gov.sandia.cognition.learning.algorithm.minimization

Class FunctionMinimizerDirectionSetPowell

java.lang.Object

gov.sandia.cognition.util.AbstractCloneableSerializable

gov.sandia.cognition.algorithm.AbstractIterativeAlgorithm

gov.sandia.cognition.algorithm.AbstractAnytimeAlgorithm<ResultType>

gov.sandia.cognition.learning.algorithm.AbstractAnytimeBatchLearner<EvaluatorType,InputOutputPair<InputType,OutputType>>

gov.sandia.cognition.learning.algorithm.minimization.AbstractAnytimeFunctionMinimizer<Vector,java.lang.Double,Evaluator<? super Vector,java.lang.Double>>

gov.sandia.cognition.learning.algorithm.minimization.FunctionMinimizerDirectionSetPowell

All Implemented Interfaces:

AnytimeAlgorithm<InputOutputPair<Vector,java.lang.Double>>, IterativeAlgorithm, StoppableAlgorithm, AnytimeBatchLearner<Evaluator<? super Vector,java.lang.Double>,InputOutputPair<Vector,java.lang.Double>>, BatchLearner<Evaluator<? super Vector,java.lang.Double>,InputOutputPair<Vector,java.lang.Double>>, FunctionMinimizer<Vector,java.lang.Double,Evaluator<? super Vector,java.lang.Double>>, CloneableSerializable, java.io.Serializable, java.lang.Cloneable

@PublicationReference(author="R. Fletcher",title="Practical Methods of Optimization, Second Edition",type=Book,year=1987,pages={87,90},notes="Section 4.2") @PublicationReference(author={"William H. Press","Saul A. Teukolsky","William T. Vetterling","Brian P. Flannery"},title="Numerical Recipes in C, Second Edition",type=Book,year=1992,pages={417,418},notes="Section 10.5",url="http://www.nrbook.com/a/bookcpdf.php")
public class FunctionMinimizerDirectionSetPowell
extends AbstractAnytimeFunctionMinimizer<Vector,java.lang.Double,Evaluator<? super Vector,java.lang.Double>>

Implementation of the derivative-free unconstrained nonlinear direction-set minimization algorithm called "Powell's Method" by Numerical Recipes. The method was originally known as Smith's Direction-Set Method, to which Powell made an ingenious improvement. Powell's Method was later improved upon by Brent. This algorithm creates a basis set of search directions and repeatedly searches along each direction until a local minimum is found using only function evaluations, that is, no gradient information is needed. This algorithm is amazingly good at finding a minimum, and is my method of choice for derivative-free minimization. However, be sure to check the performance this algorithm's cousin, the Nelder-Mead downhill simplex (FunctionMinimizerNelderMead) before deciding on a derivative-free minimization algorithm.

That being said, it is sometimes more effective to use approximated gradients and algorithms like BFGS (FunctionMinimizerBFGS) than derivative-free minimization algorithms. Thus, I would try them both.

Since:

2.0

Author:

Kevin R. Dixon

See Also:

Serialized Form

Field Summary

Fields

Modifier and Type	Field and Description
static LineMinimizer<?>	DEFAULT_LINE_MINIMIZER Default line minimization algorithm, LineMinimizerDerivativeFree
static int	DEFAULT_MAX_ITERATIONS Default maximum number of iterations before stopping, 1000
static double	DEFAULT_TOLERANCE Default tolerance, 1.0E-5

Fields inherited from class gov.sandia.cognition.learning.algorithm.minimization.AbstractAnytimeFunctionMinimizer

initialGuess, result, tolerance

Fields inherited from class gov.sandia.cognition.learning.algorithm.AbstractAnytimeBatchLearner

data, keepGoing

Fields inherited from class gov.sandia.cognition.algorithm.AbstractAnytimeAlgorithm

maxIterations

Fields inherited from class gov.sandia.cognition.algorithm.AbstractIterativeAlgorithm

DEFAULT_ITERATION, iteration

Constructor Summary

Constructors

Constructor and Description
FunctionMinimizerDirectionSetPowell() Default constructor
FunctionMinimizerDirectionSetPowell(LineMinimizer<?> lineMinimizer) Creates a new instance of FunctionMinimizerDirectionSetPowell
FunctionMinimizerDirectionSetPowell(LineMinimizer<?> lineMinimizer, Vector initialGuess, double tolerance, int maxIterations) Creates a new instance of FunctionMinimizerDirectionSetPowell

Method Summary

Modifier and Type	Method and Description
protected void	cleanupAlgorithm() Called to clean up the learning algorithm's state after learning has finished.
LineMinimizer<?>	getLineMinimizer() Getter for lineMinimizer
protected boolean	initializeAlgorithm() Called to initialize the learning algorithm's state based on the data that is stored in the data field.
void	setLineMinimizer(LineMinimizer<?> lineMinimizer) Setter for lineMinimizer
protected boolean	step() Called to take a single step of the learning algorithm.

Methods inherited from class gov.sandia.cognition.learning.algorithm.minimization.AbstractAnytimeFunctionMinimizer

getInitialGuess, getResult, getTolerance, setInitialGuess, setResult, setTolerance

Methods inherited from class gov.sandia.cognition.learning.algorithm.AbstractAnytimeBatchLearner

clone, getData, getKeepGoing, learn, setData, setKeepGoing, stop

Methods inherited from class gov.sandia.cognition.algorithm.AbstractAnytimeAlgorithm

getMaxIterations, isResultValid, setMaxIterations

Methods inherited from class gov.sandia.cognition.algorithm.AbstractIterativeAlgorithm

addIterativeAlgorithmListener, fireAlgorithmEnded, fireAlgorithmStarted, fireStepEnded, fireStepStarted, getIteration, getListeners, removeIterativeAlgorithmListener, setIteration, setListeners

Methods inherited from class java.lang.Object

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

Methods inherited from interface gov.sandia.cognition.learning.algorithm.minimization.FunctionMinimizer

learn

Methods inherited from interface gov.sandia.cognition.util.CloneableSerializable

clone

Methods inherited from interface gov.sandia.cognition.algorithm.AnytimeAlgorithm

getMaxIterations, setMaxIterations

Methods inherited from interface gov.sandia.cognition.algorithm.IterativeAlgorithm

addIterativeAlgorithmListener, getIteration, removeIterativeAlgorithmListener

Methods inherited from interface gov.sandia.cognition.algorithm.StoppableAlgorithm

isResultValid, stop

Field Detail

DEFAULT_MAX_ITERATIONS

public static final int DEFAULT_MAX_ITERATIONS

Default maximum number of iterations before stopping, 1000

See Also:

Constant Field Values

DEFAULT_TOLERANCE

public static final double DEFAULT_TOLERANCE

Default tolerance, 1.0E-5

See Also:

Constant Field Values

DEFAULT_LINE_MINIMIZER

public static final LineMinimizer<?> DEFAULT_LINE_MINIMIZER

Default line minimization algorithm, LineMinimizerDerivativeFree

Constructor Detail

FunctionMinimizerDirectionSetPowell

public FunctionMinimizerDirectionSetPowell()

Default constructor

FunctionMinimizerDirectionSetPowell

public FunctionMinimizerDirectionSetPowell(LineMinimizer<?> lineMinimizer)

Creates a new instance of FunctionMinimizerDirectionSetPowell

Parameters:

lineMinimizer - Work-horse algorithm that minimizes the function along a direction

FunctionMinimizerDirectionSetPowell

public FunctionMinimizerDirectionSetPowell(LineMinimizer<?> lineMinimizer,
                                           Vector initialGuess,
                                           double tolerance,
                                           int maxIterations)

Creates a new instance of FunctionMinimizerDirectionSetPowell

Parameters:

initialGuess - Initial guess about the minimum of the method

tolerance - Tolerance of the minimization algorithm, must be >= 0.0, typically ~1e-10

lineMinimizer - Work-horse algorithm that minimizes the function along a direction

maxIterations - Maximum number of iterations, must be >0, typically ~100

Method Detail

initializeAlgorithm

protected boolean initializeAlgorithm()

Description copied from class: AbstractAnytimeBatchLearner

Called to initialize the learning algorithm's state based on the data that is stored in the data field. The return value indicates if the algorithm can be run or not based on the initialization.

Specified by:

initializeAlgorithm in class AbstractAnytimeBatchLearner<Evaluator<? super Vector,java.lang.Double>,InputOutputPair<Vector,java.lang.Double>>

Returns:

True if the learning algorithm can be run and false if it cannot.

step

protected boolean step()

Description copied from class: AbstractAnytimeBatchLearner

Called to take a single step of the learning algorithm.

Specified by:

step in class AbstractAnytimeBatchLearner<Evaluator<? super Vector,java.lang.Double>,InputOutputPair<Vector,java.lang.Double>>

Returns:

True if another step can be taken and false it the algorithm should halt.

cleanupAlgorithm

protected void cleanupAlgorithm()

Description copied from class: AbstractAnytimeBatchLearner

Called to clean up the learning algorithm's state after learning has finished.

Specified by:

cleanupAlgorithm in class AbstractAnytimeBatchLearner<Evaluator<? super Vector,java.lang.Double>,InputOutputPair<Vector,java.lang.Double>>

getLineMinimizer

public LineMinimizer<?> getLineMinimizer()

Getter for lineMinimizer

Returns:

Work-horse algorithm that minimizes the function along a direction

setLineMinimizer

public void setLineMinimizer(LineMinimizer<?> lineMinimizer)

Setter for lineMinimizer

Parameters:

lineMinimizer - Work-horse algorithm that minimizes the function along a direction