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 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:

    • Constructor Detail

      • CMAESOptimizer

        public CMAESOptimizer​(int maxIterations,
                              double stopFitness,
                              boolean isActiveCMA,
                              int diagonalOnly,
                              int checkFeasableCount,
                              org.apache.commons.rng.UniformRandomProvider rng,
                              boolean generateStatistics,
                              ConvergenceChecker<PointValuePair> checker)
        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.
        rng - Random generator.
        generateStatistics - Whether statistic data is collected.
        checker - Convergence checker.
    • Method Detail

      • optimize

        public PointValuePair optimize​(OptimizationData... optData)
        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.

        optimize in class MultivariateOptimizer
        optData - Optimization data. In addition to those documented in MultivariateOptimizer, this method will register the following data:
        • Sigma values define the initial coordinate-wise standard deviations for sampling new search points around the initial guess. It is suggested to set them to the estimated distance from the initial to the desired optimum. Small values induce the search to be more local (and very small values are more likely to find a local optimum close to the initial guess). Too small values might however lead to early termination.
        • PopulationSize is the number of offsprings and the primary strategy parameter. In the absence of better clues, a good default could be an integer close to 4 + 3 ln(n), where n is the number of optimized parameters. Increasing the population size improves global search properties at the expense of speed (which in general decreases at most linearly with increasing population size).
        a point/value pair that satisfies the convergence criteria.
        TooManyEvaluationsException - if the maximal number of evaluations is exceeded.
        DimensionMismatchException - if the initial guess, target, and weight arguments have inconsistent dimensions.