A Decoupled Basis-Vector-Driven Generative Framework for Dynamic Multi-Objective Optimization

Dynamic multiobjective optimization problems (DMOPs) feature time-varying objectives, which cause the Pareto optimal solution (POS) set to drift over time and make it difficult to maintain both convergence and diversity under limited response time. Many existing prediction-based dynamic multiobjective evolutionary algorithms (DMOEAs) either depend on learned models with nontrivial training cost or employ one-step population mapping, which may overlook the gradual nature of POS evolution. This paper proposes DD-DMOEA, a training-free diffusion-based dynamic response mechanism for DMOPs. The key idea is to treat the POS obtained in the previous environment as a "noisy" sample set and to guide its evolution toward the current POS through an analytically constructed multi-step denoising process. A knee-point-based auxiliary strategy is used to specify the target region in the new environment, and an explicit probability-density formulation is derived to compute the denoising update without neural training. To reduce the risk of misleading guidance caused by knee-point prediction errors, an uncertainty-aware scheme adaptively adjusts the guidance strength according to the historical prediction deviation. Experiments on the CEC2018 dynamic multiobjective benchmarks show that DD-DMOEA achieves competitive or better convergence-diversity performance and provides faster dynamic response than several state-of-the-art DMOEAs.

Dynamic multi-objective optimization with a variable number of objectives is difficult because objective-dimensional variations may significantly change the Pareto front and degrade algorithm adaptability. This paper proposes an unbounded archive-based transfer strategy (UATS), which maintains an unbounded archive of offspring solutions within each environment stage and extracts feasible nondominated solutions as transferable elites when objective changes occur. UATS is embedded into SPEA2SDE to construct UATS-SPEA2SDE, enabling the algorithm to reuse historical evolutionary information while retaining the convergence and diversity advantages of shift-based density estimation. Experiments are conducted on four benchmark problems under three objective-changing settings, where UATS-SPEA2SDE is compared with a restart-based SPEA2SDE baseline and four representative dynamic multi-objective optimization algorithms. The results indicate that the archive-guided transfer improves recovery after environmental changes and enhances adaptability to objective-number variations.

Streaming data-driven dynamic multi-objective optimization requires algorithms to track time-varying Pareto fronts using only sequential observations under concept drift. However, systematic evaluation remains difficult because real-world problems usually lack ground-truth optima, drift annotations, and controllable conditions, while existing benchmarks provide limited support for standardized comparison. This paper proposes SDDMO-Bench, a benchmark suite that transforms classical dynamic multi-objective test problems into streaming environments by combining intrinsic objective-mapping evolution, controllable distributional drift, and sequential data revelation. By combining five representative time-dependent base functions with six distributional drift patterns, SDDMO-Bench constructs 30 scenarios with diverse levels of non-stationarity, problem complexity, sample-distribution variation, and Pareto-front evolution. Experiments with representative evolutionary algorithms demonstrate that SDDMO-Bench provides challenging and discriminative test scenarios, offering a standardized, controllable, and reproducible benchmark for evaluating adaptability, robustness, and Pareto-front tracking in streaming data-driven dynamic multi-objective optimization.