EvoDR: Evolving Dispatching Rules via Large Language Model for Dynamic Flexible Assembly Flow Shop Scheduling

Junhao Qiu; Haoyang Zhuang; Fei Liu; Jianjun Liu; Qingfu Zhang

cs.NEJan 22, 2026

EvoDR: Evolving Dispatching Rules via Large Language Model for Dynamic Flexible Assembly Flow Shop Scheduling

Authors: Junhao Qiu, Haoyang Zhuang, Fei Liu, Jianjun Liu, Qingfu Zhang

Organizations: Department of Computer Science, City University of Hong Kong, Hong Kong, China. · School of Electromechanical Engineering, Guangdong University of Technology, Guangzhou, China.

Abstract

Dynamic flexible assembly flow shop scheduling with multi-product delivery, often with kitting supply and machine-level flexibility, can be found in many applications. It is difficult to design rules manually for it. Genetic programming (GP) has been used to automatically generate dispatching rules, enabling responsive scheduling while meeting high responsiveness demands. However, GP methods are dependent on fixed terminal sets and have poor interpretability. In this work, we develop an evolving dispatching rules framework (EvoDR) that leverages the semantic understanding and generation capabilities of large language models to achieve cross-domain integration of rule design and scheduling knowledge. In our proposed framework, multi-stage assembly supply decisions are modeled as priority sorting of directed edges based on heterogeneous graphs. A dual-expert co-evolution mechanism is proposed, which allows LLM-A to generate code and LLM-S conduct scheduling analysis and reflection. Guided by improvements in hybrid evaluation, adaptive rules that fit dynamic features are continuously evolved. Experimental results show that EvoDR can achieve lower average tardiness than other automatically designed state-of-the-art approaches. It also outperforms expert-designed competitors across 480 instances over 24 distinct scenarios with varying resource configurations and disturbance levels, and EvoDR demonstrates robust adaptability across diverse operating conditions.

Figures & tables

Indices
$i$	Order index, $i\in I$
$p$	Product index, $p\in P$
$j$	Job index, $j_{1},j_{2}\in J$
$m$	Machine index, $m\in M$
Parameters
${{Q}_{j,m}}$	1 if the machine $m$ is qualified to process the job $j$ , 0 otherwise

TABLE I: Notations of mathematical model.

Type	Index	Description
Order	$\bm{f}_{1}$	Processing status binary variables of each job $j\in J_{t}$ at step $t$ ,
		1 if job is processed or not, 0 otherwise.
	$\bm{f}_{2}$	Actual processing time at step $t$ , cumulative time if the job has
		been processed, otherwise average $PT_{i}$ on available machines.
	$\bm{f}_{3}$	Number of available processing machines for job $j$ at step $t$ .
Arc	$\bm{f}_{4}$	Arrival time for each job $j\in J_{t}$ .

TABLE II: State features at decision step

t

Fig. 1: Automated dynamic PDR design based on EvoDR framework for FAFSP. By leveraging LLM to design a PDR that adapts to state changes, it achieves rapid sorting of $j$ - $m$ pairs to perform job sequencing and machine allocation.

Fig. 2: Design strategies and prompt engineering.

Fig. 3: Automated design and evolution process for dynamic PDR. LLM-S introduces domain and elite knowledge to guide the initial rule initialization, and continuously guides the rule evolution through differentiated empirical evaluation of individuals.

LLM	$T_{train}$	$T_{test}$	$T_{all}$	Token	Acc	Cost	Ratio
QW8†	1244.02	1052.85	1148.44	0.37M	80.5%	0.40	0.000647
QW235†	1015.66	951.93	983.79	0.38M	94.5%	1.67	0.002133
deepseek chat	1090.51	1074.69	1082.61	0.28M	91.5%	0.65	0.000950
claude	1021.45	896.38	958.91	0.53M	75.0%	5.77	0.007144
gpt-4o-mini	1082.17	974.07	1028.12	0.33M	96.0%	0.09	0.000122

TABLE III: Comparison of different LLMs.

Fig. 4: Convergence of different AHD methods.

Fig. 5: Convergence analysis for dynamic PDR evolution.

$(U_{low},U_{up})$	$T_{train}$	$T_{test}$	$T_{all}$	$u$	Acc
(0, 2)	1041.15±90.07	1353.29±50.42	1197.22±62.35	0.67±0.23	92.26%
(0, 1.6)	1004.23±29.63	1312.88±67.22	1158.56±19.18	0.64±0.32	94.09%
(0, 1)	1025.20±66.64	1356.91±26.29	1191.06±45.40	0.33±0.42	95.92%
(0.3, 1.5)	1013.00±78.45	1266.10±69.66	1139.55±7.40	0.94±0.55	80.06%
(0.5, 1.25)	978.03±20.98	1307.64±61.56	1142.84±35.29	0.90±0.17	90.54%

TABLE VII: Comparison of different temperature ranges.

Method	$T_{train}$	$T_{test}$	$T_{all}$	Token	Acc	Cost
EoH	1161.2	1433.6	1297.4	0.32M	87.3%	0.131
ReEvo	1053.2	1432.5	1242.9	1.36M	70.4%	0.558
EvoDR	987.8	1382.4	1185.1	0.30M/0.16M	89.3%	0.123/0.066

TABLE VIII: Comparison of costs for different methods.

Fig. 6: Convergence analysis for 4 (left) and 37 (right) suggestions.

Fig. 7: Box plot of tardiness performance in different AHD methods.

Fig. 8: Box plot of tardiness performance under different conditions.

Automated Heuristic Design

Automated heuristic design creates or adapts problem-solving rules for optimization, planning, scheduling, and related search tasks.

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DSevolve: Enabling Real-Time Adaptive Scheduling on Dynamic Flexible Job Shop with LLM-Evolved Heuristic Portfolios

XinLei Zhou, Jin Huang, Jie Yang, Xinyu Li+1

School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan, 430074, PR China

Flexible Job Shop Scheduling Real-Time Scheduling Combinatorial Optimization Automated Heuristic Design Metaheuristic Optimization

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In dynamic flexible job shops, order arrivals, machine breakdowns, and processing-time deviations continually reshape the scheduling state and the priority trade-offs behind dispatching decisions. Dispatching rules are well suited to this setting because they are fast, interpretable, and easy to deploy, and recent LLM-assisted automatic heuristic design further expands their expressiveness by evolving composite priority functions. The key challenge is to make these evolved rule behaviors state-adaptive without losing the rapid response needed for online rescheduling. This paper proposes a dynamic self-evolutionary framework DSevolve, which separates offline rule-library construction from online state-conditioned rule selection. Offline, an LLM-guided quality-diversity search combines multi-persona seeding, a MAP-Elites behavioral archive, and behavior-guided variation to evolve a library of complementary rules rather than a single elite, and event-level simulation then trains a neural selector to rank the rules by state. Online, after each rescheduling event, a neural selector maps a 22-dimensional state fingerprint to rule scores and dispatches the top-ranked rule within about a second, meeting the response-time requirement after each disruption. Experiments on dynamic instances derived from standard flexible job shop benchmarks show that DSevolve achieves lower mean makespan than individual LLM-evolved rules, classical dispatching rules, and learning-based baselines under a one-active-rule deployment protocol. Trained only on small instances, the selector transfers zero-shot to substantially larger dynamic shops. These results show that state-conditioned selection preserves the speed and interpretability of dispatching rules while improving adaptability.

Abstract

Automated Heuristic Design

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