A manifold prediction strategy for evolutionary dynamic multiobjective optimization

Prediction-based evolutionary algorithms have shown impressive effectiveness in solving dynamic multiobjective optimization problems (DMOPs). Typically, these algorithms utilize the historical information of specific representative points, such as center and knee points, to predict the moving trend of the Pareto-optimal set (PS). However, the changing pattern of PS may be inconsistent with that of the representative points, potentially leading to inaccurate prediction of the new PS. Manifold learning captures the overall distribution of PS. Therefore, the changing trend of the manifold reflects the changing pattern of PS. This work introduces a manifold prediction strategy (MPS) for evolutionary dynamic multiobjective optimization algorithms. The MPS predicts the manifold of the PS in a new environment based on the trend observed in historical PSs. Specifically, the Local Principal Component Analysis (LPCA) algorithm is enhanced to learn the manifolds of historical PSs. Using these learned manifolds, MPS estimates the manifold of the PS in the new environment with a linear prediction model. Recognizing that the accuracy of manifold learning results will affect the accuracy of manifold prediction, two methods are proposed to improve the learning results. These methods focus on determining an appropriate number of local manifolds and reducing the randomness during the modeling process. The proposed MPS is tested and compared with several state-of-the-art dynamic multiobjective evolutionary algorithms on various benchmark test instances. Experimental results indicate that MPS outperforms other algorithms on most instances.