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API References

Metaheuristics.optimize — Function
  optimize(
        f::Function, # objective function
        search_space,
        method::AbstractAlgorithm = ECA();
        logger::Function = (status) -> nothing,
  )

Minimize a n-dimensional function f with domain search_space (2×n matrix) using method = ECA() by default.

Example

Minimize f(x) = Σx² where x ∈ [-10, 10]³.

Solution:

julia> f(x) = sum(x.^2)
f (generic function with 1 method)

julia> bounds = [  -10.0 -10 -10; # lower bounds
                    10.0  10 10 ] # upper bounds
2×3 Array{Float64,2}:
 -10.0  -10.0  -10.0
  10.0   10.0   10.0

julia> result = optimize(f, bounds)
+=========== RESULT ==========+
  iteration: 1429
    minimum: 2.5354499999999998e-222
  minimizer: [-1.5135301653303966e-111, 3.8688354844737692e-112, 3.082095708730726e-112]
    f calls: 29989
 total time: 0.1543 s
+============================+
optimize(F, f, bounds_ul, bounds_ll, method = BCA(); logger = (status) -> nothing)

Approximate an optimal solution for the bilevel optimization problem x ∈ argmin F(x, y) with x ∈ bounds_ul subject to y ∈ argmin{f(x,y) : y ∈ bounds_ll}.

Parameters

  • F upper-level objective function.
  • f lower-level objective function.
  • bounds_ul, bounds_ll upper and lower level boundaries (2×n matrices), respectively.
  • logger is a functions called at the end of each iteration.

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
+============================+
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