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

TL;DR

This paper introduces an eigenspace divide-and-conquer method for large-scale optimization that improves problem decomposition by leveraging eigenspaces derived from high-quality solutions, enhancing efficiency and scalability.

Contribution

The paper proposes a novel eigenspace-based decomposition approach that weakens variable dependencies, enabling more effective optimization of large-scale problems compared to existing methods.

Findings

EDC is robust to parameter settings.

It demonstrates good scalability with problem dimension.

EDC outperforms several state-of-the-art algorithms on complex LSOPs.

Abstract

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.