  Real-world optimization problems may have a different underlying structure.
In black-box optimization, the dependencies between decision variables remain
unknown. However, some techniques can discover such interactions accurately. In
Large Scale Global Optimization (LSGO), problems are high-dimensional. It was
shown effective to decompose LSGO problems into subproblems and optimize them
separately. The effectiveness of such approaches may be highly dependent on the
accuracy of problem decomposition. Many state-of-the-art decomposition
strategies are derived from Differential Grouping (DG). However, if a given
problem consists of non-additively separable subproblems, DG-based strategies
may discover many non-existing interactions. On the other hand, monotonicity
checking strategies proposed so far do not report non-existing interactions for
any separable subproblems but may miss discovering many of the existing ones.
Therefore, we propose Incremental Recursive Ranking Grouping (IRRG) that
suffers from none of these flaws. IRRG consumes more fitness function
evaluations than the recent DG-based propositions, e.g., Recursive DG 3 (RDG3).
Nevertheless, the effectiveness of the considered Cooperative Co-evolution
frameworks after embedding IRRG or RDG3 was similar for problems with
additively separable subproblems that are suitable for RDG3. After replacing
the additive separability with non-additive, embedding IRRG leads to results of
significantly higher quality.
