# 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 1.1 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.

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)