A deep-based Gaussian mixture model algorithm for large-scale many objective optimization

As the number of decision variables increases, the curse of dimensionality becomes a significant challenge in many practical multi-objective optimization problems. This issue is further exacerbated in large-scale many-objective optimization problems (MaOPs), where the growing number of optimization objectives makes it increasingly difficult for evolutionary algorithms to find optimal solutions. In this study, we propose a deep Gaussian mixture model algorithm tailored for large-scale MaOPs. The novelty of this approach lies in its hierarchical detection of interactions and redundancies among decision variables, enabling a more effective grouping of variables. Specifically, a Gaussian mixture model-based framework is used to model the problem, allowing for the preliminary grouping of decision variables. The proposed Grouping Decision Variables using the Gaussian Mixture Model (GDVG) algorithm categorizes variables into two types: convergence-related and diversity-related variables. Additionally, a Linkage Identification Measurement with Chaos (LIMC) method is introduced for grouping convergence-related variables based on their interactions. For diversity-related variables, we present a Trivial Variable Detection Scheme (TVDS) to identify and group variables that contribute to diversity. The experimental results demonstrate that the proposed method outperforms other competitive algorithms on most benchmark test cases, particularly showcasing its effectiveness in large-scale MaOPs.