Title: DHEvo: Data-Algorithm Based Heuristic Evolution for Generalizable MILP Solving
Primary area: optimization
Keywords: optimization, LLMs

Abstract: Primal heuristics are crucial for accelerating the solving process of mixed integer programming (MILP) problems. While large language models (LLMs) have shown great promise in generating effective heuristics, existing methods often fail to generalize across instances within the same problem class, where we define a problem class as a set of MILP instances derived from the same mathematical model. This limitation arises because MILP instances within the same class can exhibit substantial structural and distributional heterogeneity. However, existing methods treat instances uniformly, averaging performance over limited samples and yielding heuristics that lack generalization. To address this, we propose DHEvo, a data-algorithm co-evolution framework that jointly evolves representative instances and tailored heuristics integrated into the open-source solver SCIP. DHEvo employs an LLM-based multi-agent system to generate and refine data-algorithm pairs iteratively, guided by fitness feedback. Experiments on diverse MILP benchmarks show that DHEvo significantly outperforms state-of-the-art hand-crafted, learning-based, and  LLM-based methods in solution quality and generalization.