BilevelJuMP.jl is a JuMP extension for modeling and solving bilevel optimization problems.
BilevelJuMP.jl is licensed under the MIT license.
You can find the documentation at https://joaquimg.github.io/BilevelJuMP.jl/stable/.
If you need help, please open a GitHub issue.
import Pkg
Pkg.add("BilevelJuMP")
Pkg.add("HiGHS")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...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.