#optimization #nalgebra #plot


An implementation of the CMA-ES optimization algorithm

4 releases

0.2.1 May 18, 2022
0.2.0 Apr 21, 2022
0.1.1 Mar 4, 2022
0.1.0 Feb 16, 2022

#413 in Algorithms

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Crates.io Rust

A Rust implementation of the CMA-ES optimization algorithm. It is used to minimize or maximize the value of an objective function and performs well on high-dimension, non-linear, non-convex, ill-conditioned, and/or noisy problems. See this paper for details on the algorithm itself.


cmaes uses some external libraries, so the following dependencies are required:

  • Rust (tested with rustc 1.57, earlier versions may work)
  • FreeType (required for plotters feature, enabled by default)
  • Depending on the selected LAPACK implementation (which can be enabled by feature, but by default is not), you need the libraries for that particular choice, which is at least
    • Make
    • CMake
    • A C compiler
    • A Fortran compiler (GCC's gfortran works)

Quick Start

Add this to your Cargo.toml:

cmaes = "0.2"

The LAPACK implementation used may be selected through Cargo features (see Cargo.toml). By default, pure Rust implementation from nalgebra is used.

Then, to optimize a function:

use cmaes::DVector;

let sphere = |x: &DVector<f64>| x.iter().map(|xi| xi.powi(2)).sum();
let dim = 10;
let solution = cmaes::fmin(sphere, vec![5.0; dim], 1.0);

More options can be accessed through the CMAESOptions type, including data plots (requires the plotters feature):

use cmaes::{CMAESOptions, DVector, PlotOptions};

let sphere = |x: &DVector<f64>| x.iter().map(|xi| xi.powi(2)).sum();

let dim = 10;
let mut cmaes_state = CMAESOptions::new(vec![1.0; dim], 1.0)
    .enable_plot(PlotOptions::new(0, false))

let results = cmaes_state.run();

cmaes_state.get_plot().unwrap().save_to_file("plot.png", true).unwrap();

The produced plot will look like this:

For more complex problems, automatic restarts are also provided:

use cmaes::restart::{RestartOptions, RestartStrategy};
use cmaes::DVector;

let sphere = |x: &DVector<f64>| x.iter().map(|xi| xi.powi(2)).sum();

let strategy = RestartStrategy::BIPOP(Default::default());
let dim = 10;
let search_range = -5.0..=5.0;
let restarter = RestartOptions::new(dim, search_range, strategy)

let results = restarter.run(|| sphere);

For more information, see the documentation and examples.


The library's tests can be run with cargo test --release. Note that some tests may fail occasionally due to the random nature of the algorithm, but as long as no tests fail consistently then they can be considered to have passed.

Benchmarks can be run with cargo bench.


Contributions are welcome! You can contribute by reporting any bugs or issues you have with the library, adding documentation, or opening pull requests.

Unless you explicitly state otherwise, any contribution intentionally submitted for inclusion in the work by you, as defined in the Apache-2.0 license, shall be dual licensed as below, without any additional terms or conditions.


Licensed under either of

Apache License, Version 2.0, (LICENSE-APACHE or http://www.apache.org/licenses/LICENSE-2.0)
MIT license (LICENSE-MIT or http://opensource.org/licenses/MIT)

at your option.


The following contain more detailed information on the algorithms implemented by this library or were referenced in its implementation.

Auger, Anne and Hansen, Nikolaus. “A Restart CMA Evolution Strategy with Increasing Population Size.” 2005 IEEE Congress on Evolutionary Computation, vol. 2, 2005, pp. 1769-1776 Vol. 2, https://doi.org/10.1109/CEC.2005.1554902.

Hansen, Nikolaus. “Benchmarking a BI-Population CMA-ES on the BBOB-2009 Function Testbed.” GECCO (Companion), July 2009, https://doi.org/10.1145/1570256.1570333.

Auger, Anne, and Nikolaus Hansen. Tutorial CMA-ES. 2013, https://doi.org/10.1145/2464576.2483910.

Hansen, Nikolaus, Akimoto, Youhei, and Baudis, Petr. CMA-ES/Pycma on Github. Feb. 2019, https://doi.org/10.5281/zenodo.2559634.


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