GCMAES.jl

GCMAES is a Julia package implementing the Gradient-based Covariance Matrix Adaptation Evolutionary Strategy, which can utilize the gradient information to speed up the optimization process.

Installation: OptimizationGCMAES.jl

To use this package, install the OptimizationGCMAES package:

import Pkg;
Pkg.add("OptimizationGCMAES");

Global Optimizer

Without Constraint Equations

The GCMAES algorithm is called by GCMAESOpt() and the initial search variance is set as a keyword argument σ0 (default: σ0 = 0.2)

The method in GCMAES is performing global optimization on problems without constraint equations. However, lower and upper constraints set by lb and ub in the OptimizationProblem are required.

GCMAESOpt()

Example

The Rosenbrock function can be optimized using the GCMAESOpt() without utilizing the gradient information as follows:

using OptimizationBase, OptimizationGCMAES
rosenbrock(x, p) = (p[1] - x[1])^2 + p[2] * (x[2] - x[1]^2)^2
x0 = zeros(2)
p = [1.0, 100.0]
f = OptimizationFunction(rosenbrock)
prob = OptimizationProblem(f, x0, p, lb = [-1.0, -1.0], ub = [1.0, 1.0])
sol = solve(prob, GCMAESOpt())

retcode: Success
u: 2-element Vector{Float64}:
 1.000000012637654
 1.0000000287797859

We can also utilize the gradient information of the optimization problem to aid the optimization as follows:

using ADTypes, ForwardDiff
f = OptimizationFunction(rosenbrock, ADTypes.AutoForwardDiff())
prob = OptimizationProblem(f, x0, p, lb = [-1.0, -1.0], ub = [1.0, 1.0])
sol = solve(prob, GCMAESOpt())

retcode: Success
u: 2-element Vector{Float64}:
 1.0000000021641313
 1.0000000046078465