# BilevelHeuristics - Heuristics and Metaheuristics for Bilevel Optimization

Author: Jesus Mejía (@jmejia8)

Approximate algorithms for bilevel optimization.

## Introduction

Bilevel Optimization is a very challenging task that require high-performance algorithms to optimize hierarchical problem. This package implements a variety of approximate algorithms for bilevel optimization.

BilevelHeuristics extends the Metaheuristics.jl API to implement bilevel optimization algorithms.

## Installation

Open the Julia (Julia 1.6 or later) REPL and press ] to open the Pkg prompt. To add this package, use the add command:

Or, equivalently, via the Pkg API:

## Example

julia> F(x, y) = sum(x.^2) + sum(y.^2)
F (generic function with 1 method)

julia> f(x, y) = sum((x - y).^2) + y[1]^2
f (generic function with 1 method)

julia> bounds_ul = bounds_ll = [-ones(5)'; ones(5)']
2×5 Matrix{Float64}:
-1.0  -1.0  -1.0  -1.0  -1.0
1.0   1.0   1.0   1.0   1.0

julia> res = optimize(F, f, bounds_ul, bounds_ll)
+=========== RESULT ==========+
iteration: 108
minimum:
F: 7.68483e-08
f: 3.96871e-09
minimizer:
x: [1.0283390421119262e-5, -0.00017833559080058394, -1.612275010196171e-5, 0.00012064585960330227, 4.38964383738248e-5]
y: [1.154609166391327e-5, -0.0001300400306798623, 1.1811981430188257e-6, 8.868498295184257e-5, 5.732849695863675e-5]
F calls: 2503
f calls: 5044647
Message: Stopped due UL function evaluations limitations.
total time: 21.4550 s
+============================+