arXiv subjects

Renáta Rusnáková

Publications and source records attributed to Renáta Rusnáková.

3 recordsLinked to original sources

arXiv2026

Minimum Bisection Problem: Machine Learning-Based Penalty Parameter Tuning for Optimization on Quantum Annealers

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.

quant-ph↗

arXiv2026

Quantum Annealing for Realistic Traffic Flow Optimization: Clustering and Data-Driven QUBO

This article presents a scalable, data-driven formulation of city-wide Traffic Flow Optimization as a Quadratic Unconstrained Binary Optimization problem and evaluates its performance using quantum annealing and classical solvers on realistic urban networks. The framework builds a time-resolved congestion model from simulated mobility data by sampling vehicle trajectories at fixed intervals, identifying leader-follower interactions on shared road segments. In addition to congestion, the model incorporates route-duration penalties and an analytically derived penalty parameter that enforces one-hot route selection, ensuring feasible assignments while balancing network-wide congestion reduction and individual travel times. To mitigate the combinatorial growth of interactions in large-scale instances, the approach employs Leiden clustering to partition vehicles into dense communities that can be optimized independently. The resulting subproblems are solved using D-Wave's quantum annealer, exact mixed-integer programming via Gurobi, and several classical metaheuristics, and are evaluated on multiple city maps with up to 25,000 vehicles. Across large scenarios, the hybrid quantum annealing approach consistently produces feasible solutions within approximately 1% of Gurobi's objective values, while maintaining stable runtimes. Both methods outperform shortest-route baselines, achieving reductions in the proposed congestion-cost objective of up to 24.4% for the hybrid quantum approach and 29.4% for Gurobi. Finally, the study highlights the critical role of the underlying city map, showing that network structure directly influences interaction density, problem formulation, and the efficiency of embedding and solving on current quantum annealing hardware.

quant-ph↗

arXiv2026

Multi-Agent Route Planning as a QUBO Problem

Multi-Agent Route Planning considers selecting vehicles, each associated with a single predefined route, such that route-level coverage utility is maximized while redundant spatial overlaps are limited. This paper gives a formal problem definition, proves NP-hardness by reduction from the Weighted Set Packing problem, and derives a Quadratic Unconstrained Binary Optimization formulation whose coefficients directly encode route utility rewards and pairwise overlap penalties. A single penalty parameter $λ$ controls the coverage--overlap trade-off. We distinguish between a soft regime, which supports multi-objective exploration, and a hard regime, in which the penalty is strong enough to effectively enforce near-disjoint routes. We describe a practical pipeline for generating city instances, constructing candidate routes, building the QUBO matrix, and solving it with a binary quadratic programming baseline (Gurobi), simulated annealing, and D-Wave hybrid quantum annealing. Experiments on Barcelona instances with up to $10{,}000$ vehicles reveal a clear coverage--overlap knee and show that Pareto-optimal solutions are mainly obtained under the hard-penalty regime, while D-Wave hybrid solvers and Gurobi achieve very similar objective values on matching configurations with only minor runtime differences as problem size grows.

cs.RO↗