Class CMAESOptimizer

java.lang.Object

org.apache.commons.math3.optim.BaseOptimizer<PointValuePair>

org.apache.commons.math3.optim.BaseMultivariateOptimizer<PointValuePair>

org.apache.commons.math3.optim.nonlinear.scalar.MultivariateOptimizer

org.apache.commons.math3.optim.nonlinear.scalar.noderiv.CMAESOptimizer

public class CMAESOptimizer
extends MultivariateOptimizer

An implementation of the active Covariance Matrix Adaptation Evolution Strategy (CMA-ES) for non-linear, non-convex, non-smooth, global function minimization.

The CMA-Evolution Strategy (CMA-ES) is a reliable stochastic optimization method which should be applied if derivative-based methods, e.g. quasi-Newton BFGS or conjugate gradient, fail due to a rugged search landscape (e.g. noise, local optima, outlier, etc.) of the objective function. Like a quasi-Newton method, the CMA-ES learns and applies a variable metric on the underlying search space. Unlike a quasi-Newton method, the CMA-ES neither estimates nor uses gradients, making it considerably more reliable in terms of finding a good, or even close to optimal, solution.

In general, on smooth objective functions the CMA-ES is roughly ten times slower than BFGS (counting objective function evaluations, no gradients provided). For up to $N=10$ variables also the derivative-free simplex direct search method (Nelder and Mead) can be faster, but it is far less reliable than CMA-ES.

The CMA-ES is particularly well suited for non-separable and/or badly conditioned problems. To observe the advantage of CMA compared to a conventional evolution strategy, it will usually take about $30\; N$ function evaluations. On difficult problems the complete optimization (a single run) is expected to take roughly between $30\; N$ and $300\; N2$ function evaluations.

This implementation is translated and adapted from the Matlab version of the CMA-ES algorithm as implemented in module cmaes.m version 3.51.

For more information, please refer to the following links:

• Matlab code
• Introduction to CMA-ES
• Wikipedia

Since:

3.0

Nested Class Summary

Nested Classes

Modifier and Type	Class	Description
static class	CMAESOptimizer.PopulationSize	Population size.
static class	CMAESOptimizer.Sigma	Input sigma values.

Field Summary

Fields inherited from class BaseOptimizer

evaluations

Constructor Summary

Constructors

Constructor	Description
CMAESOptimizer(int maxIterations, double stopFitness, boolean isActiveCMA, int diagonalOnly, int checkFeasableCount, RandomGenerator random, boolean generateStatistics, ConvergenceChecker<PointValuePair> checker)

Method Summary

Modifier and Type	Method	Description
protected PointValuePair	doOptimize()	Performs the bulk of the optimization algorithm.
List<RealMatrix>	getStatisticsDHistory()
List<Double>	getStatisticsFitnessHistory()
List<RealMatrix>	getStatisticsMeanHistory()
List<Double>	getStatisticsSigmaHistory()
PointValuePair	optimize(OptimizationData... optData)	Stores data and performs the optimization.
protected void	parseOptimizationData(OptimizationData... optData)	Scans the list of (required and optional) optimization data that characterize the problem.

Methods inherited from class MultivariateOptimizer

computeObjectiveValue, getGoalType

Methods inherited from class BaseMultivariateOptimizer

getLowerBound, getStartPoint, getUpperBound

Methods inherited from class BaseOptimizer

getConvergenceChecker, getEvaluations, getIterations, getMaxEvaluations, getMaxIterations, incrementEvaluationCount, incrementIterationCount, optimize

Methods inherited from class Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Details

CMAESOptimizer

public CMAESOptimizer(int maxIterations,
 double stopFitness,
 boolean isActiveCMA,
 int diagonalOnly,
 int checkFeasableCount,
 RandomGenerator random,
 boolean generateStatistics,
 ConvergenceChecker<PointValuePair> checker)

Parameters:

maxIterations - Maximal number of iterations.

stopFitness - Whether to stop if objective function value is smaller than stopFitness.

isActiveCMA - Chooses the covariance matrix update method.

diagonalOnly - Number of initial iterations, where the covariance matrix remains diagonal.

checkFeasableCount - Determines how often new random objective variables are generated in case they are out of bounds.

random - Random generator.

generateStatistics - Whether statistic data is collected.

checker - Convergence checker.

Since:

3.1

Method Details

getStatisticsSigmaHistory

public List<Double> getStatisticsSigmaHistory()

Returns:

History of sigma values.

getStatisticsMeanHistory

public List<RealMatrix> getStatisticsMeanHistory()

Returns:

History of mean matrix.

getStatisticsFitnessHistory

public List<Double> getStatisticsFitnessHistory()

Returns:

History of fitness values.

getStatisticsDHistory

public List<RealMatrix> getStatisticsDHistory()

Returns:

History of D matrix.

optimize

public PointValuePair optimize(OptimizationData... optData)
                        throws TooManyEvaluationsException,
DimensionMismatchException

Stores data and performs the optimization.

The list of parameters is open-ended so that sub-classes can extend it with arguments specific to their concrete implementations.

When the method is called multiple times, instance data is overwritten only when actually present in the list of arguments: when not specified, data set in a previous call is retained (and thus is optional in subsequent calls).

Important note: Subclasses must override BaseOptimizer.parseOptimizationData(OptimizationData[]) if they need to register their own options; but then, they must also call super.parseOptimizationData(optData) within that method.

Overrides:

optimize in class MultivariateOptimizer

Parameters:

optData - Optimization data. In addition to those documented in MultivariateOptimizer, this method will register the following data:

• CMAESOptimizer.Sigma
• CMAESOptimizer.PopulationSize

Returns:

a point/value pair that satisfies the convergence criteria.

Throws:

TooManyEvaluationsException - if the maximal number of evaluations is exceeded.

DimensionMismatchException - if the initial guess, target, and weight arguments have inconsistent dimensions.

doOptimize

protected PointValuePair doOptimize()

Performs the bulk of the optimization algorithm.

Specified by:

doOptimize in class BaseOptimizer<PointValuePair>

Returns:

the point/value pair giving the optimal value of the objective function.

parseOptimizationData

protected void parseOptimizationData(OptimizationData... optData)

Scans the list of (required and optional) optimization data that characterize the problem.

Overrides:

parseOptimizationData in class MultivariateOptimizer

Parameters:

optData - Optimization data. The following data will be looked for:

• CMAESOptimizer.Sigma
• CMAESOptimizer.PopulationSize