genopt.algorithm
Class NelderMeadONeill

java.lang.Object
  genopt.algorithm.Optimizer
      genopt.algorithm.NelderMeadONeill

public class NelderMeadONeill
extends Optimizer

Class for minimizing a function using the Simplex algorithm of Nelder and Mead with an extension by O'Neill.
The restart criterion can be modified (optimality condition is then only checked if we have just a partial inside contraction or a total contraction done and if d(i)^T*d(i-1) < 0 holds where d(i) = (x(i)-x(i-1)).

This project was carried out at:

• Lawrence Berkeley National Laboratory (LBNL), Simulation Research Group,

and supported by

• the U.S. Department of Energy (DOE),
• the Swiss Academy of Engineering Sciences (SATW),
• the Swiss National Energy Fund (NEFF), and
• the Swiss National Science Foundation (SNSF)

GenOpt Copyright (c) 1998-2011, The Regents of the University of California, through Lawrence Berkeley National Laboratory (subject to receipt of any required approvals from the U.S. Dept. of Energy). All rights reserved.

Version:

GenOpt(R) 3.1.0 (December 8, 2011)

Author:

Michael Wetter

Field Summary

protected double	cFactor The step size factor for perturbation and reconstruction
protected int[]	con The kind of constraints
protected int	dimX The dimension of the problem
protected int	dimXP1 The dimension of the problem plus 1
protected int	konvge A flag whether the convergence check is only allowed after 'konvge' main iterations
protected double[]	low The lower bounds
protected boolean	modStoCri A flag whether the stopping criterion has to be modified or not
protected double	sqEps The required accuracy of the variance (eps*eps)
protected double[]	upp The upper bounds
protected Point[]	x The points

Fields inherited from class genopt.algorithm.Optimizer

done, EXCLUDING, FS, INCLUDING, LS, MAINITERATION, ORIGINAL, SUBITERATION, TRANSFORMED

Constructor Summary

NelderMeadONeill(GenOpt genOptData)
Constructor

Method Summary

protected int	getBest() Gets the number of the best point
protected int	getWorst() Gets the number of the worst point
protected double[]	getXCenter(int worst) Gets the center point for the reflection
protected int	rank(double f) Compares a trial with the other vertices
protected double[]	reflect(double[] xCenter, double[] xWorst) Reflects a point
protected boolean	restartCriterion() Determines whether a restart with a smaller simplex should be tried or not
int	run(Point x0) Runs the optimization process until a termination criteria is satisfied

Methods inherited from class genopt.algorithm.Optimizer

algorithmRequiresUsageOfStepNumber, appendToOutputListing, checkMaxIteration, checkObjectiveFunctionValue, ensureOnlyContinuousParameters, ensureOnlyDiscreteParameters, getAbsAccuracyFunction, getDimensionContinuous, getDimensionDiscrete, getDimensionF, getDimensionX, getDiscreteValueDouble0, getDx, getDx0, getF, getF, getIndex0, getIndex0, getInputValueBoolean, getInputValueDouble, getInputValueDouble, getInputValueInteger, getInputValueInteger, getInputValueString, getInputValueString, getKindOfConstraint, getL, getLengthDiscrete, getMainIterationNumber, getMaximumThreadPoolSize, getMaxIterationNumber, getMinimumPoint, getMode, getObjectiveFunctionName, getOutputPath, getPointerToEqualPoints, getRelAccuracyFunction, getSimulationNumber, getStepNumber, getU, getVariableNameContinuous, getVariableNameDiscrete, getX0, getX0, goToEndOfCommandFile, increaseStepNumber, increaseStepNumber, isFeasible, isNextToken, maxIterationReached, mustStopOptimization, print, println, replace, report, reportCurrentLowestPoint, reportMinimum, resetStepNumber, roundCoordinates, run, setInfo, setMode, setNumberOfMatchingResults, setToFeasibleCoordinate, setToFeasibleCoordinate, setWarning, simulate, throwInputError, useStepNumber, writeStepNumber

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Field Detail

x

protected Point[] x

The points

low

protected double[] low

The lower bounds

upp

protected double[] upp

The upper bounds

con

protected int[] con

The kind of constraints

dimX

protected int dimX

The dimension of the problem

dimXP1

protected int dimXP1

The dimension of the problem plus 1

sqEps

protected double sqEps

The required accuracy of the variance (eps*eps)

konvge

protected int konvge

A flag whether the convergence check is only allowed after 'konvge' main iterations

cFactor

protected double cFactor

The step size factor for perturbation and reconstruction

modStoCri

protected boolean modStoCri

A flag whether the stopping criterion has to be modified or not

Constructor Detail

NelderMeadONeill

public NelderMeadONeill(GenOpt genOptData)
                 throws OptimizerException,
                        java.io.IOException,
                        java.lang.Exception,
                        InputFormatException

Constructor

Parameters:

genOptData - a reference to the GenOpt object.
Note: the object is used as a reference. Hence, the datas of GenOpt are modified by this Class.

Throws:

OptimizerException - if algorithm is used for problems with less than 2 independent variables

java.lang.Exception - if an exception occurs

java.io.IOException - if an I/O exception occurs

InputFormatException - if an input format is wrong

Method Detail

run

public int run(Point x0)
        throws OptimizerException,
               java.lang.Exception

Runs the optimization process until a termination criteria is satisfied

Specified by:

run in class Optimizer

Parameters:

x0 - initial point

Returns:

-1 if the maximum number of iteration is exceeded
+1 if the required accuracy is reached

Throws:

java.lang.Exception

OptimizerException

InputFormatException - if an InputFormatException occurs

java.lang.NoSuchMethodException - if a method that should be invoked could not be found

java.lang.IllegalAccessException - if an invoked method enforces Java language access control and the underlying method is inaccessible

java.lang.reflect.InvocationTargetException - if an invoked method throws an exception

restartCriterion

protected boolean restartCriterion()

Determines whether a restart with a smaller simplex should be tried or not

Returns:

true if restart can be tried, false otherwise

getWorst

protected int getWorst()

Gets the number of the worst point

Returns:

the index w such that f(x(k,w)) = max(f(x(k,i)), i=0..dimX(x))

getBest

protected int getBest()

Gets the number of the best point

Returns:

the index w such that f(x(k,w)) = min(f(x(k,i)), i=0..dimX(x))

getXCenter

protected double[] getXCenter(int worst)

Gets the center point for the reflection

Parameters:

worst - the index of the worst point

Returns:

the center point for the reflection, such that x = 1 / dimX(x) * sum(x(k,i), i = 0..dimX(x), i != worst)

reflect

protected double[] reflect(double[] xCenter,
                           double[] xWorst)

Reflects a point

Parameters:

xCenter - the center point for normal reflection

xWorst - the point that has to be reflected

Returns:

the new point, such that xNew = 2 * xCenter - xWorst

rank

protected int rank(double f)

Compares a trial with the other vertices

Parameters:

f - the trial to be compared

Returns:

the number of ranking where 0 stands for the best point