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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- 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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- 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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- @throws(classOf[java.lang.CloneNotSupportedException]) @native() @HotSpotIntrinsicCandidate()
- 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
- 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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- 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
- 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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- final def flaw(method: String, message: String): Unit
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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
- 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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- 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
- final def ne(arg0: AnyRef): Boolean
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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
- 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
- def shrink(): Unit
Shrink: fixing the best/lowest point (l=n), move the rest of the points toward it.
- 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
- Definition Classes
- NelderMeadSimplex → Minimizer
- 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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