Juan Yan

The Flexible Job-shop Scheduling Problem (FJSP), a pivotal NP-hard challenge in intelligent manufacturing, has been increasingly addressed by Deep Reinforcement Learning (DRL) methods. However, existing approaches face a dilemma: Proximal Policy Optimization (PPO) ensures stability but suffers from conservative exploration, while Soft Actor–Critic (SAC) enhances exploration but lacks stability in discrete scheduling spaces. To resolve this trade-off, this study proposes PPO-Graph Explorer, a novel framework that integrates a Graph Isomorphism Attention Network (GIAN) with an Entropy-Adjusted PPO (EAE-PPO). Unlike generic Graph Transformers, our GIAN employs a structure-aware hybrid design specifically tailored for FJSP’s disjunctive graph topology. EAE-PPO introduces a structured exploration curriculum that enables the agent to mimic aggressive search behaviors early in training without sacrificing on-policy stability. Extensive experiments on standard benchmarks (Brandimarte, Hurink, Dauzère–Pérès) demonstrate our method’s superiority. Compared to state-of-the-art DRL baselines, it achieves an average makespan gap reduction of 5.1 percentage points with zero statistical outliers. Qualitative analysis further reveals an 8.95% reduction in makespan on representative instances, accompanied by a significant increase in average machine utilization from 89.0% to 98.1%.

Due to numerous distributed power sources connecting to the grid, which results in strong grid volatility and diminished power quality, the traditional energy storage configuration is limited in terms of flexibility and economy. Based on this, integrating electric vehicles (EVs) into the distribution network as energy storage devices has emerged as a promising development direction. This paper proposes a frequency-response optimization study considering the strong uncertainty model of EVs. First, from the perspective of temporal-spatial characteristics, energy storage resources, and users’ willingness to respond, the strong uncertainty model of EVs is constructed by fitting the trip chain and the access probability of their participation in energy storage. Second, the frequency optimization model is integrated and constructed according to the response capability of a single EV. Finally, examples and scenarios are analyzed to verify that the maximum and minimum frequency offsets are reduced by 69.41% and 66.69%, respectively, which significantly reduces frequency fluctuations and stabilizes the output of EV clusters.