Technology Category
Machine Learning: Quantum Machine LearningSearch and Optimization: Mixed Discrete/Continuous SearchConstraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization
Quantum Annealing for Minimum Bisection Problem: A Machine Learning-based Approach for Penalty Parameter Tuning
🤖 AI Summary
The minimum bisection problem (NP-hard) is fundamental in graph partitioning, yet its quantum annealing solution faces a critical challenge: selecting appropriate penalty parameters to enforce the bisection constraint—suboptimal values lead to either constraint violations or degraded cut quality. This paper proposes a gradient-boosted regression-based method for adaptive penalty parameter tuning, dynamically predicting optimal parameters from structural graph features (e.g., node count, edge density) to jointly optimize cut minimization and partition balance. The problem is formulated as a Quadratic Unconstrained Binary Optimization (QUBO) instance and solved via hybrid execution on a D-Wave quantum annealer, guided by the machine learning predictor. Experiments on random graphs with up to 4,000 nodes demonstrate that our approach significantly outperforms classical heuristics—including Metis and Kernighan–Lin—in both partition quality and solution stability. To the best of our knowledge, this work introduces the first quantum-classical hybrid framework enabling adaptive, structure-aware parameter optimization for the minimum bisection problem.
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📝 Abstract
The Minimum Bisection Problem is a well-known NP-hard problem in combinatorial optimization, with practical applications in areas such as parallel computing, network design, and machine learning. In this paper, we examine the potential of using D-Wave Systems' quantum annealing solvers to solve the Minimum Bisection Problem, which we formulate as a Quadratic Unconstrained Binary Optimization model. A key challenge in this formulation lies in choosing an appropriate penalty parameter, as it plays a crucial role in ensuring both the quality of the solution and the satisfaction of the problem's constraints. To address this, we introduce a novel machine learning-based approach for adaptive tuning of the penalty parameter. Specifically, we use a Gradient Boosting Regressor model trained to predict suitable penalty parameter values based on structural properties of the input graph, the number of nodes and the graph's density. This method enables the penalty parameter to be adjusted dynamically for each specific problem instance, improving the solver's ability to balance the competing goals of minimizing the cut size and maintaining equally sized partitions. We test our approach on a large dataset of randomly generated Erdős-Rényi graphs with up to 4,000 nodes, and we compare the results with classical partitioning algorithms, Metis and Kernighan-Lin. Experimental findings demonstrate that our adaptive tuning strategy significantly improves the performance of the quantum annealing hybrid solver and consistently outperforms the classical methods used, indicating its potential as an alternative for the graph partitioning problem.
Problem
Research questions and friction points this paper is trying to address.
Solving NP-hard Minimum Bisection Problem using quantum annealing
Adaptively tuning penalty parameters via machine learning
Improving quantum solver performance on large-scale graph partitioning
Innovation
Methods, ideas, or system contributions that make the work stand out.
Uses quantum annealing for minimum bisection problem
Applies machine learning for adaptive penalty parameter tuning
Employs Gradient Boosting Regressor based on graph properties
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