PLAN: Parallel Liquid-Inspired Approximation Network for Efficient Representation Learning in Flexible Job Shop Scheduling
Authors: Dhivya Dharshini Kannan, Wei Zhang, Jieyi Bi, Yingpeng Du, Tianjun Wei, Jie Zhang, Zuming Liu, Anupam Trivedi
Organizations: Singapore Institute of Technology (SIT) · Nanyang Technological University (NTU) · Shanghai Jiao Tong University · Agency for Science, Technology and Research (A*STAR)
Abstract
Deep reinforcement learning (DRL) approaches for flexible job shop scheduling (FJSP) heavily rely on attention-centric architectures to achieve state-of-the-art performance. However, these models suffer from excessive parameter counts and prohibitive inference latency as problem scales expand. While liquid neural networks (LNNs) offer a parameter-efficient alternative for modeling adaptive state evolution, their inherently sequential dynamics bottleneck computational efficiency. To resolve this trade-off, we propose PLAN (Parallel Liquid-inspired Approximation Network), a lightweight representation learning framework that reformulates continuous liquid-state dynamics into a discretized and parallelizable formulation. PLAN structurally decouples state evolution from context aggregation, where liquid-inspired updates handle the primary evolving state representation, and a lightweight context aggregation module provides complementary global context. Furthermore, PLAN acts as a versatile, plug-and-play backbone that generalizes to complex FJSP variants, pairing with a compact stochastic module for stochastic FJSP and replacing heavy heterogeneous graph transformers in multi-faceted dynamic FJSP. Extensive evaluations across deterministic, stochastic, and multi-faceted dynamic FJSP benchmarks show that PLAN reduces the average makespan by 1.2%, 1.4%, and 2.3%, respectively, compared with the corresponding state-of-the-art baselines, with the improvement reaching 10.2% in one benchmark setting. PLAN also reduces average inference latency by 13.2%, 31.7%, and 26.9%, respectively, with a maximum reduction of 69.2% on the largest instances, while using only 22−47% of the baseline parameters.
The Flexible Job Shop Scheduling Problem (FJSP) is the optimal allocation of a set of jobs to machines. Two primary challenges persist in FJSP: the unpredictable arrival of future jobs and the combinatorial complexity of the problem, rendering it intractable for conventional mixed-integer linear programming solvers. This paper proposes an event-based \gls{DRL} approach to solve FJSP with random job arrivals. Specifically, we employ the Proximal Policy Optimization algorithm and use lightweight Multi-Layer Perceptrons to train the \gls{DRL} agent for minimizing the total completion time of all jobs. We design the state representation to be directly accessible from the environment, and limit the learning agent to selecting from among a set of well-established dispatching rules. Simulations show that our \gls{DRL} approach outperforms any of the individual dispatching rules on datasets with varying heterogeneity and job arrival rates. We benchmark our \gls{DRL} against an arrival-triggered mixed-integer linear programming solution and show that our method achieves good performance especially when the datasets are heterogeneous.
The Dynamic Flexible Job Shop Scheduling Problem (DFJSP) necessitates a trade-off between instant reaction to stochastic disturbances and global optimization of production goals. Conventional priority rules are insufficiently flexible to handle complex disruptions, whereas learning-based approaches often compromise interpretability or fail to generalize across problem scales. Although Large Language Models (LLMs) offer advanced reasoning capabilities to bridge this gap, their substantial inference latency is incompatible with the millisecond-level decision cycles of industrial control systems. To resolve this conflict, we introduce RACE-Sched, an asynchronous agent-based framework that decouples policy execution from logical reasoning via a dual-stream architecture. The Reactive Stream executes low-latency symbolic heuristics to enable real-time dispatching, while the parallel Deliberative Stream leverages an LLM to synthesize, validate, and evolve these rules. Candidate rules undergo rigorous testing in a sandbox and are deployed via atomic updates, ensuring safety without blocking the control loop. Additionally, a semantic rule repository indexes validated heuristics for retrieval-based initialization which enhances transferability across problem scales. Extensive evaluations on GEN-Bench, MK-Bench, and JMS-Bench demonstrate that RACE-Sched outperforms leading Deep Reinforcement Learning and other LLM-based baselines. This approach harmonizes real-time constraints with long-horizon reasoning to achieve superior solution quality and robust adaptation to dynamic events.
This paper proposes a novel Variational Graph-to-Scheduler (VG2S) framework for solving the Job Shop Scheduling Problem (JSSP), a critical task in manufacturing that directly impacts operational efficiency and resource utilization. Conventional Deep Reinforcement Learning (DRL) approaches often face challenges such as non-stationarity during training and limited generalization to unseen problem instances because they optimize representation learning and policy execution simultaneously. To address these issues, we introduce variational inference to the JSSP domain for the first time and derive a probabilistic objective based on the Evidence of Lower Bound (ELBO) with maximum entropy reinforcement learning. By mathematically decoupling representation learning from policy optimization, the VG2S framework enables the agent to learn robust structural representations of scheduling instances through a variational graph encoder. This approach significantly enhances training stability and robustness against hyperparameter variations. Extensive experiments demonstrate that the proposed method exhibits superior zero-shot generalization compared with state-of-the-art DRL baselines and traditional dispatching rules, particularly on large-scale and challenging benchmark instances such as DMU and SWV.