Learning for Dynamic Combinatorial Optimization without Training Data
Yiqiao Liao, Farinaz Koushanfar, Parinaz Naghizadeh
TL;DR
DyCO-GNN is an unsupervised learning framework for dynamic combinatorial optimization that uses structural similarities in evolving graphs to produce high-quality solutions efficiently without requiring training data.
Contribution
It introduces DyCO-GNN, a novel unsupervised method that leverages problem instance structure for fast, high-quality solutions in dynamic combinatorial optimization without training data.
Findings
Achieves solutions 3-60x faster than baselines.
Performs well across multiple problems and datasets.
Maintains high solution quality under tight time constraints.
Abstract
We introduce DyCO-GNN, a novel unsupervised learning framework for Dynamic Combinatorial Optimization that requires no training data beyond the problem instance itself. DyCO-GNN leverages structural similarities across time-evolving graph snapshots to accelerate optimization while maintaining solution quality. We evaluate DyCO-GNN on dynamic maximum cut, maximum independent set, and the traveling salesman problem across diverse datasets of varying sizes, demonstrating its superior performance under tight and moderate time budgets. DyCO-GNN consistently outperforms the baseline methods, achieving high-quality solutions up to 3-60x faster, highlighting its practical effectiveness in rapidly evolving resource-constrained settings.
Peer Reviews
Decision·ICLR 2026 Conference Withdrawn Submission
1. The paper is clearly written and well-structured. 2. The paper tackles a practical and important problem (DCO) that has been relatively neglected by the learning-based CO community. 3. The empirical investigation is thorough. The method is validated on three distinct NP-hard problems (MaxCut, MIS, TSP) using multiple real-world dynamic graph datasets.
1. There may be an overclaim in line 53: "To the best of our knowledge, our work is the first to apply machine learning to DCO problems". To my knowledge, there are also some works studying how to solve dynamic/stochastic COPs, such as [1,2]. 2. It is unclear why we do not use learned models to solve each snapshot of dynamic COPs. The importance of using UL to solve dynamic COPs is not well illustrated. 3. The experiment involves three dynamic COPs, but for dynamic TSP, the problem size is to
- The direction of solving qubo problems over dynamic graphs is an interesting and underexplored one. - The paper provides results for the proposed method in multiple qubo problems.
- I have some issues with the experimental setion of the paper. I provide a brief list: - I think a simple fast non-neural baseline should be included in the main tables. I noticed in the appendix that some of your non-neural algorithms timed out. However, for example the Boppana algorithm is an approximation algorithm and not greedy heuristic. Its performance is guaranteed, but it can be much slower than a heuristic. You may want to consider something like the heuristic for MIS that was us
The paper has many strengths. I personally like tackling the dynamic graph optimization domain as most of the work in this area is about the static setting. The choice to not train on an independent dataset is a well done problem framing choice. It would have simply complicated the investigation. The gains over PI-GNN static appear to be consistent across datasets and tasks. The spread of datasets and CO tasks is extensive and incredibly thorough.
I have some questions about theorem 1, see questions. As with every paper in this domain, I must ask how the neural approach compares to simple baselines like gurobi. Or even the truly simplest random walk, simulated annealing, etc. Without a solver baseline of any form it becomes exceptionally difficult to judge the performance of the models.
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Taxonomy
TopicsDNA and Biological Computing · semigroups and automata theory · Algorithms and Data Compression