# A QUBO Model to the Tail Assignment Problem

### Luis Martins, Ana Rocha, Antonio Castro

#### Abstract

Tail Assignment is the problem of allocating individual aircraft to a set of flights subject to multiple constraints while optimising an objective function, such as operational costs. Given the enormous amount of possibilities and constraints involved, this problem has been a case study over the last decade. Many solutions have emerged using classical computing, but with limitations. Quantum Annealing (QA) is a heuristic technique to solve combinatorial optimisation problems by finding global minimum energy levels over an energy landscape using quantum mechanics. In this study, Tail Assignment Problem was framed as a Quadratic Unconstrained Binary Optimisation (QUBO) model and was solved using a classical and two hybrid solvers. The considered hybrid solvers made use of the D-Wave 2000Q quantum annealer. Tests were run based on extractions from real-world data, analysing, empirically, the performance of the implementation in terms of quality (i.e., the lowest operational costs) of the obtained solutions. We concluded that, for the considered datasets, there was a higher probability of obtaining better solutions for this problem using one of the hybrid solvers when compared with a classical heuristic algorithm such as Simulated Annealing (SA).

Download#### Paper Citation

#### in Harvard Style

Martins L., Rocha A. and Castro A. (2021). **A QUBO Model to the Tail Assignment Problem**.In *Proceedings of the 13th International Conference on Agents and Artificial Intelligence - Volume 2: ICAART,* ISBN 978-989-758-484-8, pages 899-906. DOI: 10.5220/0010259608990906

#### in Bibtex Style

@conference{icaart21,

author={Luis Martins and Ana Rocha and Antonio Castro},

title={A QUBO Model to the Tail Assignment Problem},

booktitle={Proceedings of the 13th International Conference on Agents and Artificial Intelligence - Volume 2: ICAART,},

year={2021},

pages={899-906},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0010259608990906},

isbn={978-989-758-484-8},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 13th International Conference on Agents and Artificial Intelligence - Volume 2: ICAART,

TI - A QUBO Model to the Tail Assignment Problem

SN - 978-989-758-484-8

AU - Martins L.

AU - Rocha A.

AU - Castro A.

PY - 2021

SP - 899

EP - 906

DO - 10.5220/0010259608990906