Neural Networks as Black-Box Benchmark Functions Optimized for Exploratory Landscape Features

Artificial benchmark functions are commonly used in optimization research because of their ability to rapidly evaluate potential solutions, making them a preferred substitute for real-world problems. However, these benchmark functions have faced criticism for their limited resemblance to real-world problems. In response, recent research has focused on automatically generating new benchmark functions for areas where established test suites are inadequate. These approaches have limitations, such as the difficulty of generating new benchmark functions that exhibit exploratory landscape analysis (ELA) features beyond those of existing benchmarks. The objective of this work is to develop a method for generating benchmark functions for single-objective continuous optimization with user-specified structural properties. Specifically, we aim to demonstrate a proof of concept for a method that uses an ELA feature vector to specify these properties in advance. To achieve this, we begin by generating a random sample of decision space variables and objective values. We then adjust the objective values using CMA-ES until the corresponding features of our new problem match the predefined ELA features within a specified threshold. By iteratively transforming the landscape in this way, we ensure that the resulting function exhibits the desired properties. To create the final function, we use the resulting point cloud as training data for a simple neural network that produces a function exhibiting the target ELA features. We demonstrate the effectiveness of this approach by replicating the existing functions of the well-known BBOB suite and creating new functions with ELA feature values that are not present in BBOB.