GalacticOptim.jl

GalacticOptim.jl is a package with a scope that is beyond your normal global optimization package. GalacticOptim.jl seeks to bring together all of the optimization packages it can find, local and global, into one unified Julia interface. This means, you learn one package and you learn them all! GalacticOptim.jl adds a few high-level features, such as integrating with automatic differentiation, to make its usage fairly simple for most cases, while allowing all of the options in a single unified interface.

Note: This package is still in active development.

Installation

Assuming that you already have Julia correctly installed, it suffices to import GalacticOptim.jl in the standard way:

import Pkg; Pkg.add("GalacticOptim")

The packages relevant to the core functionality of GalacticOptim.jl will be imported accordingly and, in most cases, you do not have to worry about the manual installation of dependencies. Below is the list of packages that need to be installed explicitly if you intend to use the specific optimization algorithms offered by them:

• BlackBoxOptim.jl (solver: BBO())
• NLopt.jl (usage via the NLopt API; see also the available algorithms)
• MultistartOptimization.jl (see also this documentation)
• QuadDIRECT.jl
• Evolutionary.jl (see also this documentation)
• CMAEvolutionStrategy.jl

Tutorials and Documentation

For information on using the package, see the stable documentation. Use the in-development documentation for the version of the documentation, which contains the unreleased features.

Examples

 using GalacticOptim, Optim
 rosenbrock(x,p) =  (p[1] - x[1])^2 + p[2] * (x[2] - x[1]^2)^2
 x0 = zeros(2)
 p  = [1.0,100.0]

 prob = OptimizationProblem(rosenbrock,x0,p)
 sol = solve(prob,NelderMead())


 using BlackBoxOptim
 prob = OptimizationProblem(rosenbrock, x0, p, lb = [-1.0,-1.0], ub = [1.0,1.0])
 sol = solve(prob,BBO())

Note that Optim.jl is a core dependency of GalaticOptim.jl. However, BlackBoxOptim.jl is not and must already be installed (see the list above).

Warning: The output of the second optimization task (BBO()) is currently misleading in the sense that it returns Status: failure (reached maximum number of iterations). However, convergence is actually reached and the confusing message stems from the reliance on the Optim.jl output struct (where the situation of reaching the maximum number of iterations is rightly regarded as a failure). The improved output struct will soon be implemented.

The output of the first optimization task (with the NelderMead() algorithm) is given below:

* Status: success

* Candidate solution
   Final objective value:     3.525527e-09

* Found with
   Algorithm:     Nelder-Mead

* Convergence measures
   √(Σ(yᵢ-ȳ)²)/n ≤ 1.0e-08

* Work counters
   Seconds run:   0  (vs limit Inf)
   Iterations:    60
   f(x) calls:    118

We can also explore other methods in a similar way:

 f = OptimizationFunction(rosenbrock, GalacticOptim.AutoForwardDiff())
 prob = OptimizationProblem(f, x0, p)
 sol = solve(prob,BFGS())

For instance, the above optimization task produces the following output:

* Status: success

* Candidate solution
   Final objective value:     7.645684e-21

* Found with
   Algorithm:     BFGS

* Convergence measures
   |x - x'|               = 3.48e-07 ≰ 0.0e+00
   |x - x'|/|x'|          = 3.48e-07 ≰ 0.0e+00
   |f(x) - f(x')|         = 6.91e-14 ≰ 0.0e+00
   |f(x) - f(x')|/|f(x')| = 9.03e+06 ≰ 0.0e+00
   |g(x)|                 = 2.32e-09 ≤ 1.0e-08

* Work counters
   Seconds run:   0  (vs limit Inf)
   Iterations:    16
   f(x) calls:    53
   ∇f(x) calls:   53

 prob = OptimizationProblem(f, x0, p, lb = [-1.0,-1.0], ub = [1.0,1.0])
 sol = solve(prob, Fminbox(GradientDescent()))

The examples clearly demonstrate that GalacticOptim.jl provides an intuitive way of specifying optimization tasks and offers a relatively easy access to a wide range of optimization algorithms.