An eigenspace divide-and-conquer approach for large-scale optimization

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 solution 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 decomposition 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. (C) 2020 Elsevier B.V. All rights reserved.

Automated summary

The study proposes an eigenspace divide-and-conquer approach, EDC, which establishes an eigenspace by conducting singular value decomposition on high-quality solutions to significantly weaken dependencies among eigenvariables. Experimental results show that EDC is robust to parameters and has good scalability in problem dimension. Comparisons with state-of-the-art algorithms demonstrate EDC's competitiveness and superior performance on complex optimization problems.