benchmarkfcns.multifidelity.robotarm

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

Computes the value of the multi-fidelity Robot Arm function. SCORES = robotarm(X) computes the value of the Robot Arm function at point X. multifidelity.robotarm accepts a matrix of size M-by-8 and returns a matrix SCORES of size M-by-2. Properties (High-fidelity):

• Dimensions: 8

• Recommended domain: L in [0, 1], theta in [0, 2pi]

Mathematical Definition

\[\begin{aligned}\]

u &= sum_{i=1}^4 L_i cos(sum_{j=1}^i theta_j), quad v = sum_{i=1}^4 L_i sin(sum_{j=1}^i theta_j) \ f(theta, textbf{L}) &= sqrt{u^2 + v^2} \ f_{hf}(mathbf{x}) &= f(theta, textbf{L}) \ f_{lf}(mathbf{x}) &= f(theta, textbf{L} + 0.05) end{aligned}

Visualization

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