Package org.apache.commons.math4.legacy.optim.linear

Class SimplexSolver

java.lang.Object

org.apache.commons.math4.legacy.optim.BaseOptimizer<PAIR>

org.apache.commons.math4.legacy.optim.BaseMultivariateOptimizer<PointValuePair>

org.apache.commons.math4.legacy.optim.nonlinear.scalar.MultivariateOptimizer

org.apache.commons.math4.legacy.optim.linear.LinearOptimizer

org.apache.commons.math4.legacy.optim.linear.SimplexSolver

public class SimplexSolver
extends LinearOptimizer

Solves a linear problem using the "Two-Phase Simplex" method.

The SimplexSolver supports the following OptimizationData data provided as arguments to optimize(OptimizationData...):

• objective function: LinearObjectiveFunction - mandatory
• linear constraints LinearConstraintSet - mandatory
• type of optimization: GoalType - optional, default: MINIMIZE
• whether to allow negative values as solution: NonNegativeConstraint - optional, default: true
• pivot selection rule: PivotSelectionRule - optional, default PivotSelectionRule.DANTZIG
• callback for the best solution: SolutionCallback - optional
• maximum number of iterations: MaxIter - optional, default: Integer.MAX_VALUE

Note: Depending on the problem definition, the default convergence criteria may be too strict, resulting in NoFeasibleSolutionException or TooManyIterationsException. In such a case it is advised to adjust these criteria with more appropriate values, e.g. relaxing the epsilon value.

Default convergence criteria:

• Algorithm convergence: 1e-6
• Floating-point comparisons: 10 ulp
• Cut-Off value: 1e-10

The cut-off value has been introduced to handle the case of very small pivot elements in the Simplex tableau, as these may lead to numerical instabilities and degeneracy. Potential pivot elements smaller than this value will be treated as if they were zero and are thus not considered by the pivot selection mechanism. The default value is safe for many problems, but may need to be adjusted in case of very small coefficients used in either the LinearConstraint or LinearObjectiveFunction.

Since:

2.0

Constructor Summary

Constructors

Constructor	Description
SimplexSolver()	Builds a simplex solver with default settings.
SimplexSolver(double epsilon)	Builds a simplex solver with a specified accepted amount of error.
SimplexSolver(double epsilon, int maxUlps)	Builds a simplex solver with a specified accepted amount of error.
SimplexSolver(double epsilon, int maxUlps, double cutOff)	Builds a simplex solver with a specified accepted amount of error.

Method Summary

Modifier and Type	Method	Description
protected void	doIteration(org.apache.commons.math4.legacy.optim.linear.SimplexTableau tableau)	Runs one iteration of the Simplex method on the given model.
PointValuePair	doOptimize()	Performs the bulk of the optimization algorithm.
PointValuePair	optimize(OptimizationData... optData)	Stores data and performs the optimization.
protected void	parseOptimizationData(OptimizationData... optData)	Scans the list of (required and optional) optimization data that characterize the problem.
protected void	solvePhase1(org.apache.commons.math4.legacy.optim.linear.SimplexTableau tableau)	Solves Phase 1 of the Simplex method.

Methods inherited from class org.apache.commons.math4.legacy.optim.linear.LinearOptimizer

getConstraints, getFunction, isRestrictedToNonNegative

Methods inherited from class org.apache.commons.math4.legacy.optim.nonlinear.scalar.MultivariateOptimizer

computeObjectiveValue, createLineSearch, getGoalType, getObjectiveFunction, lineSearch

Methods inherited from class org.apache.commons.math4.legacy.optim.BaseMultivariateOptimizer

getLowerBound, getStartPoint, getUpperBound

Methods inherited from class org.apache.commons.math4.legacy.optim.BaseOptimizer

getAbsoluteTolerance, getConvergenceChecker, getEvaluations, getIterations, getMaxEvaluations, getMaxIterations, getRelativeTolerance, incrementEvaluationCount, incrementIterationCount, optimize

Methods inherited from class java.lang.Object

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

Constructor Detail

SimplexSolver

public SimplexSolver()

Builds a simplex solver with default settings.

SimplexSolver

public SimplexSolver(double epsilon)

Builds a simplex solver with a specified accepted amount of error.

Parameters:

epsilon - Amount of error to accept for algorithm convergence.

SimplexSolver

public SimplexSolver(double epsilon,
                     int maxUlps)

Builds a simplex solver with a specified accepted amount of error.

Parameters:

epsilon - Amount of error to accept for algorithm convergence.

maxUlps - Amount of error to accept in floating point comparisons.

SimplexSolver

public SimplexSolver(double epsilon,
                     int maxUlps,
                     double cutOff)

Builds a simplex solver with a specified accepted amount of error.

Parameters:

epsilon - Amount of error to accept for algorithm convergence.

maxUlps - Amount of error to accept in floating point comparisons.

cutOff - Values smaller than the cutOff are treated as zero.

Method Detail

optimize

public PointValuePair optimize(OptimizationData... optData)
                        throws TooManyIterationsException

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.

Overrides:

optimize in class LinearOptimizer

Parameters:

optData - Optimization data. In addition to those documented in LinearOptimizer, this method will register the following data:

• SolutionCallback
• PivotSelectionRule

Returns:

a point/value pair that satisfies the convergence criteria.

Throws:

TooManyIterationsException - if the maximal number of iterations is exceeded.

DimensionMismatchException - if the dimension of the constraints does not match the dimension of the objective function

parseOptimizationData

protected void parseOptimizationData(OptimizationData... optData)

Scans the list of (required and optional) optimization data that characterize the problem.

Overrides:

parseOptimizationData in class LinearOptimizer

Parameters:

optData - Optimization data. In addition to those documented in LinearOptimizer, this method will register the following data:

• SolutionCallback
• PivotSelectionRule

doIteration

protected void doIteration(org.apache.commons.math4.legacy.optim.linear.SimplexTableau tableau)
                    throws TooManyIterationsException,
                           UnboundedSolutionException

Runs one iteration of the Simplex method on the given model.

Parameters:

tableau - Simple tableau for the problem.

Throws:

TooManyIterationsException - if the allowed number of iterations has been exhausted.

UnboundedSolutionException - if the model is found not to have a bounded solution.

solvePhase1

protected void solvePhase1(org.apache.commons.math4.legacy.optim.linear.SimplexTableau tableau)
                    throws TooManyIterationsException,
                           UnboundedSolutionException,
                           NoFeasibleSolutionException

Solves Phase 1 of the Simplex method.

Parameters:

tableau - Simple tableau for the problem.

Throws:

TooManyIterationsException - if the allowed number of iterations has been exhausted.

UnboundedSolutionException - if the model is found not to have a bounded solution.

NoFeasibleSolutionException - if there is no feasible solution?

doOptimize

public PointValuePair doOptimize()
                          throws TooManyIterationsException,
                                 UnboundedSolutionException,
                                 NoFeasibleSolutionException

Performs the bulk of the optimization algorithm.

Specified by:

doOptimize in class BaseOptimizer<PointValuePair>

Returns:

the point/value pair giving the optimal value of the objective function.

Throws:

TooManyIterationsException

UnboundedSolutionException

NoFeasibleSolutionException