Characteristic analysis of noise-induced artificial landscape functions using a virtual instrument-based framework

Optimisation under uncertainty requires understanding not only variations in objective values but also noise-induced relocation of the detected optimum. This study presents a reproducible LabVIEW virtual-instrument framework to characterise the intrinsic robustness of benchmark optimisation landscapes, rather than evaluate an optimisation algorithm. Seven two-dimensional and three three-dimensional benchmark functions were discretised and subjected to variance-matched Gaussian, Laplace, and Bernoulli–Gaussian perturbations across six noise levels. For each condition, 100 independent noisy realisations were generated to quantify minimum-value sensitivity, radial positional dispersion, bias distance, drift ratio, stability index, robustness-growth coefficient, and confidence-based repeatability. The results show that noise response depends jointly on local landscape geometry and disturbance distribution. Strong, directionally balanced confinement generally preserved positional stability, whereas weakly confined directions, narrow basins, and multimodality promoted relocation of the detected minimum. Matyas exhibited the largest Gaussian 2D dispersion-growth coefficient (4.54), while 3D Griewank showed substantially greater sensitivity, reaching 19.18 under Gaussian noise. Most conditions were dispersion-dominated, indicating stochastic relocation rather than persistent directional drift; Easom showed more pronounced systematic displacement under selected impulsive and heavy-tailed conditions. The framework uniquely integrates value sensitivity, spatial dispersion, systematic bias, and noise-dependent growth within one automated protocol, providing a geometry-sensitive basis for robustness assessment under uncertainty.