Metaheuristics.jl
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High-performance metaheuristics for optimization coded purely in Julia.
Metaheuristics
High-performance metaheuristics for 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")
Algorithms
Some representative metaheuristics are developed here, including those for single- and multi-objective optimization. Moreover, some constraint handling techniques have been considered in most of the implemented algorithms.
Single-Objective Optimization
- ECA: Evolutionary Centers Algorithm
- DE: Differential Evolution
- PSO: Particle Swarm Optimization
- ABC: Artificial Bee Colony
- GSA: Gravitational Search Algorithm
- SA: Simulated Annealing
- WOA: Whale Optimization Algorithm
- MCCGA: Machine-coded Compact Genetic Algorithm
- GA: Genetic Algorithm
Multi-Objective Optimization
- MOEA/D-DE: Multi-objective Evolutionary Algorithm based on Decomposition
- NSGA-II: A fast and elitist multi-objective genetic algorithm: NSGA-II
- NSGA-III: Evolutionary Many-Objective Optimization Algorithm Using Reference-Point-Based Nondominated Sorting Approach
- SMS-EMOA: An EMO algorithm using the hypervolume measure as the selection criterion
- SPEA2: Improved Strength Pareto Evolutionary Algorithm
- CCMO: Coevolutionary Framework for Constrained Multiobjective Optimization
Performance Indicators
- GD: Generational Distance
- IGD, IGD+: Inverted Generational Distance (Plus)
- C-metric: Covering Indicator
- HV: Hypervolume
- Δₚ (Delta p): Averaged Hausdorff distance
- Spacing Indicator
- and more...
Multi-Criteria Decision-Making
Multi-Criteria Decision Making methods are available, including:
- Compromise Programming
- Region of Interest Archiving
- Interface for JMcDM (a package for Multiple-criteria decision-making)
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 $x\in [-5, 5]^D$, that is, each coordinate in $x$ is between -5 and 5. Use $D=10$.
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 an approximation.
@show minimum(result)
@show minimizer(result)
Documentation
See the documentation for more details, examples and options.
Contributing
Please, be free to send me your PR, issue or any comment about this package for Julia.