DirectSearchOptimizer ("The Adobe AEM Quickstart and Web Application.")

java.lang.Object
- org.apache.commons.math.optimization.direct.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

See Also:

MultivariateRealFunction, NelderMead, MultiDirectional

Method Summary

All Methods Instance Methods Concrete Methods
Modifier and Type	Method and Description
`RealConvergenceChecker`	`getConvergenceChecker()` Get the convergence checker.
`int`	`getEvaluations()` Get the number of evaluations of the objective function.
`int`	`getIterations()` Get the number of iterations realized by the algorithm.
`int`	`getMaxEvaluations()` Get the maximal number of functions evaluations.
`int`	`getMaxIterations()` Get the maximal number of iterations of the algorithm.
`RealPointValuePair`	`optimize(MultivariateRealFunction function, GoalType goalType, double[] startPoint)` Optimizes an objective function.
`void`	`setConvergenceChecker(RealConvergenceChecker convergenceChecker)` Set the convergence checker.
`void`	`setMaxEvaluations(int maxEvaluations)` Set the maximal number of functions evaluations.
`void`	`setMaxIterations(int maxIterations)` Set the maximal number of iterations of the algorithm.
`void`	`setStartConfiguration(double[] steps)` Set start configuration for simplex.
`void`	`setStartConfiguration(double[][] referenceSimplex)` Set start configuration for simplex.

Methods inherited from class java.lang.Object
equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

- 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
  - setConvergenceChecker
```
public void setConvergenceChecker(RealConvergenceChecker convergenceChecker)
```
    Set the convergence checker.
    
    Specified by:
    
    setConvergenceChecker in interface MultivariateRealOptimizer
    
    Parameters:
    
    convergenceChecker - object to use to check for convergence
  - getConvergenceChecker
```
public RealConvergenceChecker getConvergenceChecker()
```
    Get the convergence checker.
    
    Specified by:
    
    getConvergenceChecker in interface MultivariateRealOptimizer
    
    Returns:
    
    object used to check for convergence
  - optimize
```
public RealPointValuePair optimize(MultivariateRealFunction function,
                                   GoalType goalType,
                                   double[] startPoint)
                            throws FunctionEvaluationException,
                                   OptimizationException,
                                   java.lang.IllegalArgumentException
```
    Optimizes an objective function.
    
    Specified by:
    
    optimize in interface MultivariateRealOptimizer
    
    Parameters:
    
    function - objective function
    
    goalType - type of optimization goal: either GoalType.MAXIMIZE or GoalType.MINIMIZE
    
    startPoint - the start point for optimization
    
    Returns:
    
    the point/value pair giving the optimal value for objective function
    
    Throws:
    
    FunctionEvaluationException - if the objective function throws one during the search
    
    OptimizationException - if the algorithm failed to converge
    
    java.lang.IllegalArgumentException - if the start point dimension is wrong

Class DirectSearchOptimizer

Method Summary

Methods inherited from class java.lang.Object

Method Detail

setStartConfiguration

setStartConfiguration

setMaxIterations

getMaxIterations

setMaxEvaluations

getMaxEvaluations

getIterations

getEvaluations

setConvergenceChecker

getConvergenceChecker

optimize