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Journal of Advanced Transportation

Study on Quantum Approximation Optimization Algorithm in Airport Cargo Transportation Problem

Xudong Zhao, Jianping Chen, Lan Liu, Leilei Kang

Published Jan 1, 2026• 0 citations

Abstract

The vehicle routing problem (VRP) is a core NP‐hard combinatorial optimization problem in logistics and supply chain management. Quantum computing, particularly the Quantum Approximate Optimization Algorithm (QAOA), is being explored as a promising heuristic tool for tackling such problems. Therefore, this study employs the QAOA approach to solve the airport cargo VRP. Subsequently, through a concrete airport cargo case study, the paper analyzes the process of solving single‐vehicle TSP and multivehicle VRP problems using QAOA. It compares the performance of different classical optimizers and discusses the impact of parameter settings (e.g., penalty factors, QAOA depth, and number of iterations) on the solution quality and feasibility, especially comparing the convergence speed of dynamic and fixed penalty coefficients. The paper also describes the design principles of QAOA quantum circuits for such VRP problems. Furthermore, the study presents a preliminary benchmark on a real quantum computer, demonstrating that its computation time for the problem’s QUBO matrix (14 ms) is approximately comparable to that of classical algorithms. Finally, it summarizes the current scalability challenges and limitations faced by QAOA in VRP applications concerning qubit count, circuit depth, and classical optimizer performance, and offers an outlook on future development directions. The research indicates that although QAOA demonstrates solution capabilities on specific small‐scale VRP instances, the complexity of parameter tuning and sensitivity to the spatial distribution of aircraft stands are critical considerations before practical application.

DOI: 10.1155/atr/4046578

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Intelligent transportation systems (ITS) are a critical component of Industry 4.0 and 5.0, particularly having applications in logistic management. One of their crucial utilization is in supply-chain management and scheduling for optimally routing transportation of goods by vehicles at a given set of locations. This paper discusses the broader problem of vehicle traffic management, more popularly known as the Vehicle Routing Problem (VRP), and investigates the possible use of near-term quantum devices for solving it. For this purpose, we give the Ising formulation for VRP and some of its constrained variants. Then, we present a detailed procedure to solve VRP by minimizing its corresponding Ising Hamiltonian using a hybrid quantum-classical heuristic called Quantum Approximate Optimization Algorithm (QAOA), implemented on the IBM Qiskit platform. We compare the performance of QAOA with classical solvers such as CPLEX on problem instances of up to 15 qubits. We find that performance of QAOA has a multifaceted dependence on the classical optimization routine used, the depth of the ansatz parameterized by

p

, initialization of variational parameters, and problem instance itself.

The Vehicle Routing Problem (VRP) is a fundamental combinatorial optimization challenge with broad applications in logistics and transportation. In this work, we present a quantum-assisted framework that integrates the Quantum Approximate Optimization Algorithm (QAOA) with a link-based formulation of VRP. Our approach encodes flow conservation and subtour elimination directly into the cost Hamiltonian, preserving graph structure while minimizing resource requirements for practical hardware implementation. We design and implement the full pipeline on a gate-based quantum computer, including problem formulation, encoding, circuit synthesis, and execution on IBM Quantum System One. Experimental results on small VRP instances highlight the effects of penalty scaling, coefficient normalization, and circuit depth on solution feasibility under hardware noise. While scalability remains constrained by circuit complexity and decoherence, the study demonstrates a practical pathway for implementing VRP on quantum hardware and identifies methodological directions for advancing near-term quantum optimization.

Vehicle Routing Problem (VRP) is considered one of the most challenging problems with application in several domains, including transportation and logistics distribution. VRP is known to be NP-Hard problem. Several algorithms have been proposed to solve VRP in polynomial time. However, these algorithms are inefficient if the VRP instance increases. Recently, researchers investigated how quantum computing can be used to solve VRP. In particular, two promising variational quantum algorithms have been studied, i.e., Variational Quantum Eigensolver (VQE) and Quantum Approximate Optimization Algorithm (QAOA). In this paper, we implement both algorithms on IBM Qiskit and compare their evaluation in solving several instances of VRP. We observe that current Noisy-Intermediate Scale Quantum (NISQ) devices cannot solve VRP instances beyond 5 nodes and 2 vehicles. Furthermore, we observe that classical optimizers still provide better results. However, we believe that with the rapid advancement of quantum computing manufacturing, VQE and QAOA can provide better performance as compared to classical computing,

The Traveling Salesman Problem (TSP) is a fundamental challenge in combinatorial optimization, widely applied in logistics and transportation. As the size of TSP instances grows, traditional algorithms often struggle to produce high-quality solutions within reasonable timeframes. This study investigates the potential of the Quantum Approximate Optimization Algorithm (QAOA), a hybrid quantum-classical method, to solve TSP under realistic constraints. We adopt a QUBO-based formulation of TSP that integrates real-world logistical constraints reflecting operational conditions, such as vehicle capacity, road accessibility, and time windows, while ensuring compatibility with the limitations of current quantum hardware. Our experiments are conducted in a simulated environment using high-performance computing (HPC) resources to assess QAOA's performance across different problem sizes and quantum circuit depths. In order to improve scalability, we propose clustering QAOA (Cl-QAOA), a hybrid approach combining classical machine learning with QAOA. This method decomposes large TSP instances into smaller sub-problems, making quantum optimization feasible even on devices with a limited number of qubits. The results offer a comprehensive evaluation of QAOA's strengths and limitations in solving constrained TSP scenarios. This study advances quantum optimization and lays groundwork for future large-scale applications.

Reinforcement Learning–based Quantum Approximate Optimization Algorithm (QAOA-RL) is used to solve the Vehicle Routing Problem (VRP) by transforming it into a Quadratic Unconstrained Binary Optimization (QUBO) form. The RL agent learns to optimize QAOA parameters for better route selection. Results show that QAOA-RL achieves a lower total cost compared to exact ILP and heuristic Greedy Search methods. Although the training time is higher, the solution quality improves significantly for larger problem sizes. This study highlights QAOA-RL as a scalable and promising hybrid quantum–classical approach for real-world logistics optimization.

The Traveling Salesman Problem (TSP) is a cornerstone of combinatorial optimization with widespread applications in logistics and transportation. As problem sizes increase, classical algorithms often fail to deliver high-quality solutions within practical time constraints. This paper explores the use of the Quantum Approximate Optimization Algorithm (QAOA), a hybrid quantum-classical algorithm, to address TSP instances under realistic conditions. We present a QUBO-based formulation of the TSP that integrates practical constraints reflecting real-world conditions—such as vehicle capacity, road accessibility, and time windows—while maintaining compatibility with limitations of current quantum hardware. Our analysis is conducted in a simulated environment, leveraging high-performance computing (HPC) resources to evaluate the algorithm’s performance across varying problem sizes and circuit depths. This approach enables a comprehensive assessment of QAOA’s capabilities and limitations in solving constrained TSP scenarios, thereby laying the groundwork for its deployment on future large-scale quantum hardware.