From Walls to Synergy: A Joint LLM-Evolution Framework for MILP Solvers

Machine learning (ML) methods have achieved notable success in enhancing individual components of mixed-integer linear programming (MILP) solvers. However, most existing approaches focus on single-component enhancement, neglecting critical interactions among components and often yielding diminishing returns when multiple approaches are integrated. The emergence of large language models (LLMs) provides a promising paradigm for jointly optimizing multiple solver components within a unified framework. In this paper, we propose Jolly-MILP, an LLM-guided framework to jointly optimize presolving, cut selection, and branching variable selection in exact MILP solvers. Our approach introduces a synergistic Coordinator to align component-level generators and a hierarchical Controller to produce adaptive, multi-stage strategies. Extensive experiments on nine MILP datasets demonstrate that Jolly-MILP consistently outperforms both ML-based approaches and existing LLM-based methods. These results show that explicit joint optimization, rather than isolated component-wise enhancement, is crucial for acquiring further gains in exact MILP solving, offering a new pathway for more advanced solver design.