# A Deep Learning-Driven Black-Box Benchmark Generation Method via Exploratory Landscape Analysis
## 1 Introduction  
The evaluation of optimization algorithms critically depends on benchmark problems that reflect the complexity and diversity of real-world tasks [1]. Widely used standardized artificial benchmark suites, such as the annually updated Congress on Evolutionary Computation (CEC) benchmark suite [2], BBOB suite [3], and Nevergrad [4], offer controlled environments with characteristics like multimodality, separability, and ill-conditioning. While these suites are invaluable tools, there is an ongoing debate about their ability to truly reflect the complexities of real-world problems [5]. However, many real-world problems exhibit landscape characteristics such as irregular multimodality, deceptive basins, and poorly conditioned structures. These features are underrepresented in widely used benchmark suites, such as the BBOB. These limitations restrict the generalizability of the benchmarking results and contribute to the performance gap observed when algorithms are deployedin practice. This work aims to address this issue by generating benchmark functions that occupy previously unpopulated regions of the ELA feature space, thus expanding the test coverage to better reflect real-world complexity. Research indicates that these artificial problems do not capture the intricacies of practical applications, potentially leading to biased development and evaluation of algorithms [6]. Consequently, algorithms excel on these benchmarks but underperform in real-world applications. Real-world optimization tasks are often high-cost, proprietary, or noisy, making them impractical for standardized benchmarking [7, 8], and current artificial benchmarks offer limited coverage of the landscape diversity necessary for robust generalization [9]. Efforts are being made to incorporate real-world data characteristics and simulate more complex problem landscapes that better reflect practical challenges [10]. To bridge this gap, recent research has explored landscape-aware benchmarks and machine learning-based function generation to simulate more realistic problem characteristics. In this work, the benchmark diversity challenge is addressed by a neural network-based framework to generate fitness functions conditioned on target Exploratory Landscape Analysis (ELA) features. This enables both the emulation of known benchmarks and the creation of novel problem instances with user-specified structural properties. The generated functions preserve topological coherence through Inverse Distance Weighting Regression (IDWR) interpolation, which allows for smooth and controllable landscapes. Two distinct experimental setups are presented in this paper. The first focuses on validating the neural network-based method through the emulation of established benchmark functions (NNBBOB). The other set of experiments explored the potential of this approach to generate completely new functions and deeper insights into optimization behavior under varied landscape conditions. These two categories are conceptually different in their placement within the ELA feature space: NNBBOB functions reside in densely sampled, known regions, while new functions explore sparse and previously unrepresented areas. The main contributions of this paper are summarized as follows:  
* The devised approach uses neural networks to generate problem instances with arbitrary combinations of properties regarding the chosen ELA features and target fitness landscape properties. * The method interpolates and extrapolates beyond the existing feature spaces, which allows the generation of problem instances that enhance the diversity and complexity of the benchmark suite. * The topological map point with the IDWR interpolation method is adopted to enhance the capability to test optimization algorithms against a wider variety of problem landscapes leading to the development of more robust and versatile algorithms. The remainder of this paper is organized as follows. Related work is presented in Section 2. The ELA is described in Section 3.