Class 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 \(300 n^2\) 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:

  • Constructor Details

    • CMAESOptimizer

      public CMAESOptimizer(int maxIterations, double stopFitness, boolean isActiveCMA, int diagonalOnly, int checkFeasableCount, RandomGenerator random, boolean generateStatistics, ConvergenceChecker<PointValuePair> checker)
      Simple constructor.
      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.
  • Method Details