Venue: NeurIPS 2022 Conference

Reviews:

final_score: rating: 5: Borderline accept: Technically solid paper where reasons to accept outweigh reasons to reject, e.g., limited evaluation. Please use sparingly.
review_content: summary: Branch and bound is a fundamental component for solving the mixed integer linear programming problem. As one of the building block, node comparison function takes the responsibility of choosing next node to subdivide. In this work, a graph neural network (GNN) method is proposed by formalizing the way to represent the nodes when searching the next step to go. Different from previous work, the node features are extracted from the associated properties of linear equations and objective function. Oracle node division is regarded as the supervised data to train the scoring function based on GNN model. It's interesting to see the application of GNN method to solve NP hard problems after revisiting the original optimization task. The novelty of this work lies at the employment of GNN to learn the node representations to mimic the ideal branch-and-bound solution.
strengths_and_weaknesses: Strengths:
1. This work gives alternative way to represent the nodes with extracted features from the linear constraints and objective function. A bipartite graph to show the connection between constraints and variables builds the basics for applying the GNN method to score the node in branch-and-bound when comparing a pair of nodes.
2. As one of the most important part, the proposed method employs imitation learning to optimize the scoring function through learning from the oracle branch-and-bound progress.
3. Thorough experiments are conducted over real NP hard problems to valid how the proposed method works.

Weaknesses:
1. The motivation about the reason why employing GNN works is not clear enough. It's better to further comment on why the formalized bipartite graph works and what kinds of benefits that the other methods can not bring?
2. It's hard to understand how the proposed method can adapt to a new MILP problem. From the presentation of this work, we can see that the training data to learn a node selection policy is based on oracle optimization progress for the problems in hand. One important question that needs to answer is how we can apply the learned GNN-based scoring function to a new problem. After reading the manuscript several times, it's still difficult to catch up with this point.
3. The experimental results seem to be not strong enough to demonstrate the superiority of the proposed. From the results shown in Table 1 and 2, we can see that GNN-based method can beat the baseline in some tasks, but not show absolute advantage. It deserves more words and insight to explain the function of GNN method.

Minor Issue:
1. It's difficult to draw connection between Figure 1 and the description shown from Line 111-117. The illustration only shows the comparison between a pair of nodes, but missing key concepts of Markov Decision Process, such as the state, action, and the environment.
questions: Please refer to the weaknesses.
limitations: yes
review_title: null

final_score: rating: 3: Reject: For instance, a paper with technical flaws, weak evaluation, inadequate reproducibility and incompletely addressed ethical considerations.
review_content: summary: In this paper, the authors design a GNN model for comparing two Branch and Bound (BnB) search nodes of Mixed Integer Linear Programming (MILP) and use this model to replace the node comparison function of an existing MILP solver SCIP. 
strengths_and_weaknesses: Strengths:
1.	The idea of using a GNN model to evaluate two BnB search nodes is novel and it has great significance to BnB search in other research fields of combinatorial optimization, such as SAT, Traveling Salesman Problem, Maximum Clique Problem, Graph Coloring Problem, etc. 

Weaknesses:
1.	This work uses an antiquated GNN model and method, it seriously impacts the performance of this framework. The baseline algorithms/methods are also antiquated.
2.	The experimental results did not show that this work model obviously outperforms other variant comparison algorithms/models. 
3.	The innovations of network architecture design and constraint embedding are rather limited.

questions: See the above weaknesses.
limitations: The authors discussed that the performance is limited by the performance of the oracle expert.
review_title: null

final_score: rating: 3: Reject: For instance, a paper with technical flaws, weak evaluation, inadequate reproducibility and incompletely addressed ethical considerations.
review_content: summary: This paper proposes a variable selection method for MILPs based on GNNs, diving oracle, and imitation learning.
strengths_and_weaknesses: # Strengths

- The proposed method outperforms the SCIP solver in the experiments.
- Three hard problems with standard and transfer settings are used in the evaluations.

# Weaknesses

- The proposed method is a combination of known techniques and provides few technical insights. This paper does not reach the NeurIPS standards of technical contributions.
- The proposed approach looks very similar to Solving Mixed Integer Programs Using Neural Networks (Nair et al., 2021). Please discuss the differences and qualitative merits of the proposed method and compare them in the experiments.
- There are many other ML methods for MILPs, e.g., learn2branch (Gasse et al., 2019) and many others cited in this submission. Please discuss the qualitative merits of the proposed method and compare them in the experiments.

Overall, I feel that this paper fails to contextualize itself. More discussions and evaluations are needed to demonstrate the effectiveness of the proposed method over other approaches.
questions: - What is the most significant contribution of this paper that the authors want to inform the NeurIPS community?
- What are the qualitative differences against the existing GNN-based approaches for MIP variable selection?
limitations: N/A
review_title: null

Meta-review: metareview: This paper clearly documents a well-executed exploration of an imitation learning / neural diving approach to improving node selection in BB solvers using a GNN approach.
I believe this paper is a useful contribution that pushes forward the important project of integrating modern ML techniques to improve integer programming.

The reviewers were less sanguine than the meta-reviewer. I will explain why. 

The authors note, and I concur, that node selection strategies in modern BB solvers have been *heavily* researched for decades, so beating their performance on the majority of these difficult tasks is quite an achievement! (This point confused the first reviewer.)

The second reviewer was disappointed that the authors used an "antiquated" GNN architecture, or compared to "antiquated" baselines, but did not substantiate which modern architectures or comparisons would have been better. In the absence of constructive criticism, I construe these as a misapplication of the standards of deep learning (very fast progress in beating benchmarks) to integer programming (a mature field where progress is slower). 

While several GNN approaches are available for variable selection in BB solvers, node selection is an important and independent challenge. 
I am not aware of any previous work on deep learning for node selection (nor are the authors), 
which explains why the authors chose to compare their GNN-based approach to other strategies they created and the default strategy in SCIP rather than the (non-existent) deep-learning SOTA for the problem.
 (This point confused the third reviewer.)
confidence: Less certain
Decision: Accept