c

scalation.minima

RevisedSimplex

class RevisedSimplex extends MinimizerLP

The RevisedSimplex 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 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 Revised Simplex Algorithm operates on 'b_inv', which is the inverse of the basis-matrix ('ba' = 'B'). It has benefits over the Simplex Algorithm (less memory and reduced chance of round off errors).

Linear Supertypes
MinimizerLP, Error, AnyRef, Any
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Inherited
  1. RevisedSimplex
  2. MinimizerLP
  3. Error
  4. AnyRef
  5. Any
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Visibility
  1. Public
  2. Protected

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. 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
  2. val checker: CheckLP
    Definition Classes
    RevisedSimplex → MinimizerLP
  3. def dual: VectoD

    Return the dual solution vector (y).

  4. 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.

  5. final def flaw(method: String, message: String): Unit
    Definition Classes
    Error
  6. 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

  7. def objF(x: VectoD): 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
    RevisedSimplex → MinimizerLP
  8. 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

  9. def primal: VectorD

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

  10. def primalFull(x: VectorD): VectorD

    Return the full primal solution vector (xx).

  11. def rebuild(): Unit

    Rebuild the b_inv matrix from the original a matrix, by setting basis columns and inverting that matrix in-place.

  12. 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

  13. def showTableau(iter: Int): Unit

    Show the current revised tableau.

    Show the current revised tableau.

    iter

    the number of iterations do far

  14. def solve(): VectorD

    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. Return the optimal vector x.

    Definition Classes
    RevisedSimplex → MinimizerLP
  15. def toString(): String

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

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

    Definition Classes
    RevisedSimplex → AnyRef → Any
  16. def unbounded(u: VectoD): Boolean

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

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

    u

    the vector for leaving

  17. var x_B: Array[Int]