Gradient-based Covariance Matrix Adaptation Evolutionary Strategy for Real Blackbox Optimization

using Pkg
pkg"add GCMAES"

• use low level BLAS operations to ensure performance
• use Elemental to do distributed eigendecomposition, which is crutial for high dimensional (>10000) problem
• compatible with julia's native parallelism
• compatible with MPI.jl, therefore suitable to be run on clusters without good TCP connections
• handling constraints and transformations

using GCMAES
D = 2000            # dimension of x
x0 = fill(0.3, D)   # initial x
σ0 = 0.2            # initial search variance
lo = fill(-5.12, D) # lower bound for each dimension
hi = fill(5.12, D)  # upper bound for each dimension

Minimize a blackbox function

rastrigin(x) = 10length(x) + sum(x.^2 .- 10 .* cos.(2π .* x))
xmin, fmin, status = GCMAES.minimize(rastrigin, x0, σ0, lo, hi, maxiter = 200)

If the optimization terminate prematurely before maxiter is reached, status will be 1, otherwise 0.

A checkpoint file named CMAES.bson will be created in the current working directory during optimization, which will be loaded back to initilize CMAESOpt if dimensions are equal.

You can speed up the optimization process by providing additional gradient infomation if the loss function is differentialble but noisy. The evolution part can help escaping local minima while the gradient part can speed up convergence in non-noisy regions.

using ForwardDiff
∇rastrigin(x) = ForwardDiff.gradient(rastrigin, x)
GCMAES.minimize((rastrigin, ∇rastrigin), x0, σ0, lo, hi, maxiter = 200)

You can also enable autodiff and then GCMAES will internally use Zygote to do the gradient calculation

using Zygote
GCMAES.minimize((rastrigin, ∇rastrigin), x0, σ0, lo, hi, maxiter = 200, autodiff = true)

Just simply add @mpirun before GCMAES.minimize

# ....
@mpirun GCMAES.minimize(...)
# ....

Then you can use mpirun -n N julia ... or julia -p N ... to start your job.