Integrating adaptive divide-and-conquer and large language model for scheduling large-scale tasks in electromagnetic satellite systems

With the expanding scale and application scope of electromagnetic satellite systems, task scheduling faces significant challenges. It requires to optimize large-scale mixed decision variables, including discrete task-to-satellite assignments and continuous task execution time. Meanwhile, the schedule must satisfy various stringent physical and operational constraints. To address these challenges, this paper proposes an evolutionary algorithm (ADC-LLM, for short) integrating an adaptive divide-and-conquer solver with a large language model (LLM) assistance. Specifically, the solver utilizes a spatio-temporal information-driven grouping mechanism to partition the large-scale variables. It also employs a resource allocation mechanism that adaptively distributes evolutionary opportunities to each group based on its historical contributions. Furthermore, an LLM-assisted population generation mechanism is designed. This mechanism leverages LLMs’ strong reasoning capabilities to extract patterns from historical elite solutions, and then generates high-quality individuals to accelerate convergence and enhance global search ability. Extensive computational experiments compare ADC-LLM with four state-of-the-art algorithms across 48 test cases. The results show that ADC-LLM consistently outperforms all four algorithms. As the task scale increases, the performance advantage of ADC-LLM becomes more pronounced. In cases with 2000 tasks, ADC-LLM improves overall revenue by up to 4.28% and raises the task completion ratio by 5.8%. Ablation studies further confirm the individual contributions of variable grouping (3.71%), adaptive resource allocation (1.94%), and LLM-assisted generation (0.97%) to overall performance.