org.apache.commons.math3.optim.linear

## Class SimplexSolver

- java.lang.Object
- - org.apache.commons.math3.optim.BaseOptimizer<PAIR>
  - - org.apache.commons.math3.optim.BaseMultivariateOptimizer<PointValuePair>
    - - org.apache.commons.math3.optim.nonlinear.scalar.MultivariateOptimizer
      - - org.apache.commons.math3.optim.linear.LinearOptimizer
        - - org.apache.commons.math3.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
  Version:
    $Id: SimplexSolver.java 1553855 2013-12-28 15:55:24Z erans $

- - ### Field Summary

    - ### Fields inherited from class org.apache.commons.math3.optim.BaseOptimizer

      `evaluations, iterations`

  - ### Constructor Summary

    Constructors
    Constructor and 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

    Methods
    Modifier and Type | Method and Description
    --- | ---
    `protected void` | `doIteration(org.apache.commons.math3.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.math3.optim.linear.SimplexTableau tableau)` Solves Phase 1 of the Simplex method.

    - ### Methods inherited from class org.apache.commons.math3.optim.linear.LinearOptimizer

      `getConstraints, getFunction, isRestrictedToNonNegative`

    - ### Methods inherited from class org.apache.commons.math3.optim.nonlinear.scalar.MultivariateOptimizer

      `computeObjectiveValue, getGoalType`

    - ### Methods inherited from class org.apache.commons.math3.optim.BaseMultivariateOptimizer

      `getLowerBound, getStartPoint, getUpperBound`

    - ### Methods inherited from class org.apache.commons.math3.optim.BaseOptimizer

      `getConvergenceChecker, getEvaluations, getIterations, getMaxEvaluations, getMaxIterations, 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.

    - #### 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.math3.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.math3.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`

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