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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- 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
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- 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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- 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
- var g: FunctionV2S
- def g0(x: VectorD): Double
- 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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- def solution: (VectorD, Double)
Return the optimal (minimal) integer solution.
- 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
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- val x_ge: VectorD
- val x_le: VectorD
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