A Julia implementation of the Black-Box-Optimization-Benchmarking (BBOB) functions.

The average sucess rate (meaning the optimizer reached the minimum + 1e-6) in function of the number of objective function evaluations :

Since some global optimizers have poor final convergence, they were chained into a Nelder-Mead using 10% of the objective function evaluation budget.

Note that the Python algorithms are called from Julia, which might cause some overhead.

Functions can be accessed as `BlackBoxOptimizationBenchmarking.F1`

, which returns a `BBOBFunction`

with fields `f`

containing the function itself, `f_opt`

its minimal value, and `x_opt`

its minimizer, i.e. `f(x_opt) = f_opt`

.

Functions can be listed using `list_functions()`

:

```
julia> BlackBoxOptimizationBenchmarking.list_functions()
20-element Array{BlackBoxOptimizationBenchmarking.BBOBFunction,1}:
Sphere
Ellipsoidal Function
Discus Function
Bent Cigar Function
Sharp Ridge Function
Different Powers Function
Rastrigin Function
Weierstrass Function
Schaffers F7 Function
Schaffers F7 Function, moderately ill-conditioned
Composite Griewank-Rosenbrock Function F8F2
Ellipsoidal
Schwefel Function
Rastrigin
Buche-Rastrigin
Linear Slope
Attractive Sector
Step Ellipsoidal Function
Rosenbrock Function, original
Rosenbrock Function, rotated
```

A benchmark for a single optimizer and function can be run with:

`benchmark(optimizer::Any, f::BBOBFunction, run_lengths, Ntrials, dimensions, Δf)`

Or for a collection of optimizers with:

`benchmark(optimizers::Vector{T}, funcs, run_lengths, Ntrials, dimensions, Δf)`

See test/runtests.jl

The optimizer must implement the methods `optimize`

, `minimum`

and `minimizer`

, see

scripts/optimizers_interface.jl

To avoid overfiting and test if algorithms are robust with respect to rotations of the error function, rotation matrices are randomly generated the first time the package is used.

If needed new rotations can be generated by running the following:

```
@eval BlackBoxOptimizationBenchmarking begin
@memoize function Q(D)
r = randn(D); r = r/norm(r)
Q = [r nullspace(Matrix(r'))]
end
@memoize function R(D)
r = randn(D); r = r/norm(r)
R = [r nullspace(Matrix(r'))]
end
end
```

http://coco.lri.fr/downloads/download15.01/bbobdocfunctions.pdf