Exploring high-dimensional optimization by sparse and low-rank evolution strategy

Evolution strategies (ESs) are a robust family of algorithms for black-box optimization, yet their applicability to high-dimensional problems remains constrained by computational challenges. To address this, we propose a novel evolution strategy, SLR-ES, leveraging a sparse plus low-rank covariance matrix model. The sparse component utilizes a diagonal matrix to exploit separability along coordinate axes, while the low-rank component identifies promising subspaces and parameter dependencies. To maintain distribution fidelity, we introduce a decoupled update mechanism for the model parameters. Comprehensive experiments demonstrate that SLR-ES achieves state-of-the-art performance on both separable and non-separable functions. Furthermore, evaluations on the CEC’2010 and CEC’2013 large-scale global optimization benchmarks reveal consistent superiority in average ranking, highlighting the algorithm's robustness across diverse problem conditions. These results establish SLR-ES as a scalable and versatile solution for high-dimensional optimization. © 2024 Elsevier B.V.