CoMILP: Evolving Collaborative Solver Components for Mixed-Integer Linear Programming

Mixed-integer linear programming (MILP) is a fundamental framework for solving combinatorial optimization problems. Modern MILP solvers rely on multiple interacting components whose design and configuration strongly influence performance. During the solving process, these components interact repeatedly, with decisions made in one component reshaping the solver states encountered by others. Although existing work in automated algorithm design has improved MILP solving performance, such approaches typically focus on either parameter tuning or heuristic design for a single selected component rather than optimizing jointly across the solver, leaving improvements that require complementary changes across components unexplored. To address this limitation, we propose CoMILP, a large language model (LLM)-driven framework for cross-component algorithm design in MILP solvers. Specifically, CoMILP jointly optimizes initial parameter settings, dynamic configuration policies across components, and decision rules for cut selection and branching. CoMILP employs a multi-agent coordination framework in which LLM agents repeatedly select solver components and edit type, propose a local update, and reflect on solver feedback, thereby enabling scalable optimization across multiple components. Tree search retains alternative refinement paths and balances exploration and exploitation, enabling complementary updates to build on earlier component changes. Experiments on five problem families and MIPLIB 2017 show large improvements over default SCIP, including a 34.4% reduction in primal–dual integral on MIPLIB. Ablations further establish the benefits of cross-component evolution.