TL;DR
DHEvo introduces a data-algorithm co-evolution framework leveraging LLMs to generate and refine primal heuristics tailored for specific MILP problem classes, significantly improving generalization and solving efficiency.
Contribution
The paper proposes a novel co-evolution approach that combines data selection and heuristic evolution using LLMs, addressing generalization issues in MILP solving.
Findings
Outperforms existing heuristics and LLM-based methods on diverse benchmarks.
Effectively captures problem class characteristics for better heuristic generalization.
Significantly improves MILP solving efficiency across various problem instances.
Abstract
Primal heuristics play a critical role in improving the efficiency of mixed integer programming (MILP) solvers. As large language models (LLMs) have demonstrated superior code generation abilities, recent MILP works are devoted to leveraging the evolutionary computation approaches with LLMs to generate effective primal heuristics. Although the generated heuristics have achieved better solving performance than the hand-crafted ones with little adaptability, the advantage of current LLM-based methods is limited to few MILP instances in one problem class, as they fail to capture the instance characteristics in the problem class (the MILP instances generated from the same mathematical model are defined as a problem class). Since MILP instances often differ significantly in structure and feature distribution, the neglect of their characteristics in the evolution process results in poor…
Peer Reviews
Decision·ICLR 2026 Conference Withdrawn Submission
- The paper provides a solid theoretical motivation, offering guidance for the joint evolution of heuristics and data. - The experiments include ablation studies on the main components of DHEvo, showing a well-structured evaluation.
Several parts of the paper are unclear or insufficiently explained; see the questions below.
- Interesting and timely idea: jointly evolving data (instances) and algorithms (heuristics) to improve generalization within a problem class. - Clear instantiation: multi-agent LLM pipeline, well-described evolutionary operators, and fitness-driven selection with temperature-based sampling. - Strong empirical results: consistent gains over hand-crafted, learning-based, and LLM-based baselines; improvements carry over to full B&B with SCIP, and to real-world datasets. - Ablations are helpful: sh
- Missing a key baseline: ReEvo is a prominent agent-based code-generation/evolution approach. Lack of comparison weakens the contribution claim, especially since DHEvo’s pipeline shares the agentic-evolution flavor. - Benchmark breadth: classic LLM+EC works (e.g., EoH, FunSearch) commonly report on canonical CO tasks like Bin Packing and TSP. Not evaluating on such benchmarks limits comparability to the broader literature and makes it harder to assess transferability beyond MILP templates used
- The idea of simultaneously evolving both instances and heuristics is well-motivated, justified, and proven effective through ablation studies. - Using multiple LLM agents to generate, review, and select heuristics is methodologically sound. Ablation studies show this approach improves both solution quality and heuristic diversity. - The experiments use synthetic and real-world datasets with clear performance metrics—such as primal gap and primal-dual integral—supporting the authors' claims thr
- **Scope Limited to Diving Heuristics:** While the use case is well-motivated and relevant, DHEvo is applied only to diving heuristics. It remains unclear why the method targets this specific class of heuristics and whether it can extend to other MILP heuristics or broader combinatorial optimization problems. A discussion of limitations or necessary adaptations for other domains would strengthen the paper. - **Computational and Resource Cost Reporting:** The paper lacks a fair comparison of com
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