Large Language Model-Driven Cooperative Operator Ensemble Evolution for Permutation Flow Shop Scheduling

2026-06-13

AI Summary

This work addresses the limited exploration and premature convergence of traditional Iterated Greedy (IG) algorithms for the Permutation Flowshop Scheduling Problem (PFSP), which stem from reliance on a single destruction operator. To overcome this, we propose IG-DOE, a novel algorithm featuring a stagnation-triggered mechanism that dynamically switches among heterogeneous destruction operators. Furthermore, IG-DOE integrates a Large Language Model (LLM)-driven Synergistic Collaborative Operator Evolution (SCOE) framework to automatically construct high-quality operator ensembles, thereby reducing dependence on manual design. Experimental results demonstrate that IG-DOE significantly outperforms QIG—the current state-of-the-art IG variant—on both the VRF-hard-large benchmark and real-world industrial datasets. Notably, operator sets evolved on small-scale instances exhibit strong generalization, effectively transferring to larger and out-of-distribution problem instances.

Abstract

The permutation flow shop scheduling problem (PFSP) is a classical NP-hard combinatorial optimization problem in intelligent manufacturing. In practice, PFSP is commonly addressed using metaheuristic algorithms, among which the iterated greedy (IG) algorithm is widely adopted due to its simplicity and strong empirical performance. However, classical IG relies on a single fixed destruction operator, which often limits exploration and leads to search stagnation on large and complex problem instances. To address this issue, this work proposes a multi-operator IG algorithm, termed IG-DOE, which enhances exploration by switching among heterogeneous destruction operators along a single search trajectory. The core mechanism, called stagnation-triggered sequential switching, activates the next destruction operator in an ordered destruction operator ensemble (DOE) when stagnation is detected, thereby enriching the perturbation behavior of classical IG. Moreover, to reduce reliance on expert-crafted operators, a large language model (LLM)-assisted framework, termed SCOE, is introduced to automatically construct a high-quality DOE through stagewise evolution, state-awareness, and cooperative evaluation. Experiments on the challenging \textit{VRF-hard-large} benchmark show that the DOE evolved from smaller problem instances generalizes well to larger unseen instances. Under the same CPU-time limit, IG-DOE obtained much better average performance than QIG, a state-of-the-art IG algorithm. Additional experiments on real-world industrial-data-derived instances further show that the evolved DOE can generalize effectively to different data distributions without additional adaptation.

Problem

• Permutation Flow Shop Scheduling
• Iterated Greedy Algorithm
• Search Stagnation
• Destruction Operator
• Combinatorial Optimization

Innovation

• Large Language Model
• Iterated Greedy Algorithm
• Destruction Operator Ensemble
• Permutation Flow Shop Scheduling
• Cooperative Evolution