensively documented in the PDF documentation, but they are hard to find.

• Options when solving a linear program are defined in Section 2.8.1
• Options when solving a mixed-integer program are defined in Section 2.10.5

However, the following options are likely to be the most useful:

Callbacks

Here is an example using GLPK's solver-specific callbacks.

using JuMP, GLPK, Test

model = Model(GLPK.Optimizer)
@variable(model, 0 <= x <= 2.5, Int)
@variable(model, 0 <= y <= 2.5, Int)
@objective(model, Max, y)
reasons = UInt8[]
function my_callback_function(cb_data)
    reason = GLPK.glp_ios_reason(cb_data.tree)
    push!(reasons, reason)
    if reason != GLPK.GLP_IROWGEN
        return
    end
    x_val = callback_value(cb_data, x)
    y_val = callback_value(cb_data, y)
    if y_val - x_val > 1 + 1e-6
        con = @build_constraint(y - x <= 1)
        MOI.submit(model, MOI.LazyConstraint(cb_data), con)
    elseif y_val + x_val > 3 + 1e-6
        con = @build_constraint(y - x <= 1)
        MOI.submit(model, MOI.LazyConstraint(cb_data), con)
    end
end
MOI.set(model, GLPK.CallbackFunction(), my_callback_function)
optimize!(model)
@test termination_status(model) == MOI.OPTIMAL
@test primal_status(model) == MOI.FEASIBLE_POINT
@test value(x) == 1
@test value(y) == 2
@show reasons

C API

The C API can be accessed via GLPK.glp_XXX functions, where the names and arguments are identical to the C API. See the /tests folder for inspiration.

Thread safety

GLPK is not thread-safe and should not be used with multithreading.