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

Linear Supertypes

Error, AnyRef, Any

Ordering

Alphabetic
By inheritance

Inherited

RevisedSimplex
Error
AnyRef
Any

Hide All
Show all

Learn more about member selection

Visibility

Public
All

Instance Constructors

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

final def !=(arg0: Any): Boolean

Definition Classes
AnyRef → Any
final def ##(): Int

Definition Classes
AnyRef → Any
final def ==(arg0: Any): Boolean

Definition Classes
AnyRef → Any
final def asInstanceOf[T0]: T0

Definition Classes
Any
def clone(): AnyRef

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

Return the dual solution vector (y).
Return the dual solution vector (y). FIX
def entering(): Int

Find the best variable x_l to enter the basis.
final def eq(arg0: AnyRef): Boolean

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

Definition Classes
AnyRef → Any
def finalize(): Unit

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

Definition Classes
AnyRef → Any
def hashCode(): Int

Definition Classes
AnyRef → Any
final def isInstanceOf[T0]: Boolean

Definition Classes
Any
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
final def ne(arg0: AnyRef): Boolean

Definition Classes
AnyRef
final def notify(): Unit

Definition Classes
AnyRef
final def notifyAll(): Unit

Definition Classes
AnyRef
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
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
def primal: VectorD

Return the primal solution vector (x).
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
def showTableau: Unit

Show the current revised tableau displaying the basis, b_inv, b_, c_.
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.
final def synchronized[T0](arg0: ⇒ T0): T0

Definition Classes
AnyRef
def toString(): String

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

if u <= 0.
if u <= 0., the solution is unbounded.
u
the ?? vector FIX
final def wait(): Unit

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

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

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

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

Inherited from Error

Inherited from AnyRef

Inherited from Any

Ungrouped