BLEMO

[hahaya001]

If there is an example for bilevel multi-objective problem with constrained conditon using BLEMO algorithm.

[jmejia8]

Here is an example:

using BilevelHeuristics

# upper-level objective function
function F(x, y)
    F1 = y[1] - x[1]   # objective function 1
    F2 = y[2]          # objective function 2
    G1 = -1.0 - sum(y) # G(x,y) <= 0 is feasible
    H1 = 0.0            # equality constraint

    Fxy = [F1, F2]
    Gxy = [G1]
    Hxy = [H1]

    return Fxy, Gxy, Hxy
end

# lower-level objective function
function f(x, y)
    f1 = y[1]   # objective function 1
    f2 = y[2]   # objective function 2
    g1 = sum(y.^2) - x[1]^2 # g(x,y) <= 0 is feasible
    h1 = 0.0                # equality constraint

    fxy = [f1, f2]
    gxy = [g1]
    hxy = [h1]

    return fxy, gxy, hxy
end

# boundaries by cols
bounds_ul = Matrix([0.0 1]')
bounds_ll = [-1.0 -1.0; 1.0 1.0]

# general options (settings)
options_ul = Options(iterations = 40, f_calls_limit=Inf, seed=1) # upper level
options_ll = Options(iterations = 40, f_calls_limit=Inf) # lower level

# Optimizer for each level
nsga2_ul = NSGA2(N = 400, p_m = 0.1, η_m = 20, η_cr = 15, p_cr = 0.9)
nsga2_ll = NSGA2(N = 40,  p_m = 0.1, η_m = 20, η_cr = 15, p_cr = 0.9)

blemo = BLEMO(;ul = nsga2_ul, ll = nsga2_ll, options_ul, options_ll)
results = optimize(F, f, bounds_ul, bounds_ll, blemo);

# Get values saved in the archive
A_ul = map(s -> s[1], blemo.parameters.archive) # upper level
A_ll = map(s -> s[2], blemo.parameters.archive) # corresponding lower level

# get objective function values 
Fxy = fvals(A_ul)
fxy = fvals(A_ll)

X = positions(A_ul)
Y = positions(A_ll)

You can save this code into test_blemo.jl and execute it in the Julia command line using include("test_blemo.jl")`

See here for more details.