c

scalation.minima

Simplex2P

class Simplex2P extends MinimizerLP

The Simplex2P class solves Linear Programming (LP) problems using a tableau based Simplex Algorithm. Given a constraint matrix 'a', limit/RHS vector 'b' and cost vector 'c', find values for the solution/decision vector 'x' that minimize the objective function 'f(x)', while satisfying all of the constraints, i.e.,

minimize f(x) = c x subject to a x <= b, x >= 0

In case of 'a_i x >= b_i', use -b_i as an indicator of a ">=" constraint. The program will flip such negative b_i back to positive as well as use a surplus and artificial variable instead of the usual slack variable, i.e., a_i x <= b_i => a_i x + s_i = b_i // use slack variable s_i with coefficient 1 a_i x >= b_i => a_i x + s_i = b_i // use surplus variable s_i with coefficient -1 For each '>=' constraint, an artificial variable is introduced and put into the initial basis. These artificial variables must be removed from the basis during Phase I of the Two-Phase Simplex Algorithm. After this, or if there are no artificial variables, Phase II is used to find an optimal value for 'x' and the optimum value for 'f'.

Creates an 'MM-by-nn' simplex tableau with -- [0..M-1, 0..N-1] = a (constraint matrix) -- [0..M-1, N..M+N-1] = s (slack/surplus variable matrix) -- [0..M-1, M+N..nn-2] = r (artificial variable matrix) -- [0..M-1, nn-1] = b (limit/RHS vector) -- [M, 0..nn-2] = c (cost vector)

Linear Supertypes
MinimizerLP, Error, AnyRef, Any
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  1. Simplex2P
  2. MinimizerLP
  3. Error
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Visibility
  1. Public
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Instance Constructors

  1. new Simplex2P(a: MatrixD, b: VectorD, c: VectorD)

    a

    the M-by-N constraint matrix

    b

    the M-length limit/RHS vector (input b_i negative for surplus)

    c

    the N-length cost vector

Value Members

  1. final def !=(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  2. final def ##(): Int
    Definition Classes
    AnyRef → Any
  3. final def ==(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  4. val EPSILON: Double
    Attributes
    protected
    Definition Classes
    MinimizerLP
  5. final def asInstanceOf[T0]: T0
    Definition Classes
    Any
  6. def check(x: VectoD, y: VectoD, f: Double): Boolean

    Determine whether the current solution is correct.

    Determine whether the current solution is correct.

    x

    the primal solution vector x

    y

    the dual solution vector y

    f

    the minimum value of the objective function

    Definition Classes
    MinimizerLP
  7. val checker: CheckLP
    Definition Classes
    Simplex2P → MinimizerLP
  8. def clone(): AnyRef
    Attributes
    protected[lang]
    Definition Classes
    AnyRef
    Annotations
    @throws( ... ) @native() @HotSpotIntrinsicCandidate()
  9. def dual: VectorD

    Return the dual solution vector y (cost row (M) under the slack columns).

  10. def entering(): Int

    Find the best variable x_l to enter the basis.

    Find the best variable x_l to enter the basis. Determine the index of entering variable corresponding to column l (e.g., using Dantiz's Rule or Bland's Rule). Return -1 to indicate no such column. 't(M).argmaxPos (jj)' // use Dantiz's rule (index of max positive, cycling possible) 't(M).firstPos (jj)' // use Bland's rule (index of first positive, FPE possible)

  11. final def eq(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  12. def equals(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  13. final def flaw(method: String, message: String): Unit
    Definition Classes
    Error
  14. final def getClass(): Class[_]
    Definition Classes
    AnyRef → Any
    Annotations
    @native() @HotSpotIntrinsicCandidate()
  15. def hashCode(): Int
    Definition Classes
    AnyRef → Any
    Annotations
    @native() @HotSpotIntrinsicCandidate()
  16. def infeasible: Boolean

    Determine whether the current solution (x = primal) is still primal feasible.

  17. def initBasis(): Unit

    Initialize the basis to the slack and artificial variables.

    Initialize the basis to the slack and artificial variables. Perform row operations to make cost row (t(M)) zero in artificial var columns. If b(i) is negative have a surplus and artificial variable, otherwise, just a slack variable.

  18. final def isInstanceOf[T0]: Boolean
    Definition Classes
    Any
  19. def leaving(l: Int): Int

    Find the best variable x_k to leave the basis given that x_l is entering.

    Find the best variable x_k to leave the basis given that x_l is entering. Determine the index of the leaving variable corresponding to row k using the Min-Ratio Rule. Return -1 to indicate no such row.

    l

    the entering variable (column)

  20. final def ne(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  21. final def notify(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native() @HotSpotIntrinsicCandidate()
  22. final def notifyAll(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native() @HotSpotIntrinsicCandidate()
  23. def objF(x: VectoD): Double

    Return the value of the objective function f(x) = c x.

    Return the value of the objective function f(x) = c x.

    x

    the coordinate values of the current point

    Definition Classes
    Simplex2P → MinimizerLP
  24. def pivot(k: Int, l: Int): Unit

    Pivot on entry (k, l) using Gauss-Jordan elimination to replace variable x_k with x_l in the basis.

    Pivot on entry (k, l) using Gauss-Jordan elimination to replace variable x_k with x_l in the basis.

    k

    the leaving variable (row)

    l

    the entering variable (column)

  25. def primal: VectorD

    Return the primal solution vector x (only the basic variables are non-zero).

  26. def removeArtificials(): Unit

    Remove the artificial variables and reset the cost row (M) in the tableau.

  27. def showTableau(iter: Int): Unit

    Show the current tableau.

    Show the current tableau.

    iter

    the number of iterations do far

  28. def solve(): VectorD

    Solve the LP minimization problem using two phases if necessary.

    Solve the LP minimization problem using two phases if necessary. Note: phase I is always minimization. Two phases are necessary if the number of artificial variables R > 0.

    Definition Classes
    Simplex2P → MinimizerLP
  29. def solve_1(): VectorD

    Run the simplex algorithm starting from an initial BFS and iteratively find a non-basic variable to replace a variable in the current basis so long as the objective function improves.

    Run the simplex algorithm starting from an initial BFS and iteratively find a non-basic variable to replace a variable in the current basis so long as the objective function improves. Runs a single phase and return the optimal vector x.

  30. final def synchronized[T0](arg0: ⇒ T0): T0
    Definition Classes
    AnyRef
  31. def toString(): String

    Convert the current tableau and basis to a string suitable for display.

    Convert the current tableau and basis to a string suitable for display.

    Definition Classes
    Simplex2P → AnyRef → Any
  32. final def wait(arg0: Long, arg1: Int): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  33. final def wait(arg0: Long): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws( ... ) @native()
  34. final def wait(): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )

Deprecated Value Members

  1. def finalize(): Unit
    Attributes
    protected[lang]
    Definition Classes
    AnyRef
    Annotations
    @throws( classOf[java.lang.Throwable] ) @Deprecated
    Deprecated

Inherited from MinimizerLP

Inherited from Error

Inherited from AnyRef

Inherited from Any

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