public class CMAESOptimizer extends BaseAbstractMultivariateSimpleBoundsOptimizer<MultivariateFunction> implements 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 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 function evaluations. On difficult problems the complete optimization (a single run) is expected to take roughly between and 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.
Modifier and Type | Field and Description |
---|---|
static int |
DEFAULT_CHECKFEASABLECOUNT
Default value for
checkFeasableCount : 0. |
static int |
DEFAULT_DIAGONALONLY
Default value for
diagonalOnly : 0. |
static boolean |
DEFAULT_ISACTIVECMA
Default value for
isActiveCMA : true. |
static int |
DEFAULT_MAXITERATIONS
Default value for
maxIterations : 30000. |
static RandomGenerator |
DEFAULT_RANDOMGENERATOR
Default value for
random . |
static double |
DEFAULT_STOPFITNESS
Default value for
stopFitness : 0.0. |
evaluations
Constructor and Description |
---|
CMAESOptimizer()
Default constructor, uses default parameters
|
CMAESOptimizer(int lambda) |
CMAESOptimizer(int lambda,
double[] inputSigma) |
CMAESOptimizer(int lambda,
double[] inputSigma,
int maxIterations,
double stopFitness,
boolean isActiveCMA,
int diagonalOnly,
int checkFeasableCount,
RandomGenerator random,
boolean generateStatistics) |
CMAESOptimizer(int lambda,
double[] inputSigma,
int maxIterations,
double stopFitness,
boolean isActiveCMA,
int diagonalOnly,
int checkFeasableCount,
RandomGenerator random,
boolean generateStatistics,
ConvergenceChecker<PointValuePair> checker) |
Modifier and Type | Method and Description |
---|---|
protected PointValuePair |
doOptimize()
Perform the bulk of the optimization algorithm.
|
List<RealMatrix> |
getStatisticsDHistory() |
List<Double> |
getStatisticsFitnessHistory() |
List<RealMatrix> |
getStatisticsMeanHistory() |
List<Double> |
getStatisticsSigmaHistory() |
getLowerBound, getUpperBound, optimize, optimize
computeObjectiveValue, getConvergenceChecker, getEvaluations, getGoalType, getMaxEvaluations, getStartPoint
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
optimize
getConvergenceChecker, getEvaluations, getMaxEvaluations
public static final int DEFAULT_CHECKFEASABLECOUNT
checkFeasableCount
: 0.public static final double DEFAULT_STOPFITNESS
stopFitness
: 0.0.public static final boolean DEFAULT_ISACTIVECMA
isActiveCMA
: true.public static final int DEFAULT_MAXITERATIONS
maxIterations
: 30000.public static final int DEFAULT_DIAGONALONLY
diagonalOnly
: 0.public static final RandomGenerator DEFAULT_RANDOMGENERATOR
random
.public CMAESOptimizer()
public CMAESOptimizer(int lambda)
lambda
- Population size.public CMAESOptimizer(int lambda, double[] inputSigma)
lambda
- Population size.inputSigma
- Initial search volume; sigma of offspring objective variables.public CMAESOptimizer(int lambda, double[] inputSigma, int maxIterations, double stopFitness, boolean isActiveCMA, int diagonalOnly, int checkFeasableCount, RandomGenerator random, boolean generateStatistics)
lambda
- Population size.inputSigma
- Initial search volume; sigma of offspring objective variables.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.public CMAESOptimizer(int lambda, double[] inputSigma, int maxIterations, double stopFitness, boolean isActiveCMA, int diagonalOnly, int checkFeasableCount, RandomGenerator random, boolean generateStatistics, ConvergenceChecker<PointValuePair> checker)
lambda
- Population size.inputSigma
- Initial search volume; sigma of offspring objective variables.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.public List<Double> getStatisticsSigmaHistory()
public List<RealMatrix> getStatisticsMeanHistory()
public List<Double> getStatisticsFitnessHistory()
public List<RealMatrix> getStatisticsDHistory()
protected PointValuePair doOptimize()
doOptimize
in class BaseAbstractMultivariateOptimizer<MultivariateFunction>
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