Metaheuristics - an Intuitive Package for Global Optimization

Author: Jesus Mejía (@jmejia8)

High performance algorithms for optimization purely coded in a high performance language.

Introduction

Optimization is one of the most common task in the scientific and industry field but real-world problems require high-performance algorithms to optimize non-differentiable, non-convex, dicontinuous functions. Different metaheuristics algorithms have been proposed to solve optimization problems but without strong assumptions about the objective function.

This package implements state-of-the-art metaheuristics algorithms for global optimization. The aim of this package is to provide easy to use (and fast) metaheuristics for numerical global optimization.

Installation

Open the Julia (Julia 1.0 or Later) REPL and press ] to open the Pkg prompt. To add this package, use the add command:

pkg> add Metaheuristics

Or, equivalently, via the Pkg API:

julia> import Pkg; Pkg.add("Metaheuristics")

Quick Start

Assume you want to solve the following minimization problem.

Rastrigin Surface

Minimize:

\[f(x) = 10D + \sum_{i=1}^{D} x_i^2 - 10\cos(2\pi x_i)\]

where $x\in[-5, 5]^{D}$, i.e., $-5 \leq x_i \leq 5$ for $i=1,\ldots,D$. $D$ is the dimension number, assume $D=10$.

Solution

Firstly, import the Metaheuristics package:

using Metaheuristics

Code the objective function:

f(x) = 10length(x) + sum( x.^2 - 10cos.(2π*x)  )

Instantiate the bounds, note that bounds should be a $2\times 10$ Matrix where the first row corresponds to the lower bounds whilst the second row corresponds to the upper bounds.

D = 10
bounds = [-5ones(D) 5ones(D)]'

Approximate the optimum using the function optimize.

result = optimize(f, bounds)

Optimize returns a State datatype which contains some information about the approximation. For instance, you may use mainly two functions to obtain such approximation.

@show minimum(result)
@show minimizer(result)