We investigate the potential of the Quantum Approximate Optimization Algorithm (QAOA) for reducing energy consumption in route planning, a key challenge in logistics due to the NP-hard nature of the Traveling Salesman and Vehicle Routing Problems. By encoding route optimization as a Quadratic Unconstrained Binary Optimization (QUBO) problem and implementing QAOA circuits at depth p = 3-5 alongside classical baselines of Simulated Annealing (SA) and Genetic Algorithms (GA), we perform systematic benchmarks on Euclidean graphs of sizes N = 5, 10, and 20. Our results demonstrate that QAOA attains higher solution quality with approximation ratios of 0.953 (N = 5), 0.921 (N = 10), and 0.903 (N = 20), outperforming SA and GA by 2.7-4.4%. Wall-clock runtimes for QAOA are 2-3x faster than SA across all tested sizes, and energy consumption measurements reveal a three-order-of-magnitude reduction, remaining in the picojoule range versus nanojoules for classical methods. Translating these gains to real-world logistics suggests an 8.2% improvement in routing efficiency could save approximately 2.62 EJ of fuel annually in the U.S., avoiding nearly 1.94 x 10^8 tonnes of CO2 emissions. These findings highlight QAOA's promise as a fast, energy-efficient optimizer for sustainable logistics applications and underscore its potential role in next-generation fleet-management systems.
We investigate the potential of the Quantum Approximate Optimization Algorithm (QAOA) for reducing energy consumption in route planning, a key challenge in logistics due to the NP-hard nature of the Traveling Salesman and Vehicle Routing Problems. By encoding route optimization as a Quadratic Unconstrained Binary Optimization (QUBO) problem and implementing QAOA circuits at depth p = 3-5 alongside classical baselines of Simulated Annealing (SA) and Genetic Algorithms (GA), we perform systematic benchmarks on Euclidean graphs of sizes N = 5, 10, and 20. Our results demonstrate that QAOA attains higher solution quality with approximation ratios of 0.953 (N = 5), 0.921 (N = 10), and 0.903 (N = 20), outperforming SA and GA by 2.7-4.4%. Wall-clock runtimes for QAOA are 2-3x faster than SA across all tested sizes, and energy consumption measurements reveal a three-order-of-magnitude reduction, remaining in the picojoule range versus nanojoules for classical methods. Translating these gains to real-world logistics suggests an 8.2% improvement in routing efficiency could save approximately 2.62 EJ of fuel annually in the U.S., avoiding nearly 1.94 x 10^8 tonnes of CO2 emissions. These findings highlight QAOA's promise as a fast, energy-efficient optimizer for sustainable logistics applications and underscore its potential role in next-generation fleet-management systems.
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.
Introduction Finding the most efficient routes for a fleet of delivery vehicles remains a critical and costly challenge for nearly any logistics business. This core idea is known as the Vehicle Routing Problem (VRP). The primary goal is to minimize operational costs, such as the total travel distance or the number of trucks deployed, while ensuring all the customers are served. Because VRP is NP-hard, finding a perfect solution is often impossible, forcing industries to rely on classical approximate algorithms. However, quantum variational algorithms offer a new paradigm by iteratively optimizing parameters to navigate the solution space, presenting a new and promising avenue for finding better and faster solutions. Methods In this paper, we introduce Symmetric Arc Reduction in Quantum Approximate Optimization Algorithm (SAR-QAOA), which systematically eliminates redundant symmetric routing variables in the binary integer programming formulation prior to the Quadratic Unconstrained Binary Optimization (QUBO) formulation. The proposed SAR-QAOA encodes edge-based VRP while reducing the qubit requirement from n ( n −1) to n ( n −1)/2, thereby improving the resource efficiency of the QUBO formulation by prioritizing regions of the solution space that are more likely to contain high-quality solutions; SAR enhances both search accuracy and computational efficiency. Results Experimental results on noiseless quantum simulators validate the feasibility of the proposed formulation and its integration with the QAOA framework, providing a promising foundation for future investigations on larger routing problems and evolving quantum hardware.
Transportation strategists increasingly handle heterogeneous fleets under tight service levels, fluctuating costs, and stated environmental targets. This paper addresses the operational Heterogeneous Vehicle Routing Problem (HVRP) with a practical, mathematically light decision framework that treats sustainability as the main goal of the design. We introduce a Quantum-Inspired Supply Chain and Logistics Optimization Algorithm (QISCLOA), solver-independent HVRP approach for transportation system. Our proposed framework builds a curated, capacity-feasible, and diversified route pool using multi-strategy generation. In our 16×16 HVRP benchmarks, our proposed algorithm reduces elapsed time by up to 98.6% compared with strong classical formulations, while matching classical distance quality and delivering higher load utilization (95–99%) under the same feasibility constraints. Compared with existing classical system, our proposed system preserves full feasibility and comparable distance, shows clear distance-per-demand gains in symmetric unit-demand cases, and attains near-zero solve time on identical Binary Quadratic Models (BQM), evidencing orders-of-magnitude speedups. The proposed model further introduces a load–carbon emission correlation with speed, road-condition, and congestion factors, and the proposed Quantum Annealing (QA) and existing Quantum Approximate Optimization Algorithm (QAOA) comparison demonstrates competitive solution quality, solver-dependent efficiency, and full logical hardware compatibility. Additionally, we extend the formulation to a multi-depot setting with depot availability, dispatch-capacity, time-window, and Electric Vehicle (EV) charging constraints, and validate it on 21 Multi-Depot Vehicle Routing Problem (MDVRP) benchmark instances to demonstrate scalable multi-depot route selection, while a reduced comparison confirms competitive solution quality and solver-dependent efficiency, with existing QAOA improving overall route distance by 0.63% and proposed QA achieving a 9.14% overall runtime advantage. In multitasking Capacitated Vehicle Routing Problem (CVRP) benchmarks used in explicit evolutionary multitasking studies, our approach achieves lower routing cost for both best and average results with a win rate of 81.48%, indicating a lower emission of CO2. Empirically, our proposed method outperforms competitive state-of-the-art approaches in our evaluation metrics while maintaining core feasibility.
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.
Abstract: This paper suggests a new method for improving routes in complicated logistics systems by combining cognitive modeling with quantum computing algorithms, especially the Quantum Approximate Optimization Algorithm (QAOA). In the classic Traveling Salesman Problem (TSP), the model shows major improvements, beating traditional methods by 25% in finding solutions accurately and cutting computation time by 30%. Simulations show a 15% drop in travel time and a 20% cut in CO₂ emissions, highlighting how the model helps improve efficiency and support environmental sustainability. The innovation comes from combining two usually separate fields: cognitive modeling, which mimics how humans make decisions, and quantum computing, which allows for fast and large‑scale optimization. This teamwork between different fields encourages quick, flexible, and scalable decision‑making, which is essential in fast‑changing, real‑time logistics settings. The model matches the move towards Industry 5.0, which focuses on working together with machines and being environmentally friendly. It also supports the United Nations Sustainable Development Goals, especially Goal 9 (Industry, Innovation and Infrastructure) and Goal 13 (Climate Action). To make sure the study is valid, it uses open‑access datasets and simulates real‑life situations, such as smart warehouse operations and fleet management systems. The results highlight how quantum‑enhanced cognitive systems can change the game, providing a modern tool to build smarter, greener, and stronger supply chains. This research not only pushes the boundaries of optimization science but also lays the groundwork for using quantum algorithms in industry in the future.
Multi-objective optimization (MOO) problems are common in logistics, where routing decisions must balance conflicting objectives such as travel distance, delivery time, and operational risk. A recently proposed Quantum Approximate Optimization Algorithm (QAOA) parameter-transfer strategy solves multi-objective MAX-CUT problems by reusing parameters trained on smaller instances, avoiding costly reoptimization for each scalarized problem. However, its effectiveness has only been demonstrated on proof-of-concept instances tailored to quantum hardware connectivity. In this work, we evaluate the applicability of this strategy to realistic routing problems. We formulate the Traveling Salesman Problem (TSP) and Vehicle Routing Problem (VRP) as Quadratic Unconstrained Binary Optimization (QUBO) models, reduce them to MAX-CUT, and assess the parameter-transfer framework under conditions matching the original study. Validation is performed through classical simulations and experiments on IBM quantum hardware. The resulting Pareto fronts are compared with those obtained using an adapted classical ε-constraint method, using hypervolume as the primary quality metric. Results indicate that parameter transfer remains effective, frequently achieving higher hypervolume and often finding competitive solutions earlier. However, performance depends on problem structure. The approach is consistently effective for TSP instances but less stable for the more constrained VRP, suggesting that QAOA parameter transferability decreases as the optimization landscape becomes more complex. These results provide the first comprehensive evaluation of QAOA parameter transfer on realistic multi-objective routing problems and demonstrate its potential beyond proof-of-concept MAX-CUT benchmarks.