benchmarkfcns.xinsheyangn3

benchmarkfcns.xinsheyangn3(x: Annotated[numpy.typing.NDArray[numpy.float64], '[m, n]', 'flags.c_contiguous'], beta: SupportsFloat | SupportsIndex = 15, m: SupportsFloat | SupportsIndex = 5) → Annotated[numpy.typing.NDArray[numpy.float64], '[m, 1]']

Computes the value of the Xin-She Yang N. 3 function. The Xin-She Yang N. 3 function is a parametric function and it is behaviour can be controlled with two additional parameters ‘beta’ and ‘m’. In this implementation, the parameters are optional and when not given, their default value will be used. SCORES = xinsheyang3(X) computes the value of the Xin-She Yang N. 3 function at point X. xinsheyang3 accepts a matrix of size P-by-N and returns a vector SCORES of size P-by-1 in which each row contains the function value for the corresponding row of X. In this case, the default values of ‘m=5’ and ‘beta=15’ is used for function parameters. SCORES = xinsheyang3(X, beta=BETA) computes the function with the given value of BETA for its ‘beta’ parameter. In this case, the default value of ‘m=5’ will be used for the parameter. SCORES = xinsheyang3(X, beta=BETA, m=M) computes the function with the given value of M for its ‘m’ parameter. Properties:

  • Global minimum: 0

  • Location of global minimum: (0, 0, …, 0)

  • Number of dimensions: n (Scalable)

  • Recommended domain: x_i ∈ [-2π, 2π]

  • Number of local minima: Numerous (Highly periodic)

  • Number of global minima: 1

  • Convexity: Non-convex

  • Separability: Separable (The terms for each x_i are summed)

  • Modality: Highly Multimodal

  • Symmetry: Symmetric

  • Differentiable: Yes

For more information, please visit: benchmarkfcns.info/doc/xinsheyangn3fcn

Mathematical Definition

Visualization

xinsheyangn3 landscape