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The Vehicle Routing Problem (VRP) is an example of a combinatorial optimization problem that has attracted academic attention due to its potential use in various contexts. VRP aims to arrange vehicle deliveries to several sites in the most…

Quantum Physics · Physics 2025-05-08 Nishikanta Mohanty , Bikash K. Behera , Christopher Ferrie

We propose a hierarchical quantum approximate optimization framework for solving large-scale Vehicle Routing Problems (VRP) using Quantum Approximate Optimization Algorithm (QAOA). The method decomposes a VRP instance into balanced clusters…

Quantum Physics · Physics 2026-05-12 Shreetam Dash , Shreya Banerjee , Prasanta K. Panigrahi

The vehicle routing problem (VRP) is an NP-hard optimization problem that has been an interest of research for decades in science and industry. The objective is to plan routes of vehicles to deliver goods to a fixed number of customers with…

Quantum Physics · Physics 2025-05-08 Nishikanta Mohanty , Bikash K. Behera , Christopher Ferrie

Quantum computing is a promising technology to address combinatorial optimization problems, for example via the quantum approximate optimization algorithm (QAOA). Its potential, however, hinges on scaling toy problems to sizes relevant for…

In this paper, we describe the usage of the Quantum Approximate Optimization Algorithm (QAOA), which is a quantum-classical heuristic, to solve a combinatorial optimization and integer programming task known as Vehicle Routing Problem…

Quantum Physics · Physics 2022-09-26 Utkarsh Azad , Bikash K. Behera , Emad A. Ahmed , Prasanta K. Panigrahi , Ahmed Farouk

Vehicle routing problem (VRP) is an NP-hard optimization problem that has been an interest of research for decades in science and industry. The objective is to plan routes of vehicles to deliver a fixed number of customers with optimal…

Quantum Physics · Physics 2022-01-14 Nishikanta Mohanty , Bikash K. Behera

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…

Quantum Physics · Physics 2026-01-28 Talha Azfar , Osama Muhammad Raisuddin , Ruimin Ke , Jose Holguin-Veras

There has never been a more exciting time for the future of quantum computing than now. Near-term quantum computing usage is now the next XPRIZE. With that challenge in mind we have explored a new approach as a hybrid quantum-classical…

Emerging Technologies · Computer Science 2024-04-23 James Holliday , Braeden Morgan , Hugh Churchill , Khoa Luu

Quantum computing offers new heuristics for combinatorial problems. With small- and intermediate-scale quantum devices becoming available, it is possible to implement and test these heuristics on small-size problems. A candidate for such…

Quantum Physics · Physics 2025-07-15 David Fitzek , Toheed Ghandriz , Leo Laine , Mats Granath , Anton Frisk Kockum

One of the most well-known problems in transportation and logistics is the Capacitated Vehicle Routing Problem (CVRP). It involves optimizing a set of truck routes to service a set of customers, subject to limits on truck capacity, to…

In this work we propose a high-quality decomposition approach for qubit routing by swap insertion. This optimization problem arises in the context of compiling quantum algorithms onto specific quantum hardware. Our approach decomposes the…

Quantum Physics · Physics 2023-05-15 Friedrich Wagner , Andreas Bärmann , Frauke Liers , Markus Weissenbäck

The Capacitated Vehicle Routing Problem (CVRP) is an NP-optimization problem (NPO) that arises in various fields including transportation and logistics. The CVRP extends from the Vehicle Routing Problem (VRP), aiming to determine the most…

Quantum Physics · Physics 2024-04-23 Ningyi Xie , Xinwei Lee , Dongsheng Cai , Yoshiyuki Saito , Nobuyoshi Asai , Hoong Chuin Lau

The Capacitated Vehicle Routing Problem (CVRP) is an NP-optimization problem (NPO) that has been of great interest for decades for both, science and industry. The CVRP is a variant of the vehicle routing problem characterized by capacity…

Many relevant problems in industrial settings result in NP-hard optimization problems, such as the Capacitated Vehicle Routing Problem (CVRP) or its reduced variant, the Travelling Salesperson Problem (TSP). Even with today's most powerful…

Solving real-world optimization problems with quantum computing requires choosing between a large number of options concerning formulation, encoding, algorithm and hardware. Finding good solution paths is challenging for end users and…

Hybrid quantum optimization for vehicle routing faces a practical bottleneck: direct QUBO encodings of CVRP quickly exceed near-term qubit and gate budgets, while quantum evaluations are expensive, noise-limited, and sensitive to backend…

Quantum Physics · Physics 2026-04-27 Monit Sharma , Hoong Chuin Lau

Vehicle Routing Problem (VRP) is one of the most complex NP-hard combinatorial optimization problem in transportation and logistics that requires a dynamic solution approach. In this paper we present a new hybrid approach that combines the…

The vehicle routing problem with time windows (VRPTW) is a common optimization problem faced within the logistics industry. In this work, we explore the use of a previously-introduced qubit encoding scheme to reduce the number of binary…

Quantum Physics · Physics 2023-09-20 Ioannis D. Leonidas , Alexander Dukakis , Benjamin Tan , Dimitris G. Angelakis

Combinatorial optimization problems have attracted much interest in the quantum computing community in the recent years as a potential testbed to showcase quantum advantage. In this paper, we show how to exploit multilevel carriers of…

Quantum Physics · Physics 2024-07-03 M. Garcia de Andoin , A. Bottarelli , S. Schmitt , I. Oregi , P. Hauke , M. Sanz

Finding a feasible and prompt solution to the Vehicle Routing Problem (VRP) is a prerequisite for efficient freight transportation, seamless logistics, and sustainable mobility. Traditional optimization methods reach their limits when…

Machine Learning · Computer Science 2024-11-08 Elija Deineko , Carina Kehrt
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