Information Bottleneck Theory-Guided Dimension Reduction for Large-Scale Multi-Objective Optimization

Dimension reduction has notably emerged in solving large-scale multi-objective optimization problems (LSMOPs). Nevertheless, the determination of the latent dimension after dimension reduction remains a critical challenge, where inappropriate dimensions risk the failure to find the Pareto optimal set. To address this issue, an information bottleneck theory-guided dimension estimation method is proposed, which theoretically derives the optimal latent dimension of LSMOPs. Specifically, the latent dimension is established in a quantitative relationship with the importance of decision variables based on information bottleneck theory. Then, the importance of decision variables with respect to convergence and diversity is quantified to determine the optimal latent dimension, and the high-dimensional decision space is subsequently projected into a low-dimensional latent space via dimension reduction techniques. Experimental results demonstrate the effectiveness of the proposed method on various problem suites, i.e., LSMOP, WFG, and ZCAT, when integrated with different dimension-reduction techniques. Furthermore, the version integrated with the weighted optimization framework also outperforms five representative competitors with superior performance on most of test problems.