Expand description
An 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.
Overview
There are three main ways to use cmaes:
The quickest and easiest way is to use a convenience function provided in the functions
module, such as fmin or fmax:
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);Further configuration of a run can be performed by creating and building a CMAESOptions and
calling CMAES::run or CMAES::run_parallel. This option provides the most flexibility and
customization and allows for visualizing runs through data plots (see Plot; requires the
plotters feature).
use cmaes::{CMAESOptions, DVector};
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)
.fun_target(1e-8)
.enable_printing(200)
.max_generations(20000)
.build(sphere)
.unwrap();
let results = cmaes_state.run();For many problems, it is useful to perform multiple independent restarts of the algorithm with
varying initial parameters. The restart module implements several automatic restart
strategies to this end. To use them, create and build a
RestartOptions and call
Restarter::run,
Restarter::run_parallel, or another run_*
method. This option provides greater robustness in solving more complex
problems but provides less control over individual runs and cannot produce data plots.
use cmaes::restart::{RestartOptions, RestartStrategy};
use cmaes::DVector;
let sphere = |x: &DVector<f64>| x.iter().map(|xi| xi.powi(2)).sum();
let dim = 10;
let strategy = RestartStrategy::BIPOP(Default::default());
let restarter = RestartOptions::new(dim, -5.0..=5.0, strategy)
.fun_target(1e-8)
.enable_printing(true)
.build()
.unwrap();
let results = restarter.run_parallel(|| sphere);Further configuration
CMAESOptions provides many configurable parameters and can be used to tune the algorithm to
each particular problem (though this is usually unnecessary beyond changing the initial mean and
step size).
The objective_function module provides traits that allow for custom objective function types
that store state and parameters.
The CMAES::next method provides finer control over iteration if needed.
Citations
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.
Re-exports
pub use crate::functions::*;pub use crate::objective_function::ObjectiveFunction;pub use crate::objective_function::ParallelObjectiveFunction;pub use crate::options::CMAESOptions;pub use crate::termination::TerminationReason;Modules
Convenience functions for easier use of the library.
Traits for types that can be used as an objective function, as well as wrapper types that modify the behavior of objective functions.
Types related to initializing a CMAES. See CMAESOptions for full documentation.
Initialization of constant parameters of the algorithm.
Types for automatic restarting of CMA-ES. Useful for solving complex problems and improving the robustness of the algorithm in general.
Algorithm termination handling. See TerminationReason for full documentation.
Structs
A type that handles algorithm iteration and printing/plotting of results. Use CMAESOptions
to create a CMAES.
An individual point with its corresponding objective function value.
Configuration of the data plot.
Data returned when the algorithm terminates.
Enums
The mode to use when optimizing a function.
The distribution of weights for the population. The default value is Negative.
Constants
The maximum number of elements to store in the objective function value histories.
Type Definitions
A dynamically sized column vector.