benchmarkfcns.salomon

benchmarkfcns.salomon(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 Salomon’s benchmark function. SCORES = salomon(X) computes the value of the Salomon’s function at point X. salomon 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: 0

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

  • Number of dimensions: n

  • Recommended domain: [-100, 100]^n

  • Number of local minima: many (The cosine of the Euclidean norm creates an

    infinite series of concentric circular “trap” valleys)

  • Number of global minima: 1

  • Convexity: non-convex

  • Separability: non-separable

  • Modality: multimodal

  • Symmetry: symmetric

  • Differentiable: Yes (Except potentially at the origin, though the limit usually

    behaves well)

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

Mathematical Definition

Visualization

salomon landscape