[Paper Review] Flight Gate Assignment with a Quantum Annealer

Tobias Stollenwerk, Elisabeth Lobe+1 more|elib (German Aerospace Center)|Nov 23, 2018

Vehicle Routing Optimization Methods7 references4 citations

TL;DR

This paper investigates the application of a D-Wave 2000Q quantum annealer to the flight gate assignment problem, a quadratic binary optimization problem aimed at minimizing total passenger transit time. By applying bin packing to reduce coefficient precision in the QUBO formulation, the authors successfully solve small-scale real-world instances with acceptable success rates, demonstrating feasibility despite current hardware limitations in qubit count and connectivity.

ABSTRACT

Optimal flight gate assignment is a highly relevant optimization problem from airport management. Among others, an important goal is the minimization of the total transit time of the passengers. The corresponding objective function is quadratic in the binary decision variables encoding the flight-to-gate assignment. Hence, it is a quadratic assignment problem being hard to solve in general. In this work we investigate the solvability of this problem with a D-Wave quantum annealer. These machines are optimizers for quadratic unconstrained optimization problems (QUBO). Therefore the flight gate assignment problem seems to be well suited for these machines. We use real world data from a mid-sized German airport as well as simulation based data to extract typical instances small enough to be amenable to the D-Wave machine. In order to mitigate precision problems, we employ bin packing on the passenger numbers to reduce the precision requirements of the extracted instances. We find that, for the instances we investigated, the bin packing has little effect on the solution quality. Hence, we were able to solve small problem instances extracted from real data with the D-Wave 2000Q quantum annealer.

Motivation & Objective

• To assess the feasibility of solving the flight gate assignment problem using a D-Wave 2000Q quantum annealer.
• To address high-precision coefficient requirements in QUBO formulations derived from real airport data.
• To evaluate the impact of bin packing on solution quality and precision reduction in quantum optimization.
• To investigate the scalability and performance limits of quantum annealing for this combinatorial optimization problem.
• To explore the potential of hybrid quantum-classical approaches for larger problem instances.

Proposed method

• Formalized the flight gate assignment problem as a quadratic binary program with objectives focused on minimizing total passenger transit time.
• Mapped the problem to a Quadratic Unconstrained Binary Optimization (QUBO) model suitable for quantum annealing.
• Extracted small, representative problem instances from real-world data of a mid-sized German airport and simulated data.
• Applied bin packing to passenger numbers to reduce coefficient precision in the QUBO, mitigating precision-related errors in the D-Wave hardware.
• Used penalty-based constraints with tunable weights to enforce one-flight-per-gate and one-gate-per-flight assignment rules.
• Executed 1000 annealing runs per instance with majority voting for chain un-embedding, and computed time-to-solution with 99% confidence.

Experimental results

Research questions

• RQ1 Can the flight gate assignment problem be effectively mapped to a QUBO formulation suitable for quantum annealing?
• RQ2 To what extent does coefficient precision in the QUBO formulation limit the success rate on current D-Wave hardware?
• RQ3 How effective is bin packing in reducing coefficient precision without degrading solution quality?
• RQ4 What is the relationship between problem size (number of flights) and success probability or time-to-solution on the D-Wave 2000Q?
• RQ5 Can quantum annealing outperform classical solvers for small-scale flight gate assignment instances?

Key findings

• Bin packing significantly reduced coefficient precision requirements in the QUBO formulation while preserving solution quality, with minimal impact on optimal objective values.
• The success probability on the D-Wave 2000Q was suppressed for large coefficient ranges due to precision limitations, particularly when intra-logical qubit coupling was too high.
• For the tested instances, the time-to-solution with 99% confidence increased with the number of flights, correlating with rising coefficient magnitude $C_{\text{Ising}}$.
• The optimal annealing success probability was achieved at an intra-logical qubit coupling of $J_F = -1$ in units of the largest coefficient, balancing precision and chain stability.
• The quantum annealer successfully found the exact optimal solution for small problem instances extracted from real airport data, as validated against a MaxSAT solver.
• The embedding overhead due to limited qubit connectivity and coupler availability restricted the maximum solvable problem size, limiting scalability assessment.