Package org.apache.commons.math.optimization.direct

Class DirectSearchOptimizer

  • All Implemented Interfaces:
    MultivariateRealOptimizer
    Direct Known Subclasses:
    MultiDirectional, NelderMead
    public abstract class DirectSearchOptimizer
extends java.lang.Object
implements MultivariateRealOptimizer
    This class implements simplex-based direct search optimization algorithms.

    Direct search methods only use objective function values, they don't need derivatives and don't either try to compute approximation of the derivatives. According to a 1996 paper by Margaret H. Wright (Direct Search Methods: Once Scorned, Now Respectable), they are used when either the computation of the derivative is impossible (noisy functions, unpredictable discontinuities) or difficult (complexity, computation cost). In the first cases, rather than an optimum, a not too bad point is desired. In the latter cases, an optimum is desired but cannot be reasonably found. In all cases direct search methods can be useful.

    Simplex-based direct search methods are based on comparison of the objective function values at the vertices of a simplex (which is a set of n+1 points in dimension n) that is updated by the algorithms steps.

    The initial configuration of the simplex can be set using either setStartConfiguration(double[]) or setStartConfiguration(double[][]). If neither method has been called before optimization is attempted, an explicit call to the first method with all steps set to +1 is triggered, thus building a default configuration from a unit hypercube. Each call to optimize will reuse the current start configuration and move it such that its first vertex is at the provided start point of the optimization. If the optimize method is called to solve a different problem and the number of parameters change, the start configuration will be reset to a default one with the appropriate dimensions.

    If setConvergenceChecker(RealConvergenceChecker) is not called, a default SimpleScalarValueChecker is used.

    Convergence is checked by providing the worst points of previous and current simplex to the convergence checker, not the best ones.

    This class is the base class performing the boilerplate simplex initialization and handling. The simplex update by itself is performed by the derived classes according to the implemented algorithms.

    implements MultivariateRealOptimizer since 2.0
    Since:
    1.2
    Version:
    $Revision: 1070725 $ $Date: 2011-02-15 02:31:12 +0100 (mar. 15 févr. 2011) $
    See Also:
    MultivariateRealFunction, NelderMead, MultiDirectional

    • Constructor Detail

      • DirectSearchOptimizer

        protected DirectSearchOptimizer()
        Simple constructor.

    • Method Detail

      • setStartConfiguration

        public void setStartConfiguration​(double[] steps)
                           throws java.lang.IllegalArgumentException
        Set start configuration for simplex.

        The start configuration for simplex is built from a box parallel to the canonical axes of the space. The simplex is the subset of vertices of a box parallel to the canonical axes. It is built as the path followed while traveling from one vertex of the box to the diagonally opposite vertex moving only along the box edges. The first vertex of the box will be located at the start point of the optimization.

        As an example, in dimension 3 a simplex has 4 vertices. Setting the steps to (1, 10, 2) and the start point to (1, 1, 1) would imply the start simplex would be: { (1, 1, 1), (2, 1, 1), (2, 11, 1), (2, 11, 3) }. The first vertex would be set to the start point at (1, 1, 1) and the last vertex would be set to the diagonally opposite vertex at (2, 11, 3).

        Parameters:
        steps - steps along the canonical axes representing box edges, they may be negative but not null
        Throws:
        java.lang.IllegalArgumentException - if one step is null

      • setStartConfiguration

        public void setStartConfiguration​(double[][] referenceSimplex)
                           throws java.lang.IllegalArgumentException
        Set start configuration for simplex.

        The real initial simplex will be set up by moving the reference simplex such that its first point is located at the start point of the optimization.

        Parameters:
        referenceSimplex - reference simplex
        Throws:
        java.lang.IllegalArgumentException - if the reference simplex does not contain at least one point, or if there is a dimension mismatch in the reference simplex or if one of its vertices is duplicated

      • setMaxIterations

        public void setMaxIterations​(int maxIterations)
        Set the maximal number of iterations of the algorithm.
        Specified by:
        setMaxIterations in interface MultivariateRealOptimizer
        Parameters:
        maxIterations - maximal number of algorithm iterations

      • getMaxIterations

        public int getMaxIterations()
        Get the maximal number of iterations of the algorithm.
        Specified by:
        getMaxIterations in interface MultivariateRealOptimizer
        Returns:
        maximal number of iterations

      • setMaxEvaluations

        public void setMaxEvaluations​(int maxEvaluations)
        Set the maximal number of functions evaluations.
        Specified by:
        setMaxEvaluations in interface MultivariateRealOptimizer
        Parameters:
        maxEvaluations - maximal number of function evaluations

      • getMaxEvaluations

        public int getMaxEvaluations()
        Get the maximal number of functions evaluations.
        Specified by:
        getMaxEvaluations in interface MultivariateRealOptimizer
        Returns:
        maximal number of functions evaluations

      • getIterations

        public int getIterations()
        Get the number of iterations realized by the algorithm.

        The number of evaluations corresponds to the last call to the optimize method. It is 0 if the method has not been called yet.

        Specified by:
        getIterations in interface MultivariateRealOptimizer
        Returns:
        number of iterations

      • getEvaluations

        public int getEvaluations()
        Get the number of evaluations of the objective function.

        The number of evaluations corresponds to the last call to the optimize method. It is 0 if the method has not been called yet.

        Specified by:
        getEvaluations in interface MultivariateRealOptimizer
        Returns:
        number of evaluations of the objective function

      • incrementIterationsCounter

        protected void incrementIterationsCounter()
                                   throws OptimizationException
        Increment the iterations counter by 1.
        Throws:
        OptimizationException - if the maximal number of iterations is exceeded

      • evaluate

        protected double evaluate​(double[] x)
                   throws FunctionEvaluationException,
                          java.lang.IllegalArgumentException
        Evaluate the objective function on one point.

        A side effect of this method is to count the number of function evaluations

        Parameters:
        x - point on which the objective function should be evaluated
        Returns:
        objective function value at the given point
        Throws:
        FunctionEvaluationException - if no value can be computed for the parameters or if the maximal number of evaluations is exceeded
        java.lang.IllegalArgumentException - if the start point dimension is wrong

      • replaceWorstPoint

        protected void replaceWorstPoint​(RealPointValuePair pointValuePair,
                                 java.util.Comparator<RealPointValuePair> comparator)
        Replace the worst point of the simplex by a new point.
        Parameters:
        pointValuePair - point to insert
        comparator - comparator to use to sort simplex vertices from best to worst