PLAN: Parallel Liquid-Inspired Approximation Network for Efficient Representation Learning in Flexible Job Shop Scheduling

2026-08-03

AI Summary

This work addresses the computational bottlenecks of deep reinforcement learning models in flexible job shop scheduling problems (FJSP), particularly their large parameter counts and high inference latency. To this end, the authors propose a lightweight, parallelized representation learning framework that, for the first time, discretizes and decouples the continuous dynamics of liquid neural networks into two parallel modules: state update and context aggregation. This design enables plug-and-play deployment and seamless integration with either stochastic policies or heterogeneous graph Transformers. Evaluated across multiple FJSP benchmarks, the proposed method reduces makespan by 1.2%–2.3% on average (up to 10.2%), cuts inference latency by 13.2%–69.2%, and achieves only 22%–47% of the baseline model’s parameter count, substantially enhancing both computational efficiency and generalization capability.

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.

Problem

• Flexible Job Shop Scheduling
• Deep Reinforcement Learning
• Liquid Neural Networks
• Computational Efficiency
• Parameter Efficiency

Innovation

• Parallel Liquid-inspired Approximation Network
• Flexible Job Shop Scheduling
• Liquid Neural Networks
• Parameter-Efficient Representation Learning
• Plug-and-Play Backbone