Quantum Annealing for Minimum Bisection Problem: A Machine Learning-based Approach for Penalty Parameter Tuning
Bibliographic record
Abstract
The Minimum Bisection Problem is a fundamental, computationally hard graph partitioning problem with applications in parallel computing, network design, and large-scale data processing. When formulated as a Quadratic Unconstrained Binary Optimization problem for quantum annealing, solution quality depends critically on the penalty parameter that enforces balanced partitions. Selecting this parameter is problem-dependent and typically relies on manual tuning or heuristics. This paper proposes a machine learning-based approach for automatic penalty-parameter tuning developed specifically for the Minimum Bisection Problem. We first derive a graph-dependent initial penalty estimate and then use two Gradient Boosting Regressor models to predict the endpoints of an effective penalty-multiplier interval from the number of nodes, graph density, and the initial estimate. The final penalty is obtained from the predicted interval and used to construct the model solved by D-Wave's quantum annealing solvers. The models were calibrated on 607 Erdős-Rényi graphs, with Metis and Kernighan-Lin as classical references, and evaluated on 126 independently generated instances with up to 4000 nodes. Under the adopted experimental setup, the predicted penalties enabled the hybrid solver to return balanced partitions for all evaluation instances and lower cut values than Metis in every case.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.005 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.003 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".