Class CMAESOptimizer
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 \(300 n^2\) 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:
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Nested Class Summary
Modifier and TypeClassDescriptionstatic class
Population size.static class
Input sigma values. -
Field Summary
Fields inherited from class org.hipparchus.optim.BaseOptimizer
evaluations
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Constructor Summary
ConstructorDescriptionCMAESOptimizer
(int maxIterations, double stopFitness, boolean isActiveCMA, int diagonalOnly, int checkFeasableCount, RandomGenerator random, boolean generateStatistics, ConvergenceChecker<PointValuePair> checker) Simple constructor. -
Method Summary
Modifier and TypeMethodDescriptionprotected PointValuePair
Performs the bulk of the optimization algorithm.Get history of D matrix.Get history of fitness values.Get history of mean matrix.Get history of sigma values.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 org.hipparchus.optim.nonlinear.scalar.MultivariateOptimizer
computeObjectiveValue, getGoalType
Methods inherited from class org.hipparchus.optim.BaseMultivariateOptimizer
getLowerBound, getStartPoint, getUpperBound
Methods inherited from class org.hipparchus.optim.BaseOptimizer
getConvergenceChecker, getEvaluations, getIterations, getMaxEvaluations, getMaxIterations, incrementEvaluationCount, incrementIterationCount, optimize
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Constructor Details
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CMAESOptimizer
public CMAESOptimizer(int maxIterations, double stopFitness, boolean isActiveCMA, int diagonalOnly, int checkFeasableCount, RandomGenerator random, boolean generateStatistics, ConvergenceChecker<PointValuePair> checker) Simple constructor.- Parameters:
maxIterations
- Maximal number of iterations.stopFitness
- Whether to stop if objective function value is smaller thanstopFitness
.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.
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Method Details
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getStatisticsSigmaHistory
Get history of sigma values.- Returns:
- History of sigma values
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getStatisticsMeanHistory
Get history of mean matrix.- Returns:
- History of mean matrix
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getStatisticsFitnessHistory
Get history of fitness values.- Returns:
- History of fitness values
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getStatisticsDHistory
Get history of D matrix.- Returns:
- History of D matrix
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optimize
public PointValuePair optimize(OptimizationData... optData) throws MathIllegalArgumentException, MathIllegalStateException 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 callsuper.parseOptimizationData(optData)
within that method.- Overrides:
optimize
in classMultivariateOptimizer
- Parameters:
optData
- Optimization data. In addition to those documented inMultivariateOptimizer
, this method will register the following data:- Returns:
- a point/value pair that satisfies the convergence criteria.
- Throws:
MathIllegalStateException
- if the maximal number of evaluations is exceeded.MathIllegalArgumentException
- if the initial guess, target, and weight arguments have inconsistent dimensions.
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doOptimize
Performs the bulk of the optimization algorithm.- Specified by:
doOptimize
in classBaseOptimizer<PointValuePair>
- Returns:
- the point/value pair giving the optimal value of the objective function.
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parseOptimizationData
Scans the list of (required and optional) optimization data that characterize the problem.- Overrides:
parseOptimizationData
in classMultivariateOptimizer
- Parameters:
optData
- Optimization data. The following data will be looked for:
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