# A Deep Learning-Driven Black-Box Benchmark Generation Method via Exploratory Landscape Analysis
## 5 Experiment Setup
### Compare Algorithms' Performance in New Benchmark Functions  
In Figure 12, the performances of multiple optimization algorithms are compared across five newly generated benchmark functions. In (a), RS ultimately achieved the lowest mean loss at the highest budget, followed by DE and COBYLA. The dCMAES and EMNA converge more slowly, while ND shows almost no improvement across the entire budget span. In (b), DE and COBYLA dominate the convergence, which reaches the normalized loss by the maximum budget. EMNA, PSO, and dCMAES exhibit moderate descent rates in the \(10^{-2}\)-\(10^{-3}\) region, whereas ND with restarts remains essentially flat above \(10^{-1}\). In (c), DE again achieves the best final performance, closely followed by RS and COBYLA. EMNA and dCMAES converge to intermediate loss levels, while ND fails to make substantive progress. In (d), COBYLA attains the lowest mean loss at high budgets, with dCMAES and PSO following it. DE and RS converge more gradually into the \(10^{-3}\) range, and ND remains stalled around \(10^{-1}\). In (e), both DE and COBYLA converge to an exceptionally low loss, which outperforms EMNA and RS. PSO and dCMAES settle at higher plateaus, and ND exhibits negligible reduction. The comparison reveals that DE, COBYLA, and RS demonstrate the most competitive performance on the \(3D\) versions of these novel functions. Notably, RS performs relatively well on a subset of generated functions, particularly those targeting simple landscape features. This highlights that our approach can generate not only complex but also trivial instances, which is useful for testing the robustness and overfitting tendencies of sophisticated algorithms.  
These algorithms consistently achieve the lowest rescaled losses, particularly under larger evaluation budgets, which indicates robust optimization capabilities even in the presence of complex and highly irregular fitness landscapes. Algorithms like DE and PSO, which achieve minimal rescaled losses across topologically diverse landscapes (as defined by the ELA feature), demonstrate robustness, meaning they adapt their search dynamics effectively, even in highly multimodal or irregular terrains. Their effectiveness suggests a strong global search behavior and adaptability to the diverse landscape features introduced by the new benchmarks. By contrast, the NMEA algorithm showed significantly inferior performance across the evaluated scenarios. Its higher loss values and slower convergence rates reflect limitations when tackling high-dimensional spaces or landscapes characterized by non-smooth and complex topologies. This performance gap underscores the importance of selecting optimization algorithms that are resilient to the increased difficulty introduced by artificially generated benchmark instances. Overall, these results highlight the ability of evolutionary and stochastic methods, such as DE and RS, to generalize better across unknown or challenging landscapes than local search-based methods like NMEA.  
Figure 11: Visualization of the fitness landscapes of five newly generated benchmark functions in 2D, created using the proposed CMA-ES and NN-based generation framework. Each subplot shows a contour plot of the generated function over the input space, highlighting the multimodality and irregular landscape structure.