class NelderMeadSimplex extends Minimizer with Error
The NelderMeadSimplex
solves Non-Linear Programming (NLP) problems using
the Nelder-Mead Simplex algorithm. Given a function 'f' and its dimension
'n', the algorithm moves a simplex defined by n + 1 points in order to find
an optimal solution. The algorithm is derivative-free.
minimize f(x)
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new
NelderMeadSimplex(f: FunctionV2S, n: Int)
- f
the vector-to-scalar objective function
- n
the dimension of the search space
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final
def
!=(arg0: Any): Boolean
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final
def
##(): Int
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final
def
==(arg0: Any): Boolean
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val
EPSILON: Double
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val
MAX_ITER: Int
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val
STEP: Double
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val
TOL: Double
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final
def
asInstanceOf[T0]: T0
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def
centroid(): Vertex
Calculate the centroid of the best-side of the simplex (excluding h=0), returning it and its functional value.
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def
clone(): AnyRef
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def
contractIn(x_c: VectorD, x_r: VectorD): Vertex
Contract: compute the inner contraction point between x_h and x_c.
Contract: compute the inner contraction point between x_h and x_c.
- x_c
the best-side centroid of the simplex
- x_r
the reflection point
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def
contractOut(x_c: VectorD, x_r: VectorD): Vertex
Contract: compute the outer contraction point between x_r and x_c.
Contract: compute the outer contraction point between x_r and x_c.
- x_c
the best-side centroid of the simplex
- x_r
the reflection point
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final
def
eq(arg0: AnyRef): Boolean
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def
equals(arg0: Any): Boolean
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def
expand(x_c: VectorD, x_r: VectorD): Vertex
Expand: compute the expansion point beyond the reflection point.
Expand: compute the expansion point beyond the reflection point.
- x_c
the best-side centroid of the simplex
- x_r
the reflection point
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def
fg(x: VectorD): Double
The objective function 'f' plus a weighted penalty based on the constraint function 'g'.
The objective function 'f' plus a weighted penalty based on the constraint function 'g'. Override for constrained optimization and ignore for unconstrained optimization.
- x
the coordinate values of the current point
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def
finalize(): Unit
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flaw(method: String, message: String): Unit
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def
getClass(): Class[_]
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hashCode(): Int
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def
improveSimplex(toler: Double = EPSILON): (Double, Double)
Improve the simplex by replacing the worst/highest vertex (x_h) with a a better one found on the line containing x_h and the centroid (x_c).
Improve the simplex by replacing the worst/highest vertex (x_h) with a a better one found on the line containing x_h and the centroid (x_c). Try the reflection, expansion, outer contraction and inner contraction points, in that order. If none succeeds, shrink the simplex and iterate. Return both distance and difference between x_h (worst) and x_l (best).
- toler
the tolerance used for termination
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def
initSimplex(x0: VectorD, step: Double): Unit
Initialize the search simplex by setting n + 1 vertices and computing their functional values.
Initialize the search simplex by setting n + 1 vertices and computing their functional values.
- x0
the given starting point
- step
the step size
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final
def
isInstanceOf[T0]: Boolean
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def
lineSearch(x: VectorD, dir: VectorD, step: Double = STEP): Double
Perform an exact (e.g.,
GoldenSectionLS
) or inexact (e.g.,WolfeLS
) line search.Perform an exact (e.g.,
GoldenSectionLS
) or inexact (e.g.,WolfeLS
) line search. Search in direction 'dir', returning the distance 'z' to move in that direction. Currently NOT USED, but may be used to find a better point to add to simplex.- x
the current point
- dir
the direction to move in
- step
the initial step size
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- NelderMeadSimplex → Minimizer
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final
def
ne(arg0: AnyRef): Boolean
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final
def
notify(): Unit
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final
def
notifyAll(): Unit
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def
reflect(x_c: VectorD): Vertex
Reflect: compute the reflection point of the worst point (h=0) across the centroid.
Reflect: compute the reflection point of the worst point (h=0) across the centroid.
- x_c
the best-side centroid of the simplex
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def
replace(x_n: VectorD): Unit
Replace the worst vertex (h=0) in the simplex with the new point.
Replace the worst vertex (h=0) in the simplex with the new point.
- x_n
the new replacement point
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def
shrink(): Unit
Shrink: fixing the best/lowest point (l=n), move the rest of the points toward it.
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def
solve(x0: VectorD, step: Double = STEP, toler: Double = EPSILON): VectorD
Solve the Non-Linear Programming (NLP) problem using the Nelder-Mead Simplex algorithm.
Solve the Non-Linear Programming (NLP) problem using the Nelder-Mead Simplex algorithm.
- x0
the given starting point
- step
the initial step size
- toler
the tolerance used for termination
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- NelderMeadSimplex → Minimizer
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def
sort(): Unit
Sort the vertices in non-increasing order (high to low).
Sort the vertices in non-increasing order (high to low). Then the key indices are worst/highest (h=0), second worst (s=1), and best/lowest (l=n).
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synchronized[T0](arg0: ⇒ T0): T0
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toString(): String
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