Research focused on the conjunction between quantum computing and routing problems has been very prolific in recent years. Most of the works revolve around classical problems such as the Traveling Salesman Problem or the Vehicle Routing Problem. The real-world applicability of these problems is dependent on the objectives and constraints considered. Anyway, it is undeniable that it is often difficult to translate complex requirements into these classical formulations. The main objective of this research is to present a solving scheme for dealing with realistic instances while maintaining all the characteristics and restrictions of the original real-world problem. Thus, a quantum-classical strategy has been developed, coined Q4RPD, that considers a set of real constraints such as a heterogeneous fleet of vehicles, priority deliveries, and capacities characterized by two values: weight and dimensions of the packages. Q4RPD resorts to the Leap Constrained Quadratic Model Hybrid Solver of D-Wave. To demonstrate the application of Q4RPD, an experimentation composed of six different instances has been conducted, aiming to serve as illustrative examples.
Research focused on the conjunction between quantum computing and routing problems has been very prolific in recent years. Most of the works revolve around classical problems such as the Traveling Salesman Problem or the Vehicle Routing Problem. The real-world applicability of these problems is dependent on the objectives and constraints considered. Anyway, it is undeniable that it is often difficult to translate complex requirements into these classical formulations. The main objective of this research is to present a solving scheme for dealing with realistic instances while maintaining all the characteristics and restrictions of the original real-world problem. Thus, a quantum-classical strategy has been developed, coined Q4RPD, that considers a set of real constraints such as a heterogeneous fleet of vehicles, priority deliveries, and capacities characterized by two values: weight and dimensions of the packages. Q4RPD resorts to the Leap Constrained Quadratic Model Hybrid Solver of D-Wave. To demonstrate the application of Q4RPD, an experimentation composed of six different instances has been conducted, aiming to serve as illustrative examples.
Recent research at the intersection of quantum computing and routing problems has been highly prolific. Much of this work focuses on classical problems such as the Traveling Salesman Problem and the Vehicle Routing Problem. The practical applicability of these problems depends on the specific objectives and constraints considered. However, it is undeniable that translating complex real-world requirements into these classical formulations often proves challenging. In this paper, we resort to our previously published quantum-classical technique for addressing real-world-oriented routing problems, known as Quantum for Real Package Delivery (Q4RPD), and elaborate on solving additional realistic problem instances. Accordingly, this paper emphasizes the following characteristics: i) simultaneous pickup and deliveries, ii) time-windows, and iii) mobility restrictions by vehicle type. To illustrate the application of Q4RPD, we have conducted an experimentation comprising seven instances, serving as a demonstration of the newly developed features.
In this paper, we explore the potential for quantum annealing to solve realistic routing problems. We focus on two NP-Hard problems, including the Traveling Salesman Problem with Time Windows and the Capacitated Vehicle Routing Problem with Time Windows. We utilize D-Wave's Quantum Annealer and Constrained Quadratic Model (CQM) solver within a hybrid framework to solve these problems. We demonstrate that while the CQM solver effectively minimizes route costs, it struggles to maintain time window feasibility as the problem size increases. To address this limitation, we implement a heuristic method that fixes infeasible solutions through a series of swapping operations. Testing on benchmark instances shows our method achieves promising results with an average optimality gap of 3.86%.
Quantum computing (QC) stands at the cusp of revolutionizing computation, yet its near-term potential, constrained by Noisy Intermediate-Scale Quantum (NISQ) devices, remains underexplored. This dissertation investigates how hybrid quantum-classical algorithms can address combinatorial optimization challenges in logistics, focusing on vehicle routing and drone delivery—NP-hard problems with exponential solution spaces that defy classical exhaustive methods. Amidst NISQ limitations like limited qubits and high noise, we confront key challenges: encoding complex constraints, e.g., time windows, battery capacity, into quantum models, balancing quantum and classical components for scalability, and accessing scarce quantum resources. By integrating quantum annealing (QA) and the Quantum Approximate Optimization Algorithm (QAOA) with classical heuristics, this work demonstrates QC’s practical utility, advancing both optimization theory and real-world logistics applications. The dissertation unfolds across four core contributions. First, the Hybrid Quantum Tabu Search (HQTS) optimally solves the 50-location Capacitated Vehicle Routing Problem (CVRP), achieving a 4.72% optimality gap. Secondly, we refine HQTS to reach a 2.15% gap with enhanced QA utilization, outperforming prior hybrids on standard datasets. Third, adapting HQTS for the CVRPTWwith D-Wave’s Constrained Quadratic Model solver yields a 3.85% gap on 100-location instances, leveraging a novel heuristic to ensure time-window feasibility where quantum outputs falter. Lastly, QUADRO, a pioneering framework for drone delivery, employs QAOA-driven routing and hybrid scheduling, minimizing transit time and makespan for fleets of 2–11 drones needing fewer than 100 qubits, rivaling classical benchmarks on adapted Augerat datasets. These advances, tested via D-Wave’s Advantage system and Qiskit simulations, showcase hybrid strategies that mitigate NISQ constraints, delivering scalable, feasible solutions to logistics challenges. This work establishes near-term QC’s viability for combinatorial optimization, bridging theoretical promise with practical impact. Synthesizing quantum exploration with classical refinement achieves competitive performance, e.g., matching or surpassing Google ORTools in select CVRPTW cases, while illuminating NISQ limits, such as feasibility degradation beyond small scales. These hybrid strategies deliver scalable, feasible solutions, from a 2.15% optimality gap for CVRP to effective drone fleet management with fewer than 100 qubits, illuminating quantum computing’s potential despite its current constraints. Ultimately, this dissertation positions hybrid QC as a transformative tool for optimization challenges, offering a robust foundation for scaling quantum optimization into operational reality.
Quantum annealing (QA) is a quantum computing algorithm that works on the principle of Adiabatic Quantum Computation (AQC), and it has shown significant computational advantages in solving combinatorial optimization problems such as vehicle routing problems (VRP) when compared to classical algorithms. This paper presents a QA approach for solving a variant VRP known as multi-depot capacitated vehicle routing problem (MDCVRP). This is an NP-hard optimization problem with real-world applications in the fields of transportation, logistics, and supply chain management. We consider heterogeneous depots and vehicles with different capacities. Given a set of heterogeneous depots, the number of vehicles in each depot, heterogeneous depot/vehicle capacities, and a set of spatially distributed customer locations, the MDCVRP attempts to identify routes of various vehicles satisfying the capacity constraints such as that all the customers are served. We model MDCVRP as a quadratic unconstrained binary optimization (QUBO) problem, which minimizes the overall distance traveled by all the vehicles across all depots given the capacity constraints. Furthermore, we formulate a QUBO model for dynamic version of MDCVRP known as D-MDCVRP, which involves dynamic rerouting of vehicles to real-time customer requests. We discuss the problem complexity and a solution approach to solving MDCVRP and D-MDCVRP on quantum annealing hardware from D-Wave.
Vehicle Routing Problem is a well-known optimization issue, which has many extensions resulting from practical appliances. The problem is NP-hard, therefore it may be impossible to find an optimal solution for big instances, with traditional computation methods. Recent development of quantum technology, may be a response for this challenge, which however requires a different formulation of the model. The problem is then modeled using Quadratic Unconstrained Binary Optimization (QUBO) equations. Such model can be run using quantum annealers (QA), designed specifically for optimization purposes. This paper is a systematic survey of Vehicle Routing Problem models that are formulated using QUBO, to be solved on quantum computers. The main goal of the paper is to check research gaps in this subject, compare and explain different approaches of modeling various problem extensions with QUBO. The results obtained in reviewed papers will be presented and analyzed. Moreover, the theoretical basis for quantum computation will be presented, with focus on D-Wave company solutions.
The paper considers the application of hybrid quantum-classical algorithms (HQCA) to optimization problems in logistics, such as the vehicle routing problem (VRP), the traveling salesman problem (TSP), as well as their generalizations with time windows and fleet constraints. A multi-level architecture of hybrid computing is presented, including the stages of problem translation into QUBO form, implementation of variational quantum algorithms (QAOA), annealing on quantum systems (e.g., D-Wave Advantage2), as well as methods for error correction and post-processing of solutions. A review of domestic and foreign developments in this area is conducted, including the results of Russian research groups (RKC, MISiS, Innopolis, MIPT). It is experimentally shown that GCQAs provide gains in quality and time for medium-sized tasks (100–1 clients), especially when using warm-start strategies and dynamic load distribution between classical and quantum subsystems. The limitations of current NISQ devices and scaling prospects, including integration with predictive analytics and digital twins of logistics systems, are discussed.