  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.
