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 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 and Description
    --- | ---
    `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

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

  - ### Method Summary

    Methods
    Modifier and Type | Method and 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 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, optimize`

    - ### 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:
        - `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`

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