BilevelJuMP.jl

BilevelJuMP.jl is a JuMP extension for modeling and solving bilevel optimization problems.

License

BilevelJuMP.jl is licensed under the MIT license.

Documentation

You can find the documentation at https://joaquimg.github.io/BilevelJuMP.jl/stable/.

Help

If you need help, please open a GitHub issue.

Example

Install

import Pkg
Pkg.add("BilevelJuMP")
Pkg.add("HiGHS")

Run

using BilevelJuMP, HiGHS

model = BilevelModel(
    HiGHS.Optimizer,
    mode = BilevelJuMP.FortunyAmatMcCarlMode(primal_big_M = 100, dual_big_M = 100)
)

@variable(Lower(model), x)
@variable(Upper(model), y)

@objective(Upper(model), Min, 3x + y)
@constraints(Upper(model), begin
    x <= 5
    y <= 8
    y >= 0
end)

@objective(Lower(model), Min, -x)
@constraints(Lower(model), begin
     x +  y <= 8
    4x +  y >= 8
    2x +  y <= 13
    2x - 7y <= 0
end)

optimize!(model)

objective_value(model) # = 3 * (3.5 * 8/15) + 8/15 # = 6.13...
value(x) # = 3.5 * 8/15 # = 1.86...
value(y) # = 8/15 # = 0.53...

Citing BilevelJuMP

If you use BilevelJuMP.jl, we ask that you please cite the following paper:

@article{diasgarcia2023bileveljump,
    title = {{BilevelJuMP.jl}: {M}odeling and {S}olving {B}ilevel {O}ptimization {P}roblems in {J}ulia},
    author = {{Dias Garcia}, Joaquim and Bodin, Guilherme and Street, Alexandre},
    journal = {INFORMS Journal on Computing},
    doi = {https://doi.org/10.1287/ijoc.2022.0135},
    pages = {1-9},
    year = {2023}
}

Here is an earlier preprint.