c

scalation.minima

IntegerNLP

class IntegerNLP extends AnyRef

This IntegerNLPsolves Integer Non-Linear Programming (INLP) and Mixed Integer Linear Non-Programming (MINLP) problems recursively using the Simplex algorithm. First, an NLP problem is solved. If the optimal solution vector 'x' is entirely integer valued, the INLP is solved. If not, pick the first 'x_j' that is not integer valued. Define two new NLP problems which bound 'x_j' to the integer below and above, respectively. Branch by solving each of these NLP problems in turn. Prune by not exploring branches less optimal than the currently best integer solution. This technique is referred to as Branch and Bound. An exclusion set may be optionally provided for MINLP problems.

Given an objective function 'f(x)' and a constraint function 'g(x)', find values for the solution/decision vector 'x' that minimize the objective function 'f(x)', while satisfying the constraint function, i.e.,

minimize f(x) subject to g(x) <= 0, some x_i must integer-valued

Make b_i negative to indicate a ">=" constraint

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Instance Constructors

  1. new IntegerNLP(f: FunctionV2S, n: Int, g: FunctionV2S = null, excl: Set[Int] = Set ())

    f

    the objective function to be minimized

    g

    the constraint function to be satisfied, if any

    excl

    the set of variables to be excluded from the integer requirement

Value Members

  1. final def !=(arg0: Any): Boolean
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  2. final def ##(): Int
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  3. final def ==(arg0: Any): Boolean
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  4. def addConstraint(j: Int, le: Boolean, bound: Double): Boolean

    Add a new constraint to the current set of bounding constraints: x_j - bound <= 0 or x_j - bound >= 0 (e.g., x_1 - 2 <= 0 or x_0 - 4 >= 0).

    Add a new constraint to the current set of bounding constraints: x_j - bound <= 0 or x_j - bound >= 0 (e.g., x_1 - 2 <= 0 or x_0 - 4 >= 0).

    j

    the index of variable x_j

    le

    whether it is a "less than or equal to" 'le' constraint

    bound

    the bounding value

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  7. final def eq(arg0: AnyRef): Boolean
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  8. def equals(arg0: Any): Boolean
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  9. def fractionalVar(x: VectorD): Int

    Return j such that x_j has a fractional (non-integer) value, -1 otherwise.

    Return j such that x_j has a fractional (non-integer) value, -1 otherwise. Make sure that j is not in the exclusion list.

    x

    the vector to check

  10. var g: FunctionV2S
  11. def g0(x: VectorD): Double
  12. def gBounds(x: VectorD): Double

    Add up all the violation of bounds constraints.

    Add up all the violation of bounds constraints.

    x

    the current point

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  19. def solution: (VectorD, Double)

    Return the optimal (minimal) integer solution.

  20. def solve(x0: VectorD, dp: Int): Unit

    Solve the Mixed Integer Non-linear, Linear Programming (MINLP) problem by using Branch and Bound and an NLP Algorithm, e.g., QuasiNewton, recursively.

    Solve the Mixed Integer Non-linear, Linear Programming (MINLP) problem by using Branch and Bound and an NLP Algorithm, e.g., QuasiNewton, recursively.

    dp

    the current depth of recursion

  21. final def synchronized[T0](arg0: ⇒ T0): T0
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  23. final def wait(arg0: Long, arg1: Int): Unit
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  25. final def wait(): Unit
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  26. val x_ge: VectorD
  27. val x_le: VectorD

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