An Eigenspace Divide-and-Conquer Approach for Large-Scale Optimization
This addresses the need for more efficient decomposition methods in evolutionary algorithms for large-scale optimization problems, though it appears incremental as it builds on existing divide-and-conquer frameworks.
The paper tackles the challenge of high-precision decomposition in divide-and-conquer evolutionary algorithms for large-scale optimization by proposing an eigenspace divide-and-conquer approach, which transforms the problem into an eigenspace to weaken variable dependencies and uses a simple random grouping strategy, resulting in robust performance and better scalability on complicated problems compared to state-of-the-art methods.
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.