Flight Gate Assignment with a Quantum Annealer

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.

Toward Quantum Gate-Model Heuristics for Real-World Planning Problems

“…Previously, our flight-gate assignment problem was mapped to quantum annealing (adiabatic quantum optimization) and small instances were successfully solved with the D-Wave 2000Q device [13]. In that work, similar to other studies toward real-world problems [7], [8], in order to obtain a problem representation suitable for implementation, the problem hard constraints were reformulated as additional penalty terms in the cost function of a transformed unconstrained problem.…”

“…Treating the hard constraints in this way, standard in the quantum annealing paradigm, has various drawbacks beyond the increase in physical qubits and couplers typically required. In [13], it was shown for this problem that the penalty terms lead to a significant increase in the precision and coupling requirements for the quantum annealer and therefore to a suppression of the success probability in practice, with similar observations made for different aerospace problems in [14]. Indeed, a motivation for gate-model approaches, such as QAOA, is to enable a wider variety of quantum algorithms to be implemented and explored than those of the more restricted setting of quantum annealing [12].…”

“…In this article, we show explicit constructions of QAOA circuits for optimization problems over the proper colorings of an important class of graphs, interval graphs, common in scheduling and assignment problems. As an application, we consider the flight-gate assignment problem [1], [13] in detail. Leveraging ideas from graph theory, we construct novel generalizations of prior QAOA mixers and show both that they preserve state feasibility always, and that any two feasible solutions can be connected by a sequence of such mixers, under mild conditions related to the problem input data.…”

Domain wall encoding of discrete variables for quantum annealing and QAOA

“…The most technologically mature continuous time quantum computing devices are the superconducting circuit quantum annealers produced by D-Wave Systems Inc. [1]. Examples of applications for quantum annealing can be found in diverse fields such as finance [2][3][4], computer science [5][6][7], mathematics [8][9][10], scheduling [11][12][13], decoding of communications [14], computational biology [15], flight gate assignment [16], and air traffic management [17]. For gate based machines, one of the most promising algorithms for optimization is the so called the quantum alternating operator ansatz also known as quantum approximate optimization algorithm [18][19][20][21][22] abbreviated as QAOA.…”

Fluctuation-guided search in quantum annealing

“…Quantum annealing, in which combinatorial optimization problems are mapped directly Hamiltonians and solved using sweeps of Hamiltonian parameters, has been a subject of much interest recently. This is in part due to the wide variety of potential applications, in a diverse range of subjects, including for instance air traffic control [1], hydrology [2], protein folding [3], flight gate assignment [4], finance [5][6][7], and even quantum field theory [8,9]. This subject has further attracted interest because of the experimental maturity of the flux qubit devices produced by D-Wave Systems Inc. which allow for large-scale experimentation.…”