benchmarkfcns.trid

benchmarkfcns.trid(arg0: Annotated[numpy.typing.NDArray[numpy.float64], '[m, n]', 'flags.c_contiguous']) → Annotated[numpy.typing.NDArray[numpy.float64], '[m, 1]']

Computes the value of the Trid benchmark function. SCORES = trid(X) computes the value of the Trid function at point X. trid accepts a matrix of size M-by-N and returns a vector SCORES of size M-by-1 in which each row contains the function value for the corresponding row of X. Properties:

  • Global minimum:

    • For n=6: -50

    • For n=10: -210

    • General formula: -n(n+4)(n-1)/6

  • Location of global minimum: x_i = i(n + 1 - i)

  • Number of dimensions: n

  • Recommended domain: x_i ∈ [-n^2, n^2]

  • Number of local minima: 0 (Unimodal)

  • Convexity: Convex

  • Separability: Non-separable

  • Symmetry: Non-symmetric

  • Differentiable: Yes

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

Mathematical Definition

Visualization

trid landscape