benchmarkfcns.zerosum

benchmarkfcns.zerosum(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 Zero Sum benchmark function. SCORES = zerosum(X) computes the value of the Zero Sum function at point X. zerosum 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: Any point where $sum_{i=1}^{n} x_i = 0$ (e.g.,

    (1, -1) or (5, -2, -3))

  • Number of dimensions: n

  • Recommended domain: [-10, 10]^n

  • Number of local minima: 0 (Technically, it is constant everywhere else)

  • Number of global minima: Infinite (Any point on the hyperplane defined by the

    sum equal to zero)

  • Convexity: Non-convex

  • Separability: Non-separable (The variables must sum to a specific value)

  • Modality: Unimodal (in terms of the target hyperplane)

  • Differentiable: No (The function “jumps” from values > 1 down to 0 instantly)

Mathematical Definition

Visualization

zerosum landscape