Multisource and Hidden Source-Based Knowledge Transfer for Solving Dynamic Multiobjective Optimization Problems

Recently, transfer-learning-based dynamic multiobjective optimization algorithms (TL-DMOAs) have been shown to be very promising in solving dynamic multiobjective optimization problems (DMOPs). However, it is difficult for them to model knowledge capable of delineating the Pareto optimal solutions (POSs) found in each historical environment, because the POSs’ distribution cannot be adequately reflected. Besides, existing TL-DMOAs normally focus on acquiring knowledge from historical environments, but neglect correlations behind them for excavating potential knowledge, restricting the performance in generating high-quality initial populations (HIPs). To address these issues, herein a DMOA with multisource and hidden source-based knowledge transfer (DMOA-MHKT) is proposed. First, we design a knowledge extraction strategy by introducing mean shift, a nonparametric clustering method, to cluster the historical POSs. As clusters’ representatives, the cluster centers are considered to represent environmental knowledge, because they can adequately reflect the POSs’ distribution. Second, the most similar historical environment through environmental match and the last one are selected as two explicit sources. In the former source the POSs’ cluster centers are treated as its knowledge. By contrast, based on the POSs’ cluster centers and knee points in the latter source, a scoring method is designed to generate environmental knowledge by depicting the dynamics between two continuous environments. Third, after aligning knowledge of the explicit sources, a hidden source is learned by excavating correlations and potential knowledge behind them, facilitating the generalization enhancement in generating HIPs. The experimental results especially performance comparisons with seven state-of-the-art DMOAs demonstrate that DMOA-MHKT brings significant improvements in solving DMOPs.