A Novel Fourier Latent Space Approach for High-Dimensional Benchmark Function Optimization with Differential Evolution

This paper introduces a fast and highly accurate optimization method called Fourier Latent Space Differential Evolution (FL-DE), designed for solving high-dimensional benchmark functions. By reducing the original 5000-dimensional problem space to a 1D or 2D latent representation using the Fourier Transform, FL-DE enables rapid and efficient search while preserving essential structural information.

The proposed method achieves up to 48,680× faster execution than standard Differential Evolution and reaches near-zero final cost on nearly all tested benchmark functions, including challenging multimodal problems like Rastrigin and Zakharov. This exceptional performance is made possible by leveraging the Fourier Transform’s ability to isolate dominant global features in the frequency domain, allowing the DE algorithm to focus on a compact and meaningful search space.

FL-DE offers a promising direction for high-dimensional optimization in computationally expensive domains such as machine learning hyperparameter tuning, signal processing, and engineering design.

🔗 Related GitHub Repositories:

• Fourier-latent-DE-optimizer (FL-DE): https://github.com/Farbodpya/Fourier-latent-DE-optimizer