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

```java.lang.Object
org.apache.commons.math3.optim.BaseOptimizer<PAIR>
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 CMAESOptimizerextends 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.

Since:
3.0
Version:
\$Id: CMAESOptimizer.java 1462503 2013-03-29 15:48:27Z luc \$

Nested Class Summary
`static class` `CMAESOptimizer.PopulationSize`
Population size.
`static class` `CMAESOptimizer.Sigma`
Input sigma values.

Field Summary

Fields inherited from class org.apache.commons.math3.optim.BaseOptimizer
`evaluations`

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

Method Summary
`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 org.apache.commons.math3.optim.nonlinear.scalar.MultivariateOptimizer
`computeObjectiveValue, getGoalType`

Methods inherited from class org.apache.commons.math3.optim.BaseMultivariateOptimizer
`getLowerBound, getStartPoint, getUpperBound`

Methods inherited from class org.apache.commons.math3.optim.BaseOptimizer
`getConvergenceChecker, getEvaluations, getIterations, getMaxEvaluations, getMaxIterations, incrementEvaluationCount, incrementIterationCount`

Methods inherited from class java.lang.Object
`clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait`

Constructor Detail

### 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 Detail

### 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:
Returns:
a point/value pair that satifies 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: