# An Eigenspace Divide-and-Conquer Approach for Large-Scale Optimization

arXiv: https://arxiv.org/abs/2004.02115 · HTML: https://mlsanity.com/paper/2004.02115/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Apr 2020.

## Built on by (most cited first, 1 of 1)

- [Island-Based Evolutionary Computation with Diverse Surrogates and Adaptive Knowledge Transfer for High-Dimensional Data-Driven Optimization](https://mlsanity.com/paper/2503.12856/) (2025)

## Abstract (arXiv)

Divide-and-conquer-based (DC-based) evolutionary algorithms (EAs) have achieved notable success in dealing with large-scale optimization problems (LSOPs). However, the appealing performance of this type of algorithms generally requires a high-precision decomposition of the optimization problem, which is still a challenging task for existing decomposition methods. This study attempts to address the above issue from a different perspective and proposes an eigenspace divide-and-conquer (EDC) approach. Different from existing DC-based algorithms that perform decomposition and optimization in the original decision space, EDC first establishes an eigenspace by conducting singular value decomposition on a set of high-quality solutions selected from recent generations. Then it transforms the optimization problem into the eigenspace, and thus significantly weakens the dependencies among the corresponding eigenvariables. Accordingly, these eigenvariables can be efficiently grouped by a simple random strategy and each of the resulting subproblems can be addressed more easily by a traditional EA. To verify the efficiency of EDC, comprehensive experimental studies were conducted on two sets of benchmark functions. Experimental results indicate that EDC is robust to its parameters and has good scalability to the problem dimension. The comparison with several state-of-the-art algorithms further confirms that EDC is pretty competitive and performs better on complicated LSOPs.