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

Dynamic multi-objective optimization requires continuous tracking of moving Pareto fronts. Existing methods struggle with irregular mutations and data sparsity, primarily facing three challenges: the non-linear coupling of dynamic modes, negative transfer from outdated historical data, and the cold-start problem during environmental switches. To address these issues, this paper proposes a decoupled basis-vector-driven generative framework (DB-GEN). First, to resolve non-linear coupling, the framework employs the discrete wavelet transform to separate evolutionary trajectories into low-frequency trends and high-frequency details. Second, to mitigate negative transfer, it learns transferable basis vectors via sparse dictionary learning rather than directly memorizing historical instances. Recomposing these bases under a topology-aware contrastive constraint constructs a structured latent manifold. Finally, to overcome the cold-start problem, a surrogate-assisted search paradigm samples initial populations from this manifold. Pre-trained on 120 million solutions, DB-GEN performs direct online inference without retraining or fine-tuning. This zero-shot generation process executes in milliseconds, requiring approximately 0.2 seconds per environmental change. Experimental results demonstrate that DB-GEN improves tracking accuracy across various dynamic benchmarks compared to existing algorithms.

IB-GRPO: Aligning LLM-based Learning Path Recommendation with Educational Objectives via Indicator-Based Group Relative Policy Optimization

Learning Path Recommendation (LPR) aims to generate personalized sequences of learning items that maximize long-term learning effect while respecting pedagogical principles and operational constraints. Although large language models (LLMs) offer rich semantic understanding for free-form recommendation, applying them to long-horizon LPR is challenging due to (i) misalignment with pedagogical objectives such as the Zone of Proximal Development (ZPD) under sparse, delayed feedback, (ii) scarce and costly expert demonstrations, and (iii) multi-objective interactions among learning effect, difficulty scheduling, length controllability, and trajectory diversity. To address these issues, we propose IB-GRPO (Indicator-Based Group Relative Policy Optimization), an indicator-guided alignment approach for LLM-based LPR. To mitigate data scarcity, we construct hybrid expert demonstrations via Genetic Algorithm search and teacher RL agents and warm-start the LLM with supervised fine-tuning. Building on this warm-start, we design a within-session ZPD alignment score for difficulty scheduling. IB-GRPO then uses the $I_{ε+}$ dominance indicator to compute group-relative advantages over multiple objectives, avoiding manual scalarization and improving Pareto trade-offs. Experiments on ASSIST09 and Junyi using the KES simulator with a Qwen2.5-7B backbone show consistent improvements over representative RL and LLM baselines.