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

## Installation

using Pkg
pkg"add GCMAES"

## Features

- 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

## Basic Usage

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.

## Incoporating Gradient

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)

## Parallel Usage

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.