Title: Dynamic Configuration for Cutting Plane Separators via Reinforcement Learning on Incremental Graph
Venue: NeurIPS 2025
Accepted: yes
Keywords: mixed-integer Linear Programming; cutting plane separator; reinforcement Learning; incremental graph
Abstract: Cutting planes (cuts) are essential for solving mixed-integer linear programming (MILP) problems, as they tighten the feasible solution space and accelerate the solving process. Modern MILP solvers offer diverse cutting plane separators to generate cuts, enabling users to leverage their potential complementary strengths to tackle problems with different structures. Recent machine learning approaches learn to configure separators based on problem-specific features, selecting effective separators and deactivating ineffective ones to save unnecessary computing time. However, they ignore the dynamics of separator efficacy at different stages of cut generation and struggle to adapt the configurations for the evolving problems after multiple rounds of cut generation. To address this challenge, we propose a novel **dyn**amic **sep**arator configuration (**DynSep**) method that models separator configuration in different rounds as a reinforcement learning task, making decisions based on an incremental triplet graph updated by iteratively added cuts. Specifically, we tokenize the incremental subgraphs and utilize a decoder-only Transformer as our policy to autoregressively predict when to halt separation and which separators to activate at each round. Evaluated on synthetic and large-scale real-world MILP problems, DynSep speeds up average solving time by 64% on easy and medium datasets, and reduces primal-dual gap integral within the given time limit by 16% on hard datasets. Moreover, experiments demonstrate that DynSep well generalizes to MILP instances of significantly larger sizes than those seen during training.


Peer reviews:
comments: SUMMARY:
The paper proposes DynSep, a reinforcement learning-based method for dynamically configuring cutting plane separators in mixed-integer linear programming (MILP) solvers.

STRENGTHS AND WEAKNESSES:
The strength of this paper:

(1) Triplet graphs are used to capture evolving problem states during branch and cut with Lightweight subgraph updates 
(2) Decoder-only design with blocked positional encoding captures temporal dependencies across rounds while ensuring permutation equivariance

The weakness of this paper:

(1) limited scope of hyperparameter tuning (separator activation/timing)
(2) limited scope of testing datasets (MIPLIB neos and supportcase)

QUESTIONS:
(1) Could you specify which instances you used to test the performance in MIPLIB. What do you mean by mixed neos and mixed suportcase specifically?
(2) For real-world use, what is the latency of policy inference during B&C?

LIMITATIONS:
(1) DynSep ​only optimizes separator activation status​ (+1, 0, -1) and round termination (m_t). It ignores critical hyperparameters like:
Cut depth/aggressiveness (e.g., sepastore/age in SCIP); Cut selection thresholds (e.g., efficacy vs. orthogonality) and Separation frequency per node.

(2) Memory/compute inference overhead is not discussed. Which scenarios and practical cases the data-driven approach is appropriate should be addressed.
TITLE: Official Review
CLARITY: 2
IMPACT: 2
ORIGINALITY: 2
DATE: 2025-06-24

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper proposes DynSep, a dynamic separator configuration method that models separator configuration in different rounds as a reinforcement learning task and tokenizes the incremental subgraphs with a transformer policy model to autoregressively predict when to half separation and which separators to activate at each round. Evaluated on synthetic and large-scale real-world MILP problems, DynSep substantially accelerates the solving time on easy and medium instances, as well as reducing integrality gap on hard instances.\n\nSTRENGTHS AND WEAKNESSES:\n**Strengths**\n\n1. The paper is clear and well-written.\n2. The extension from static separator configuration to dynamic separator configuration is non-trivial. The authors handle this extension with incremental subgraph tokenization with blocked positional encoding for the transformer architecture, and these special treatments in the architecture design makes sense.\n3. The authors show significant performance improvement over baselines on a variety of benchmarks, with detailed ablation study to justify the method’s design choices.\n\n**Weaknesses**\n\n1. I feel like the methods developed in this paper is not particularly specific to configuring cutting plane separators, and it should be able to apply to configure other parameters (e.g. branching, heuristics). Can the authors comment on the difficulty / flexibility of adapting their framework to configure other parameters, and potentially do small experiments to show the feasibility of this extension? \n2. The authors set separator frequency as 10 and set the maximum separator round as T = 5. It is unclear how these two parameters (i.e. more or less frequent separator configurations) affect the performance of the method. The authors should perform some robustness studies in terms of varying these two parameters and comparing the performance.\n3. Can the authors conduct experiments on gurobi (or other MILP solvers) and see if their algorithms can improve gurobi as well?\n\nQUESTIONS:\nSee weaknesses.\n\nLIMITATIONS:\nThe authors explain the limitation of their methods in the conclusion section “the current implementation of dynsep lacks a lightweight decision model to retrain historical information across the global B&B tree”. I wonder if the authors can slightly expand in the conclusion to propose a few potential ways that can potentially address this limitation?", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 4, "CLARITY": 4, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-06-24"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper introduces DynSep, a dynamic separator configuration method for cutting plane selection in Mixed-Integer Linear Programming (MILP) solvers. DynSep formulates the round-wise activation and deactivation of cutting plane separators as a reinforcement learning (RL) problem. By modeling the evolving MILP instance as an incremental triplet graph, DynSep uses a GCN encoder and a decoder-only Transformer to autoregressively predict both when to halt separation and which separators to activate at each round. Experiments on synthetic and large-scale real-world MILP benchmarks demonstrate that DynSep significantly accelerates solving time (by 64% on average for easy/medium datasets) and reduces the primal-dual gap integral (by 16% on challenging datasets) compared to both human-designed and learning-based baselines. The method also shows strong generalization to much larger MILP instances than those used in training.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths:\n- DynSep delivers substantial improvements over both human-designed and ML baselines across a wide range of MILP benchmarks, including large-scale industrial and public datasets.\n- The method generalizes to larger instances and unseen problem sizes, a key requirement for practical MILP solving.\n- Ablation studies confirm the necessity of each component, and visualization of learned separator policies aligns with domain insights.\n\nWeaknesses:\n- All experiments are conducted within SCIP; comparisons to commercial solvers (e.g., Gurobi, CPLEX) or other solver backends are missing, which limits claims of generality and practical impact.\n- The approach configures only the built-in separators in SCIP, and does not explore integration with advanced or user-defined cutting plane families, potentially limiting extensibility.\n\nQUESTIONS:\n- Could you add comparisons with these mainstream commercial solvers (such as Gurobi or CPLEX) so I can better understand the current level of DynSep’s capabilities in an industrial context?\n- How does DynSep handle the addition of new, user-defined, or more advanced separators beyond SCIP’s built-in set? What is required to support extensibility?\n\nLIMITATIONS:\nYes", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 4, "CLARITY": 4, "IMPACT": 4, "ORIGINALITY": 3, "DATE": "2025-06-29"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis work proposes DynSep, a reinforcement learning–based method to dynamically control how cutting planes are added during the Branch-and-Cut process in solving MILP optimization. The authors claim that instead of relying on fixed or manually tuned separator settings, DynSep learns to decide both which separators to activate in each separation round and when to stop adding more cuts at each node while adapting these choices as the problem evolves across different rounds and nodes. To keep it efficient, DynSep only looks at the incremental subgraphs added in each round, then using GCN and a decoder-only Transformer to track the context from earlier rounds and predict the next separator configuration. The authors claim this design helps the solver avoid unnecessary separation rounds, capture useful separator interaction patterns automatically, and improve both speed and solution quality. In experiments, DynSep reduced average solve times by up to 64% and improved solution quality on harder benchmarks, while also generalizing well to larger, unseen MILP instances.\n\nSTRENGTHS AND WEAKNESSES:\n## Strengths \n\n- The main strength of this work is that DynSep is an adaptive method that learns not just which separators to use but also when to stop adding cuts, adjusting dynamically as the Branch-and-Cut process evolves. \n- Its design is efficient, since it processes only new cuts each round and uses a Transformer decoder to capture temporal context. \n- The proposed DynSep has demonstrated consistent and significant improvements in runtime and/or primal-dual gaps on various benchmarks, and datasets. The ablation study also helps with interpretability. \n- Built on the open-source SCIP solver, DynSep seems to be also practical and reproducible.\n\n## Weaknesses\n- There is a lack of clarity in the formulation of the solutions. For example, it is unclear the difference between cutting planes and separators until the very end of experiments. As a key concept in the solution and graph model, the separator and how it generates cutting planes are not explained, and it is unclear if the set of separator nodes remain the same for each triplet graph. It is also unclear how separator nodes are represented in the triplet graph, do they have node features or simply represented by node identity. \n- The transformer generates an action based on the history of token blocks. But the tokenization or encoding of the vectorized action is unclear in the paper. Is the action a sequence of tokens or a single token? If an action is a token, is the token space the same as the action space? \n- Within each block, node embeddings have identical positional encoding. How about graph positional encoding such as spectral PE from graph transformer literature? If the authors deliberately choose not to use graph PE, some explanation would be good. \n- Many notations are used before their first introduction, such as PD integral, MDP, Node and Round-wise dynamic configurations. \n- It is unclear about the generalizability of the DynSep due to the lack of training information. Is it trained on the same types of NP-hard problems in the benchmarks? If so, how well does it generalize to other unseen benchmarks? This could be a major limitation and need more clarification.\n\nQUESTIONS:\n- It is unclear how the GCN encoder is trained, is it included in the transformer training? \n- How might DynSep be adapted or extended to handle nonlinear or mixed-integer nonlinear programming (MINLP) problems?\n- How does the blocked positional encoding impact performance?\n- Could alternative architectures such as graph transformers improve the modeling of separator dynamics?\n- Is the training based on the same types of MILPs in the test benchmarks? How well does it generalize to unseen types MILPs?\n\nLIMITATIONS:\n- The method is limited to MILP problems and does not cover nonlinear formulations that frequently occur in real-world applications.\n- The method maybe limited to the types of MILPs seen during training, and generaliability to unseen types of MILPs is unclear.", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 4, "ORIGINALITY": 4, "DATE": "2025-07-03"}