scalation.minima

BGSimplex

class BGSimplex extends MinimizerLP

This class solves Linear Programming (LP) problems using the Bartels-Golub (BG) Simplex Algorithm. Given a constraint matrix 'a', constant 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

The BG Simplex Algorithm performs LU Fractorization/Decomposition of the basis-matrix ('ba' = 'B') rather than computing inverses ('b_inv'). It has benefits over the (Revised) Simplex Algorithm (less runtime, less memory, and much reduced chance of round off errors).

Linear Supertypes
MinimizerLP, Error, AnyRef, Any
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Instance Constructors

  1. new BGSimplex(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: 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: VectorD, y: VectorD, 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
    BGSimplexMinimizerLP
  8. def clone(): AnyRef

    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  9. def dual: VectorD

    Return the dual solution vector (y).

  10. def entering(): Int

    Find the best variable x_l to enter the basis.

    Find the best variable x_l to enter the basis. Use Dantiz's Rule: index of max positive (cycling possible) z value. Return -1 to indicate no such column.

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

    Definition Classes
    AnyRef
  12. def equals(arg0: Any): Boolean

    Definition Classes
    AnyRef → Any
  13. def finalize(): Unit

    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @throws( classOf[java.lang.Throwable] )
  14. 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
  15. final def getClass(): Class[_]

    Definition Classes
    AnyRef → Any
  16. def hashCode(): Int

    Definition Classes
    AnyRef → Any
  17. def infeasible: Boolean

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

  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 variable chosen to enter the basis

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

    Definition Classes
    AnyRef
  21. final def notify(): Unit

    Definition Classes
    AnyRef
  22. final def notifyAll(): Unit

    Definition Classes
    AnyRef
  23. def objF(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

    Definition Classes
    BGSimplexMinimizerLP
  24. 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 (actually lu), b_ and c_.

    k

    the leaving variable

    l

    the entering variable

  25. def primal: VectorD

    Return the primal (basis only) solution vector (x).

  26. def primalFull(x: VectorD): VectorD

    Return the full primal solution vector (xx).

  27. def setBasis(j: Int = N-M, 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

  28. def showTableau(iter: Int): Unit

    Show the current BG tableau.

    Show the current BG tableau.

    iter

    the number of iterations do far

  29. def solve(): VectorD

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

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

    Definition Classes
    BGSimplexMinimizerLP
  30. final def synchronized[T0](arg0: ⇒ T0): T0

    Definition Classes
    AnyRef
  31. def toString(): String

    Convert the current BG tableau (basis, b_inv, b_, and c_) to a string.

    Convert the current BG tableau (basis, b_inv, b_, and c_) to a string.

    Definition Classes
    BGSimplex → AnyRef → Any
  32. def unbounded(u: VectorD): Boolean

    Check if u <= 0.

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

    u

    the vector for leaving

  33. final def wait(): Unit

    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  34. final def wait(arg0: Long, arg1: Int): Unit

    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  35. final def wait(arg0: Long): Unit

    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  36. var x_B: Array[Int]

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

Inherited from MinimizerLP

Inherited from Error

Inherited from AnyRef

Inherited from Any

Ungrouped