A Dynamic Multi-Objective Optimization Algorithm via Trend-Cycle Decoupling and Hybrid Time-Series Prediction

Addressing the challenge that, in real-world dynamic multi-objective optimization problems (DMOPs), the severity of changes between pareto optimal set (PS) varies at different times and exhibits nonlinear characteristics rather than simple translations or rotations—making them difficult for traditional prediction strategies to track accurately—this paper proposes a dynamic multi-objective optimization algorithm via trend-cycle decoupling and hybrid time-series prediction. The algorithm first applies the Hodrick-Prescott (HP) filter to decompose the time-series of historical PS centers into a smooth trend component and a fluctuating cycle component to cope with uncertainty in the severity of changes. Then, an AR(p) model is used to fit the trend sequence and infer the long-term linear direction of PS movement; a long short-term memory (LSTM) network learns the cycle sequence to capture nonlinear variation patterns. By fusing the two prediction results, the center of the PS in the new environment is located, and an initial population is constructed using a manifold-based population generation strategy. Comparative experiments on 13 standard dynamic test functions show that the proposed algorithm achieves an effective trade-off between prediction accuracy and computational cost and demonstrates strong robustness to complex time-varying environments. In particular, in scenarios where the pareto optimal front (PF) undergoes rotation, discontinuity, or time-varying shape (convexity/concavity) due to complex mappings in the decision space, the algorithm maintains notable tracking accuracy and population diversity by precisely capturing the PS evolution trajectory.