Evolving Interdependent Operators with Large Language Models for Multi-Objective Combinatorial Optimization

Neighborhood search operators are critical to the performance of Multi-Objective Evolutionary Algorithms (MOEAs) and rely heavily on expert design. Although recent LLM-based Automated Heuristic Design (AHD) methods have made notable progress, they primarily optimize individual heuristics or components independently, lacking explicit exploration and exploitation of dynamic coupling relationships between multiple operators. In this paper, multi-operator optimization in MOEAs is formulated as a Markov decision process, enabling the improvement of interdependent operators through sequential decision-making. To address this, we propose the Evolution of Operator Combination (E2OC) framework for MOEAs, which achieves the co-evolution of design strategies and executable codes. E2OC employs Monte Carlo Tree Search to progressively search combinations of operator design strategies and adopts an operator rotation mechanism to identify effective operator configurations while supporting the integration of mainstream AHD methods as the underlying designer. Experimental results across AHD tasks with varying objectives and problem scales show that E2OC consistently outperforms state-of-the-art AHD and other multi-heuristic co-design frameworks, demonstrating strong generalization and sustained optimization capability.

LLM-Assisted Automatic Dispatching Rule Design for Dynamic Flexible Assembly Flow Shop Scheduling

Dynamic multi-product delivery environments demand rapid coordination of part completion and product-level kitting within hybrid processing and assembly systems to satisfy strict hierarchical supply constraints. The flexible assembly flow shop scheduling problem formally defines dependencies for multi-stage kitting, yet dynamic variants make designing integrated scheduling rules under multi-level time coupling highly challenging. Existing automated heuristic design methods, particularly genetic programming constrained to fixed terminal symbol sets, struggle to capture and leverage dynamic uncertainties and hierarchical dependency information under transient decision states. This study develops an LLM-assisted Dynamic Rule Design framework (LLM4DRD) that automatically evolves integrated online scheduling rules adapted to scheduling features. Firstly, multi-stage processing and assembly supply decisions are transformed into feasible directed edge orderings based on heterogeneous graph. Then, an elite knowledge guided initialization embeds advanced design expertise into initial rules to enhance initial quality. Additionally, a dual-expert mechanism is introduced in which LLM-A evolutionary code to generate candidate rules and LLM-S conducts scheduling evaluation, while dynamic feature-fitting rule evolution combined with hybrid evaluation enables continuous improvement and extracts adaptive rules with strong generalization capability. A series of experiments are conducted to validate the effectiveness of the method. The average tardiness of LLM4DRD is 3.17-12.39% higher than state-of-the-art methods in 20 practical instances used for training and testing, respectively. In 24 scenarios with different resource configurations, order loads, and disturbance levels totaling 480 instances, it achieves 11.10% higher performance than the second best competitor, exhibiting excellent robustness.