Adaptive Manifold‑Driven Knowledge Transfer via Reinforcement Learning for Multi‑Objective Multi‑Task Optimization

Multi‑objective multi‑task optimization (MO‑MTO) improves search performance by reusing cross‑task manifold‑structured knowledge. Existing manifold‑driven MO‑MTO algorithms adopt a fixed knowledge‑transfer probability (KTP), which fails to adapt local transfer frequency according to runtime feedback including population evolution, manifold validity, and offspring survival outcomes. To address this limitation, we propose RL-EMT-MSKT, which formulates task-specific KTP adjustment as a Markov decision process and learns multiplicative KTP updates from runtime observations using proximal policy optimization. Specifically, we design a Cross‑Task Relation Encoder with scaled dot‑product attention to aggregate pairwise task states, and employ Proximal Policy Optimization to learn multiplicative KTP updates. We introduce an adaptive differential evolution (ADE) operator that adjusts its mutation and crossover parameters to strengthen intra-task search. For inter-task transfer, local structure learning (LSL) generates offspring using knowledge of task manifolds. The learned KTP then controls, for each individual, the probability of invoking LSL rather than ADE. Evaluated on the CEC21‑MTMO‑CPLX benchmark with IGD and normalized HV metrics alongside Wilcoxon statistical tests, our proposed method outperforms seven state‑of‑the‑art MO‑MTO competitors on most test instances. Ablation studies validate the individual contributions of the RL‑based KTP controller and ADE component.The source code is available at:https://github.com/tomz18690-cell/RL-EMT-MSKT