scalation.maxima

RevisedSimplex

class RevisedSimplex extends Error

This class solves Linear Programming (LP) problems using the Revised Simplex Algorithm. Given a constraint matrix a, constant vector b and cost vector c, find values for the solution/decision vector x that maximize the objective function f(x), while satisfying all of the constraints, i.e.,

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

The revised algorithm has benefits over the Simplex Algorithm (less memory and reduced chance of round off errors).

See also

math.uc.edu/~halpern/Linear.progr.folder/Handouts.lp.02/Revisedsimplex.pdf

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Instance Constructors

  1. new RevisedSimplex(a: MatrixD, b: VectorD, c: VectorD, x_B: Array[Int] = null)

    a

    the constraint matrix

    b

    the constant/limit vector

    c

    the cost/revenue vector

    x_B

    the initial basis (set of indices where x_i is in the basis)

Value Members

  1. final def !=(arg0: AnyRef): Boolean

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  2. final def !=(arg0: Any): Boolean

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  3. final def ##(): Int

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  4. final def ==(arg0: AnyRef): Boolean

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  5. final def ==(arg0: Any): Boolean

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  6. final def asInstanceOf[T0]: T0

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  7. def clone(): AnyRef

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    protected[lang]
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  8. def dual: VectorD

    Return the dual solution vector (y).

    Return the dual solution vector (y). FIX

  9. def entering(): Int

    Find the best variable x_l to enter the basis.

  10. final def eq(arg0: AnyRef): Boolean

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  11. def equals(arg0: Any): Boolean

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  12. def finalize(): Unit

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  13. def flaw(method: String, message: String): Unit

    Show the flaw by printing the error message.

    Show the flaw by printing the error message.

    method

    the method where the error occurred

    message

    the error message

    Definition Classes
    Error

  14. final def getClass(): java.lang.Class[_]

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  15. def hashCode(): Int

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  16. final def isInstanceOf[T0]: Boolean

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  17. 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.

    l

    the variable chosen to enter the basis

  18. final def ne(arg0: AnyRef): Boolean

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  19. final def notify(): Unit

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  20. final def notifyAll(): Unit

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  21. def objValue(x: VectorD): Double

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

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

    x

    the primal solution vector

  22. def pivot(k: Int, l: Int): Unit

    Pivot by replacing x_k with x_l in the basis.

    Pivot by replacing x_k with x_l in the basis. Update b_inv, b_ and c_.

    k

    the leaving variable

    l

    the entering variable

  23. def primal: VectorD

    Return the primal solution vector (x).

  24. def setBasis(j: Int = N, l: Int = M): Array[Int]

    There are M+N variables, N decision and M slack variables, of which, for each iteration, M are chosen for a Basic Feasible Solution (BFS).

    There are M+N variables, N decision and M slack variables, of which, for each iteration, M are chosen for a Basic Feasible Solution (BFS). The the variables not in the basis are set to zero. Setting j to N will start with the slack variables in the basis (only works if b >= 0).

    j

    the offset to start the basis

    l

    the size of the basis

  25. def showTableau: Unit

    Show the current revised tableau displaying the basis, b_inv, b_, c_.

  26. def solve(): (VectorD, Double)

    Solve a Linear Programming (LP) problem using the Revised Simplex Algorithm.

    Solve a Linear Programming (LP) problem using the Revised Simplex Algorithm. Iteratively pivot until there an optimal solution is found or it is determined that the solution is unbounded.

  27. final def synchronized[T0](arg0: ⇒ T0): T0

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  28. def toString(): String

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  29. def unbounded(u: VectorD): Boolean

    if u <= 0.

    if u <= 0., the solution is unbounded.

    u

    the ?? vector FIX

  30. final def wait(): Unit

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  31. final def wait(arg0: Long, arg1: Int): Unit

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  32. final def wait(arg0: Long): Unit

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  33. var x_B: Array[Int]

    the initial basis (set of indices where x_i is in the basis)

Inherited from Error

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